# oxford-handbook-gambling

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the oxford handbook of
THE ECONOMICS
OF GAMBLING

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CONSULTING EDITORS
Michael Szenberg
Lubin School of Business, Pace University
Lall Ramrattan
University of California, Berkeley Extension

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the oxford handbook of
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
THE ECONOMICS
OF GAMBLING
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Edited by
LEIGHTON VAUGHAN WILLIAMS
and
DONALD S. SIEGEL
1

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3
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Library of Congress Cataloging-in-Publication Data
Vaughan Williams, Leighton.
The Oxford handbook of the economics of gambling/Leighton Vaughan Williams
and Donald S. Siegel.
pages cm. — (Oxford handbooks)
Includes bibliographical references and index.
ISBN 978–0–19–979791–2 (cloth: alk. paper)
1. Gambling.
2. Gambling—Economic aspects.
I. Siegel, Donald S., 1959–
II. Title.
HV6710.V38 2013
338.4’7795—dc23
2012038792
1 3 5 7 9 8 6 4 2
Printed in the United States of America
on acid-free paper

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Contents
............................
Contributors
ix
Introduction
xiii
SECTION I CASINOS
1. The Employment Impact of Casino Gambling in the U.S.
3
Gary Anders
2. The Economics of Casino Taxation
18
John E. Anderson
3. The Elasticity of Casino Gambling
37
Mark W. Nichols and Mehmet Serkan Tosun
4. The Economics of Asian Casino Gaming and Gambling
55
Ricardo Chi Sen Siu
5. How does Implementation of a Smoking Ban Affect Gaming?
87
John C. Navin, Timothy S. Sullivan, and Warren D. Richards
6. Overview of the Economic and Social Impacts of Gambling in the
United States
108
Douglas M. Walker
SECTION II SPORTS BETTING
7. The Economics of Online Sports Betting
131
George Diemer and Ryan M. Rodenberg
8. The Football Pools
147
David Forrest and Levi P´erez
9. The Efficiency of Soccer Betting Markets
163
John Goddard

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vi
contents
10.
The Efficiency of Pelota Betting Markets
172
Loreto Llorente, Josemari Aizpurua, and Javier Pu´ertolas
11.
The Lure of the Pitcher: How the Baseball Betting Market Is
Influenced by Elite Starting Pitchers
194
Rodney J. Paul, Andrew P. Weinbach, and Brad R. Humphreys
12.
Information Efficiency in High-Frequency Betting Markets
210
J. James Reade and John Goddard
SECTION III HORSE RACE BETTING
13.
On the Long-Run Sustainability of Tote Betting Markets
235
David Edelman
14.
The Economics of Racetrack–Casino (Racino) Gambling
241
Richard Thalheimer
15.
The Modern Racing Landscape and the Racetrack Wagering Market:
Components of Demand, Subsidies, and Efﬁciency
256
Ramon P. DeGennaro and Ann B. Gillette
16.
What Explains the Existence of an Exchange Overround?
276
David Marginson
17.
Insider Trading in Betting Markets
298
Adi Schnytzer
18.
Pricing Decisions and Insider Trading in Fixed-Odds Horse Betting
Markets
316
Adi Schnytzer, Vasiliki Makropoulou, and Martien Lamers
SECTION IV BETTING STRATEGY
19.
Betting on Simultaneous Events and Accumulator Gambles
341
Andrew Grant
20.
A Primer on the Mathematics of Gambling
370
Robert C. Hannum
21.
The Science and Economics of Poker
387
Robert C. Hannum

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contents
vii
22.
The Kelly Criterion with Games of Chance
402
Leonard C. MacLean and William T. Ziemba
23.
Exploiting Expert Analysis? Evidence from Event Studies in an
Information-Rich Market Environment
428
Michael A. Smith
SECTION V MOTIVATION, BEHAVIOR
AND DECISION-MAKING IN
BETTING MARKETS
24.
Betting Motivation and Behavior
451
Alistair Bruce
25.
Motivation in Betting Markets: Speculation, Calculus, or Fun?
474
Les Coleman
26.
Evidence of Biased Decision-Making in Betting Markets
487
David McDonald, Ming-Chien Sung, and Johnnie Johnson
27.
Behavioral Finance and Point Spread Wagering Markets
518
Greg Durham
SECTION VI PREDICTION MARKETS AND
POLITICAL BETTING
28.
A Simple Automated Market Maker for Prediction Markets
543
David Johnstone
29.
The Long History of Political Betting Markets: An International
Perspective
560
Paul W. Rhode and Koleman Strumpf
SECTION VII LOTTERIES AND
GAMBLING MACHINES
30.
The Efficiency of Lottery Markets
589
David Forrest and O. David Gulley
31.
The National Lottery
611
John Lepper and Stephen Creigh-Tyte

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viii
contents
32.
The Benefits and Costs of Slot Machine Gambling
637
Scott Farrow and Chava Carter
33.
The Economics of Lotteries: A Survey of the Literature
670
Kent Grote and Victor A. Matheson
34.
The Taxation of Gambling Machines: A Theoretical Perspective
692
Leighton Vaughan Williams and David Paton
Name Index
701
General Index
703

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Contributors
.........................................
Josemari Aizpurua is a Professor in the Department of Economics at the Public
University of Navarre in Spain.
GaryAndersisanEmeritusProfessorof EconomicsintheW.P.CareySchoolof Business
at Arizona State University and Adjunct Professor of Global Economics at Thunderbird
School for Global Management.
John E. Anderson is the Baird Family Professor of Economics at the College of Business
Administration, University of Nebraska–Lincoln (USA).
Alistair Bruce is Professor of Decision and Risk Analysis at Nottingham University
Business School.
Chava Carter is a Research Assistant at UMBC, the University of Maryland, Baltimore
County.
Les Coleman is a Senior Lecturer in the Department of Finance at the University of
Melbourne.
Stephen Creigh-Tyte is Visiting Professor and Research Fellow at Durham Business
School.
George Diemer is Assistant Professor of Business at Chestnut Hill College.
Greg Durham is Assistant Professor of Finance in the College of Business at Montana
State University.
David Edelman is a Senior Lecturer in the School of Business at University College,
Dublin.
Scott Farrow is a Professor in the Department of Economics at UMBC, the University
of Maryland, Baltimore County.
David Forrest is Professor of Economics at the Salford Business School, University of
Salford.
Ramon P. DeGennaro is the CBA Professor in Banking and Finance at the University
of Tennessee.
Ann B. Gillette is a Professor in the Department of Economics, Finance, and
Quantitative Analysis at Kennesaw State University.

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x
contributors
John Goddard is Professor of Financial Economics at Bangor Business School, Bangor
University.
Andrew Grant is Lecturer in Finance at the University of Sydney Business School.
Kent Grote is Assistant Professor of Economics and Business in the Department of
Economics and Business at Lake Forest College.
O. David Gulley is Professor of Economics at Bentley University.
Robert Hannum is Professor of Risk Analysis and Gaming in the Remain School of
Finance at the University of Denver.
Brad R. Humphreys is Professor of Economics and Chair in the Economics of Gaming
in the Department of Economics at the University of Alberta.
Johnnie Johnson is Professor of Decision and Risk Analysis and Director of the Centre
for Risk Research at the University of Southampton.
David Johnstone is Professor in Finance at the University of Sydney Business School.
Martien Lamers is a doctoral student at the Department of Financial Economics, Ghent
University.
John Lepper is Adjunct Professor, Alfred Deakin Research Institute, Deakin University.
Loreto Llorente is Associate Professor in the Department of Economics at the Public
University of Navarre in Spain.
Leonard MacLean is Herbert S. Lamb Chair in Business Education at Dalhousie
University.
David McDonald is a Research Fellow at the Centre for Risk Research in the School of
Management, University of Southampton.
Vasiliki Makropoulou is Research Associate at Athens University of Economics and
Business.
David Marginson is Head of the Accounting and Finance Section and Professor of
Management Accounting at Cardiff Business School.
Victor Matheson is an Associate Professor in the Department of Economics at the
College of the Holy Cross in Worcester, Massachusetts.
John C. Navin is Professor and Chair of the Department of Economics and Finance at
Southern Illinois University Edwardsville.
Mark W. Nichols is Professor of Economics at the University of Nevada, Reno.
David Paton is Professor of Industrial Economics at Nottingham University Business
School.

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contributors
xi
Rodney J. Paul is a Professor in Department of Sport Management at the David B. Falk
College of Sport and Human Dynamics at Syracuse University.
Levi Pérez is anAssociate Professor in the Department of Economics at the University of
Oviedo and a Member of the Research Staff of the Fundación Observatorio Económico
del Deporte.
Javier Puértolas is Associate Professor in the Department of Economics at the Public
University of Navarre in Spain.
J. James Reade is Lecturer in Economics in the Department of Economics at the
University of Birmingham.
Paul Rhode is a Professor in the Department of Economics at the University of
Michigan.
Warren Richards is an instructor in the Department of Economics and Finance at
Southern Illinois University Edwardsville.
Ryan Rodenberg is an Assistant Professor in the Department of Sport Management at
Florida State University.
Adi Schnytzer is Associate Professor of Economics at Bar Ilan University.
Donald S. Siegel is Professor and Dean of the School of Business at the University at
Albany, SUNY.
Ricardo Siu is Associate Professor of Business Economics in the Department of Finance
and Business Economics at the University of Macau.
Michael Smith is a Senior Lecturer in Economics at Leeds Business School.
Koleman Strumpf is Koch Professor of Economics at the University of Kansas School
of Business.
Timothy S. Sullivan is an instructor in the Department of Economics and Finance at
Southern Illinois University Edwardsville.
Ming-Chien Sung is Professor of Risk and Decision Sciences and Director of MSc Risk
Management at the School of Management, University of Southampton.
Richard Thalheimer is President of Thalheimer Research Associates, Inc. in Lexington,
Kentucky.
Mehmet Serkan Tosun is an Associate Professor and Director of Graduate Programs in
the Department of Economics at the University of Nevada, Reno.
Leighton Vaughan Williams is Professor of Economics and Finance and Director
of the Betting Research Unit at Nottingham Business School, Nottingham Trent
University.

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xii
contributors
Douglas M. Walker is Professor of Economics at the College of Charleston in
Charleston, South Carolina.
Andrew P. Weinbach is the Colonel Lindsey H. Vereen Professor in the Wall College of
Business at Coastal Carolina University.
William Ziemba is Alumni Professor of Financial Modeling and Stochastic Optimiza-
tion, Emeritus at the University of British Columbia. He is also a Visiting Professor at
the Mathematical Institute of the University of Oxford.

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......................................................................................................................................................................................
INTRODUCTION
......................................................................................................................................................................................
In recent years, there has been a substantial rise in interest among academics and
policy makers in the economics of gambling. A concomitant trend in several nations
has been the implementation of major regulatory changes and modiﬁcations to the
taxation of gambling markets. Examples include a fundamental change in the United
Kingdom in 2001 from a turnover-based tax on betting operators to a tax based on gross
proﬁts, resulting in the effective abolition of taxation levied directly on bettors (Paton,
Siegel, and Vaughan Williams 2002, 2004), followed in 2005 by extensive reforms to the
gambling sector introduced in the Gambling Act. In the United States, passage of the
Unlawful Internet Gambling Enforcement Act of 2006 had profound implications for
the global online gambling sector. There have also been numerous regulatory changes
to gambling in Europe, Asia, and Australia. These changes, and an increase in attention
paid to revenue generated from this activity, have heightened interest in understanding
the economics of this sector.
Despite growing interest in the economics of gambling, there is no comprehensive
source of pathbreaking research on this very broad topic. The purpose of this handbook
is to ﬁll this gap. We commissioned chapters from leading academics on all aspects of
gambling research. Topics covered include the optimal taxation structure for various
forms of gambling, factors inﬂuencing the demand and supply of gambling services,
forecasting of gambling trends, regulation of gambling, wagering on sports, horses,
politics, gambling in casinos and on the Internet, the efﬁciency of racetrack and sports
betting markets, gambling prevalence and behavior, modeling the demand for gam-
bling services, the economic impact of gambling, substitution and complementarities
among different types of gambling activity, and the relationship between gambling and
other sectors of the economy. These are all important issues, with signiﬁcant global
implications. Speciﬁcally, we divide the handbook into sections on casinos; sports bet-
ting; horse race betting; betting strategy; motivation, behavior, and decision-making in
betting markets; prediction markets and political betting; and lotteries and gambling
machines.

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xiv
introduction
i Casinos
.............................................................................................................................................................................
The ﬁrst section explores the economic effects of casinos. Gary Anders of Arizona State
University examines the employment impact of casino gambling in the United States in
eight key industries. This is a critical issue due to the recent recession and persistently
high unemployment. Anders reports that expansion of casinos results in employment
increases in arts and entertainment, hotels, and food and beverage industries but leads
to a decline in employment in management and professional services, technology, and
manufacturing (generally high-paying jobs). The negative employment effects of casino
expansion are exacerbated in states with competing gambling venues.
In the next chapter, John Anderson of the University of Nebraska examines how
national governments tax casino gambling, including wagering taxes, admissions taxes,
and fees. He also considers the effects of taxation on equity and efﬁciency. An interesting
aspect of Professor Anderson’s analysis is that he highlights major gambling locations,
such as Las Vegas, Macau, and Singapore. Mark Nichols and Mehmet Serkan Tosun of
the University of Nevada, Reno, provide important theoretical and empirical evidence
on price and income elasticities of demand for casino gambling. Ricardo Siu of the
University of Macau analyzes the growth and evolution of Asian casino gambling.
In addition to examining the economic aspects of this activity, he also focuses on
the signiﬁcance of the unique features of Asian culture and the related institutional
structure of gaming industry performance. Finally, Professor Siu assesses the social
beneﬁts and costs of casino gaming in Asia.
John Navin, Timothy Sullivan, and Warren Richards of Southern Illinois University
Edwardsville review the literature on gaming and the restriction of smoking. They
then present an empirical analysis of the effects of a smoking ban on the riverboat
casino market in the Illinois portion of the St. Louis Metropolitan area. The section on
casinos concludes with a chapter by Douglas Walker of the College of Charleston, who
summarizes empirical research on the economic and social impacts of gambling. Issues
considered in this chapter include the effects of casino gambling on economic growth,
relationships among gambling industries and the implications of these relationships
for net government tax revenue, the social costs of gambling, casinos and crime, casinos
and political corruption, and problems with applying cost-beneﬁt analysis to gambling.
ii Sports Betting
.............................................................................................................................................................................
The second section begins with a chapter by George Diemer of Chestnut Hill College
and Ryan Rodenberg of Florida State University on a growing sector of the gambling
industry: online sports betting. Diemer and Rodenberg consider this sector from a law
and economics perspective and compare the efﬁciency of online/offshore sports books
relative to conventional sports books in Las Vegas and London.

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introduction
xv
David Forrest of the University of Salford and Levi Pérez of the University of Oviedo
examine football pools, deﬁned as any pari-mutuel wagering concerning the outcomes,
or any other aspects, of football (soccer) matches. These are long odds, high-prize
games where a share of the jackpot is linked to football results. Salford and Pérez assert
that this type of wagering closely resembles lotto, where the difference between the
two types of games is that one depends on football results while the other is based on
numbers drawn randomly. They review the literature on football pools, focusing on
the United Kingdom and Spain.
In the next chapter John Goddard of Bangor University examines the efﬁciency of
soccer betting markets. Speciﬁcally he evaluates whether certain types of forecasting
models can be used to develop proﬁtable ﬁxed-odds betting strategies. A key ﬁnd-
ing is that inefﬁciencies in the market have been largely eliminated by the increased
sophistication of contemporary sports betting markets, greatly enhanced by advances
in information technology.
Loreto Llorente, Jose Maria Aizpurua, and Javier Puértolas of the University of
Navarra examine the efﬁciency of a special type of betting market: wagering on pelota
matches. These are games with two mutually exclusive and exhaustive outcomes, where
wagers are made among viewers via a middleman who receives 16 percent of the prize.
Based on ﬁeld data, the authors analyze three different concepts of market efﬁciency
widely utilized in the literature and also provide some insights for future research on
hedging strategies in these markets.
Rodney Paul of Syracuse University, Andrew Weinbach of Coastal Carolina Univer-
sity, and Brad Humphreys of the University of Alberta study the baseball betting market.
The authors ask a very speciﬁc research question: How do elite starting pitchers affect
gambling behavior and volume? Using comprehensive data, they report that games
involving an elite pitcher attract more bettors, especially on the“under” wager. J. James
Reade of the University of Birmingham and John Goddard of Bangor University ana-
lyze information efﬁciency in high-frequency betting markets. Their analysis is based
on“betting exchanges,”which enable traders to either buy or sell bets on many sporting
events. Such continuously operating online betting markets have ensured the transition
of the use of high-frequency data from the ﬁnancial setting into the betting market con-
text. The authors review recent academic research on the topic of information efﬁciency
in high-frequency, in-play betting markets for football (soccer).
iii Horse race Betting
.............................................................................................................................................................................
David Edelman of University College Dublin examines the implications of the alleged
“takeover” of tote (totalizator) betting markets by “sophisticated” gamblers. Based on
a mathematical analysis, he concludes that their activity could not in itself seriously or
irreparably damage pari-mutuel markets. Richard Thalheimer of Thalheimer Research

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xvi
introduction
Associates examines an important trend: the rise of casino-style gambling at pari-
mutuel racetracks. Speciﬁcally he analyzes the impact of “racino” betting on pari-
mutuel racing as well as its effects on state lotteries and casino gaming.
Ramon DeGennaro of the University of Tennessee and Ann Gillette of Kennesaw
State University provide a comprehensive economic analysis of racetrack betting. The
authors examine the effects of technological change on this industry, the growth and
evolution of betting options,and the efﬁciency of the betting market. They also consider
the antecedents and consequences of subsidies for this sector, which many view as a
declining industry. David Marginson of Cardiff Business School examines starting
price–based overrounds on Betfair, the leading person-to-person Internet betting site.
His empirical analysis is based on 2,184 horse races that took place in the United
Kingdom between 2008 and 2010. He reports a positive relationship between grade
of race and Betfair overround (the higher the grade, the higher the overround). His
results imply that microstructure analysis of order-driven betting markets, such as
Betfair, constitutes a fruitful area of research for those interested in understanding
market efﬁciency.
Adi Schnyzter of Bar-Ilan University examines the incidence of insider trading in the
market for horse and greyhound racing. He analyzes whether the presence of betting
insiders at the track implies that their presence is easily detected. It is shown that this
is a function of the microstructure of the particular betting market. In some markets
the impact of insider trading is readily measured, while in others it has hitherto proven
virtually impossible to detect. The different microstructures of betting markets and the
implications for insider trading and its measurement are considered.
In the following chapter, Schnytzer,Vasiliki Makropoulou of Utrecht University, and
Martien Lamers of Ghent University analyze pricing decisions and insider trading in
ﬁxed-odds horse racing. This chapter conceptualizes ﬁxed-odds horse betting markets
asimplicitcalloptionmarkets. Thedecision-makingprocessof abookmakerismodeled
as a decision-maker who sets prices under uncertainty. The authors show that when
a bookmaker adopts this pricing process built on implicit options, the returns will
exhibit a favorite-longshot bias. By performing Monte Carlo simulations, option values
are generated and a measurement is made of the degree of insider trading.
iv Betting Strategy
.............................................................................................................................................................................
The section on betting strategy begins with a chapter by Andrew Grant of the Univer-
sity of Sydney, who examines the predictability of sports betting markets. Speciﬁcally
he analyzes wagering on simultaneous events and “accumulator gambles.” These are
situations in which multiple games occur simultaneously. In this case the gambler must
consider the problem of allocating capital across different games or events, similar to
the situation when an investor allocates capital to different stocks in a portfolio. The

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introduction
xvii
author explores the use of accumulator bets (parlays) as part of a portfolio betting
strategy.
Robert Hannum of the University of Denver presents a primer on the mathematics of
gambling. He demonstrates how the mathematics behind the games generates revenues
and drives the economics of gambling. In the following chapter, Hannum describes the
science and economics of poker, also from a mathematical standpoint. He also discusses
the history of this popular table game. Hannum asserts that poker is unique among
gambling activities for two reasons. First, it is not house-banked. Second, there is a
considerable amount of skill involved in this game, which is not the case for other
casino and lottery games.
Leonard MacLean of Dalhousie University and William Ziemba of the University of
British Columbia describe an interesting betting strategy known as the Kelly strategy,
where the expected logarithm of ﬁnal wealth is maximized. The authors consider
the advantages and disadvantages of this strategy, with reference to its application in
blackjack, horse racing, lotto, and anomalies in the index futures markets. They also
discuss the use of Kelly-type strategies by what they term “great investors.”
The section on betting strategy concludes with a chapter by Michael Smith of Leeds
Metropolitan University, who explores the performance of “experts,” or media fore-
casters, in selecting winners. He also provides a more comprehensive examination of
the degree of information efﬁciency with respect to these events. His empirical analysis
considers whether there are any betting strategies based on these“expert”picks that can
systematically beat the market.
v Motivation, Behavior, and
Decision-Making in Betting Markets
.............................................................................................................................................................................
Alistair Bruce of the University of Nottingham examines individual motivations for bet-
ting, synthesizing perspectives from economics, psychology, and sociology. His results
have important implications for policy makers designing legal and regulatory regimes
for betting as well as for those interested in treating the negative effects of “excessive”
exposure to betting. The next chapter, by Les Coleman of the University of Melbourne,
examines a variety of characteristics of betting markets. He focuses on comparing
betting markets to ﬁnancial markets and then assesses the motivations for gambling.
In a similar vein David McDonald, Johnnie Johnson, and Ming-Chien Sung of
the University of Southampton present evidence of biased decision-making in betting
markets. An interesting aspect of their research is that they demonstrate how systematic
biases that were ﬁrst identiﬁed in the laboratory are reﬂected in real-world gambling
behavior. Greg Durham of Montana State University examines sports betting, and
speciﬁcally point spread wagering, through the lens of “behavioral ﬁnance,” which
draws heavily from psychology.

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xviii introduction
vi Prediction Markets and
Political Betting
.............................................................................................................................................................................
David Johnstone of the University of Sydney examines the question of the predictability
of sports betting markets based on a simple automated “market maker” for prediction
markets. He notes that there is great potential for the use of automated “robot” market
makers in prediction markets and market simulation games, based on research in
experimental economics and behavioral ﬁnance. He outlines the beneﬁts of adopting
such an approach in terms of two key advantages: (1) the model is easy to derive and (2)
the opening security price can be set arbitrarily between zero and one, so as to match
the market maker’s prior beliefs.
The next chapter, by Paul Rhode of the University of Michigan and Koleman Strumpf
of the University of Kansas, describes the long history of political betting markets.
Contrary to popular wisdom, political futures markets are not a recent invention. The
authors trace the operation of political futures markets back to sixteenth-century Italy,
eighteenth-century Britain and Ireland, nineteenth-century Canada, and twentieth-
century Australia and Singapore. They also note that election wagering was quite
popular in the United States in the pre-1860 period but during the post-1860 period
became increasingly concentrated in the organized futures markets in New York City.
vii Lotteries and Gambling Machines
.............................................................................................................................................................................
David Forrest of the University of Salford and O. David Gulley of Bentley University
examine the efﬁciency of lottery markets. The authors conclude that lotto players act as
if they understand the “rules of the game” and appropriately use relevant information
about the games. Exceptions to efﬁciency are found, but these “inefﬁciencies” cannot
be easily exploited by bettors.
John Lepper of Deakin University and Stephen Creigh-Tyte of Durham Business
School provide an historical analysis of the U.K. National Lottery. Although the ﬁrst
National Lottery draw of the modern era occurred in November 1994, state-sponsored
lotteries had been common since the reign of Queen Elizabeth I. The authors describe
the development of the National Lottery and consider the introduction, nature, and
performance of the modern Lottery while also describing the economics of the National
Lottery.
Scott Farrow and Chava Carter of the University of Maryland, Baltimore County,
assess the costs and beneﬁts of slot machine gambling. This chapter begins by deﬁning
the slot machine segment of the gambling industry and then reviews the economics of
these machines based on beneﬁt-cost analysis. They also review illustrative empirical
studies and provide suggestions for additional research.

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introduction
xix
Kent Grote of Lake Forest College and Victor Matheson of the College of the Holy
Cross survey the literature on the economics of lotteries in terms of two central themes.
The ﬁrst section examines the microeconomic aspects of lotteries, including consumer
decision-making under uncertainty, price and income elasticities of demand for lottery
tickets, cross-price elasticities of lottery tickets to each other and to other gambling
products, consumer rationality and gambling, and the efﬁciency of lottery markets.
The second section covers topics related to public ﬁnance and public choice, including
the revenue potential of lotteries, the tax efﬁciency and dead-weight loss of lottery
games, the horizontal and vertical equity of lotteries, earmarking and the fungibility of
lottery revenues, and individual state decisions to participate in public lotteries.
Leighton Vaughan Williams of Nottingham Trent University and David Paton of
the University of Nottingham consider the taxation of gambling machines. Although
there has been considerable research on the economic impact of gambling on regional
economies in the United States and the United Kingdom, relatively little research has
focused on the optimal taxation of gambling machines within these facilities. The
authors seek to ﬁll this gap by examining the theoretical arguments for taxing gambling
machines by means of a levy on machine takings rather than by means of a licence fee
levied per machine. Recent tax debates in the United Kingdom provide an ideal context
for such a discussion.
References
Paton, David, Donald S. Siegel, and Leighton Vaughan Williams. 2002. A policy response
to the e-commerce revolution: The case of betting taxation in the UK. Economic Journal
112(480): F296–F314.
——. 2004. Taxation and the demand for gambling: New evidence from the United Kingdom.
National Tax Journal 57(4):847–861.

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s e c t i o n i
........................................................................................................
CASINOS
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chapter 1
........................................................................................................
THE EMPLOYMENT IMPACT
OF CASINO GAMBLING IN THE U.S.
........................................................................................................
gary anders
The Growth of Gambling in
the United States
.............................................................................................................................................................................
Over the past twenty years, gambling has become a growth industry in the United
States, the United Kingdom, Canada, Australia, Macau (Macao), and other nations.1
Once restricted to Nevada and, later,Atlantic City, casinos now operate in 33 U.S. states.
Since Congress passed the Indian Gaming Regulatory Act (IGRA) in 1988, tribes in 28
states have established casinos, and others are seeking federal recognition so that they
can do the same. According to the National Indian Gaming Commission, 236 Indian
tribes are currently operating casinos.2 In 2010, Indian casinos earned approximately
$26.5 billion (National Indian Gaming Commission 2011). California alone has 56
tribal casinos, making it one of the most lucrative gambling markets in the world.
Starting in 1989 with Iowa, states began to legalize land-based riverboat casinos, horse
and dog racetrack casinos (racinos), and urban casinos.3 Altogether these non-Indian
commercial gambling casinos earned over $34.6 billion in gross gambling revenues in
2011 (American Gaming Association 2011). Including those operated by Indian tribes
and regulated by the states, casinos generated over $61 billion in annual revenues.
Over a decade ago, the National Gambling Impact Study Commission (NGISC) was
established to investigate various issues regarding the legalization of gambling. After
sponsoring several major studies and conducting hearings in different cities across
the country, the NGISC issued a ﬁnal report that called for a moratorium on new
gambling venues (NGISC 1999). Despite this recommendation, new casinos continue
to be established, with urban land-based casinos and Indian casinos being the most
prevalent. The rapid growth of commercial gambling has been striking not only in

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4
casinos
the United States but also worldwide. The unprecedented growth of government-
sanctioned gambling raises a number of policy issues related to the social and economic
impacts of gambling. The purpose of this study is to examine how the introduction
of commercial gambling casinos impacts a state’s economy by focusing on changes in
industry employment.
This chapter is divided into four parts. The ﬁrst provides an overview of the literature
on the economic and social impacts of commercial gambling. This is followed by a set of
hypothesesthatareusedtoexaminetheeffectsof casinogamblingonstateemployment.
Next, a regression analysis of the relationship between changes in industry employment
and gambling is presented. The conclusion summarizes the ﬁndings and discusses the
limitations of the study and future research directions.
Literature Review
.............................................................................................................................................................................
This section summarizes some of the most relevant research on the economic and
social impact of casinos on local communities. A useful starting point is Rose (2001).
Based on a survey of more than 100 published studies, it concluded that, as a general
rule, a new casino provides positive economic beneﬁts to its host economy. Among
these beneﬁts are direct and indirect employment from the construction of the casino,
taxes collected by the state, the capture of gambling revenues from residents who
would otherwise gamble in out-of-state casinos, the increase in consumer utility from
additional recreational choices, and employment from casino jobs. Rose also mentions
such social costs as increased gambling addictions, congestion, and proﬁts going to
outside interests. He claims that most of the economic impact studies he reviewed
suffer from a number of critical ﬂaws, major omissions, or biased assumptions.
Various gambling interests have sponsored numerous studies to support the adop-
tion of casinos. Representative of this type of work is the Arthur Andersen study
conducted for the American Gaming Association (AGA). Without mentioning any
negative impacts, this study lauds the economic beneﬁts of casinos, asserting that “the
introduction of casinos leads to growth in almost all other areas: retail sales, commercial
and housing construction, restaurants, etc.” (Arthur Andersen 1997, 45) and claiming
that casinos are responsible for increased taxes, employment growth, and reductions in
the number of families on welfare. Similarly, a recent AGA-funded study by the Brattle
Group (2011) provides analysis supporting the positive impact of casinos and includes
direct, indirect, and induced multiplier effects of casinos. What is interesting is that
this study expands the scope of casino operations to include hotels, food and beverage
services, and other business lines.
William R. Eadington (1998), a leading scholar in the ﬁeld, includes tourism devel-
opment, economic revitalization, tax revenue, jobs, new investment, and employment
opportunities for minorities as expected beneﬁts from casinos. He argues that destina-
tion resort casinos are the strongest in job creation, due to the fact that these casinos

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the employment impact of casino gambling in the u.s.
5
are able to export the activity to nonresidents while capturing signiﬁcant tax revenue
for the local jurisdiction (Eadington 1999).
Douglas Walker and John Jackson’s (1998) article is one of the more rigorous empir-
ical studies of the relationship between legalized gambling and local economic growth.
This study employs regression analysis to address two research questions: (1) Does
legalized gambling contribute to state economic growth? And (2) Must gambling be
exported for economic growth to occur? They found evidence that casino gambling
and greyhound racing do increase state income but that it is not necessary for the state
to export gambling in order for these results to hold. A follow-up to this study (Walker
and Jackson 2007) employed Granger causality analysis to examine the relationship
between casino gambling and state-level economic growth as measured by Consumer
Price Index–adjusted personal income. The authors found that there does not appear
to be a signiﬁcant relationship between the introduction of casino gambling and per
capita income.
Daniel Felsenstein, Laura Littlepage and Drew Klacik (1999) use the prisoner’s
dilemma to explain the conundrum faced by many states regarding the legalization
of casinos. They believe that competitive bidding by states to attract gambling casinos
undercuts the potential economic development beneﬁts. The authors identify positive
economic impacts in terms of new investment, jobs, higher incomes, and consumer
choice. The negative effects are increases in compulsive gambling pathologies and the
regressive economic impact on those in lower income groups who are the primary
customers of casinos.
William Thompson, Ricardo Gazel, and Dan Rickman (2000) identify some of the
ways that compulsive gambling affects the economy. These include theft, forgeries, bad
debts, insurance fraud, credit card fraud, loan sharking, increased criminal justice costs,
civil court costs, divorce, bankruptcy proceedings, treatment costs, public assistance,
and suicide. They assert that, taken in full measure, these costs outweigh the beneﬁts of
casino gambling.
Earl Grinols, a professor of economics at the University of Illinois, is a leading critic of
legalized gambling. He argues that the introduction of riverboat casinos in Illinois did
not create the jobs that were promised and had little impact on local unemployment
(Grinols 1994). Grinols (1996) further reported that only when gambling is able to
tap outside markets will casinos have a positive economic impact; otherwise gambling
results in inefﬁcient transfers from one business to another. Exacerbating this problem
are the costs of problem gamblers who constitute the largest share of the casino client
base. Grinol’s book Gambling in America (2004) discusses the casino industry and
presents a theoretical cost-beneﬁt framework for assessing the net economic impact of
gambling. As with his other writings (Grinols and Mustard 2001, 2006), there is strong
anti-gambling sentiment reﬂecting his concern regarding the social costs associated
with gambling.
Louise Simmons (2000) found that while casinos do create jobs in related industries,
they also tend to divert consumer expenditures from other businesses. Furthermore
she asserts that jobs resulting from casino development are lower paying positions. She

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6
casinos
believes that gambling exacerbates social problems among lower income and minority
groups. She argues that casinos are not a sound economic development alternative for
many local communities seeking to generate increased tax revenues, especially given
the possibility of market saturation from increased numbers of casinos.
Several studies by Gary Anders and Donald Siegel have examined the possibility of
economic displacement as a result of gambling. Anders, Siegel, and Munther Yacoub
(1998) found that the operations of Indian casinos in Arizona were strongly corre-
lated with structural changes in state tax revenue. Siegel and Anders 1999 found
strong statistical evidence of displacement between riverboat casinos and other sec-
tors in Missouri. Siegel and Anders 2001 reported evidence of substitution between
casinos and state lotteries. Anthony Popp and Charles Stehwien (2002) have found
further evidence of a negative correlation between Indian casino gambling and state
revenues.
Focusing on the employment impacts, Thomas Garrett (2003) analysed monthly
data from the Bureau of Labor Statistics (BLS) for six counties: two in Mississippi,
two in Illinois, one in Iowa, and one in Missouri to examine the relationship between
employment and the opening of a casino. He found evidence that in three of the four
rural counties, establishing a casino did increase household employment. In the case
of the two urban counties, however, he found that it was much harder to detect a
signiﬁcant impact of casinos on either household employment or payroll.
Garrett’s approach uses a comparison of differences between a forecast of selected
county employment versus actual county employment after the introduction of a
casino. The ﬁve counties selected were Warren and Tunica counties, Mississippi; Mas-
sac and St. Could counties, Illinois; Lee County, Iowa; and St. Louis County, Missouri.
His analysis produced mixed results. In three counties (Warren, Tunica, and Massac)
actual household employment after the introduction of a casino was greater than fore-
casted. In two counties (St. Clair and Lee County), actual household employment after
the introduction of a casino was less than forecasted household employment. In St.
Louis County, the underlying cyclical nature of the economy undermined a compari-
son. Garrett’s study includes a comparison of six employment sectors for each county.
These include manufacturing, retail trade, services, ﬁnancial, construction, and casino
employment.
Since the data Garrett used date from the introduction of casinos until December
2001, the study presents only limited consideration of the long-term employment
effects. Moreover, differences in the size of the local economies make it difﬁcult to
draw meaningful conclusions. One signiﬁcant aspect of this study worth noting is that
Garrett ﬁnds rural counties more likely than metropolitan counties to beneﬁt in terms
of increased household employment. The reason for this may have to do with the
relative size of gambling employment compared to total employment, which would be
smaller in metropolitan counties than in less populated rural areas of the state.
In his pathbreaking book The Economics of Casino Gambling (2007), Douglas Walker
concludes his brief discussion of the impact of casinos on employment and wages with
the following observation. “Unfortunately, there has been relatively little research on

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the employment impact of casino gambling in the u.s.
7
the labor market effects of the casino industry. This is an important issue that deserves
more attention from independent researchers” (8).
Discussion
.............................................................................................................................................................................
This brief review of the existing literature presents a mixed set of results regarding the
economic impact of commercial gambling. On the one hand, proponents of gambling
argue that casinos create new jobs, increase local tax revenues, and stimulate economic
growth through induced consumption and employment multipliers. Critics of gam-
bling, on the other hand, assert that casinos displace consumer expenditures from other
businesses and largely result in transfers from one sector to another while increasing
social problems. The literature also reﬂects heightened concern about the social costs
associated with pathological gambling that increase both public and private costs as well
as the way in which these costs have been distorted by inappropriate methodologies
(Walker 2003).
Interest in the ﬁeld of gambling studies has increased due to the growing recogni-
tion of the economic signiﬁcance of gambling. New researchers are entering the ﬁeld,
and highly respected academic journals are more interested in publishing gambling-
related research. Along with this have been efforts to apply rigorous empirical analytical
approaches to gambling-related policy issues. My own research in this area has greatly
beneﬁted from collaborations in the United States and the United Kingdom, where
there has been an even greater recognition of the importance of gambling.
The following presents four testable hypotheses that will be used to structure a
regression analysis of the employment impact of casinos. These are:
Hypothesis 1: The construction and operation of casinos are expected to increase the
total number of new jobs and through income and expenditure multipliers will lead to
employment growth in other sectors of a local economy.
Hypothesis 2: The operation of casinos is expected to have a positive impact on
employment in businesses related to entertainment and recreation as well as busi-
ness services. The jobs created by new casinos are likely to include higher paying
professional/managerial positions as well as lower paying jobs in the food and beverage
industry.
Hypothesis 3: Assuming the possibility of cannibalization arising from the competition
between casinos and other recreational establishments, the growth in employment in
competing entertainment businesses and retail establishments, including restaurants
and bars, will be negatively correlated with casinos drawing a signiﬁcant number of
local customers.
Hypothesis 4: Used as an economic development tool,casinos will increase state revenue
and per capita income. This will occur because states with legalized commercialized

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8
casinos
gambling and Indian casinos will collect additional revenues as a result of revenue
sharing arrangements with the gaming establishments. In addition, jobs created by
casinos will reduce the state’s unemployment rate.
Regression Model
.............................................................................................................................................................................
A regression model for 11 states with casino gambling was used to test these hypotheses.
The states included in the study are California, Connecticut, Illinois, Iowa, Louisiana,
Michigan, Minnesota, Mississippi, Missouri, Nevada, and New Jersey. These states were
selected for two reasons. First, they have the longest history of legalized gambling.
Second, data were not available for other states, for reasons that will be delineated
below. Monthly employment data for 8 industries in these 11 states were collected from
1990 to 2004 from Bureau of Economic Analysis (BEA) website (www.bea.gov).
According to the AGA (2011), the global ﬁnancial crisis of 2008 resulted in a sig-
niﬁcant decrease in gross revenues for casinos, which have yet to return to their peak
levels of 2006–2007. Given that 8 out of 22 states with commercial casinos are con-
tinuing to experience decreases in income, employment, and tax revenues, I decided
to utilize a time period that captures an entire national business cycle, starting with
the contraction that began in the early 1990s and continuing through the recovery and
expansion that lasted into the early years of the George W. Bush administration. Among
the various possibilities, eight industries that previously have been identiﬁed as most
likely to be directly affected by the opening of a casino were selected for analysis. These
industries are
(1) Professional scientiﬁc and technical services
(2) Management of companies and enterprises
(3) Depository and non-depository institutions
(4) Construction
(5) Arts and Entertainment;
(6) Gambling
(7) Accommodations
(8) Food services and drinking establishments.
As noted above, it was not possible to include more states in the study due to the
lack of data. A major problem in collecting state employment data is one of stan-
dardizing the series. Starting in 2001 the U.S. government switched the industry
classiﬁcation system from the Standard Industrial Classiﬁcation (SIC) to the North
American Industry Classiﬁcation System (NAICS) (For a discussion of the switch see
www.census.gov/epcd/www/naicsdev.htm.) As of early 2013, many states had yet to
reconcile their industry employment data with the new classiﬁcations. Because the
industries in the NAICS were changed, only the same industries included in the old SIC

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the employment impact of casino gambling in the u.s.
9
Table 1.1 NAICS and SIC Industry Classiﬁcation Comparisons
Industry Name
NAICS Code
SIC Code
Professional Scientiﬁc and Technical Services
1200
875
Management of Companies and Enterprises
1300
400
Construction
0400
300
Depository and Non-Depository Institutions
1002
710
Real Estate
1101
734
Gambling
1703
835
Accommodations
1801
805
Food Services and Drinking Establishments
1802
627
were used. For example, the professional, scientiﬁc and technical services classiﬁcation
was SIC 875 but after 2001 became NAICS 1200. Thus because of omitted observations
it not possible to include more industries or states within the current framework. The
NAICS and SIC codes for the industries used are given in table 1.1.
Another issue that needs to be mentioned is the problem of collecting data on Indian
casinos. While data on gaming revenues by casino are available for commercial casinos
from state gaming commissions, actual revenue data for most Indian-run casinos can-
not be obtained.4 As of this writing, only highly aggregated tribal gaming revenue data
are available from the National Indian Gaming Commission. Because of this, proxies
in the form of additional measures of gambling activity were used. These variables
include the number of casinos, the number of admissions into casinos, the total num-
ber of tables, the total number of slot machines, the number of wins per admission,
the total square footage of the casinos, and the number of tables, information available
from industry publications, such as International Gaming & Wagering Business.
Additional explanatory variables were created using this data set. For gambling these
variables include win per admission, win per table, win per slot machine, and win per
square foot.5 Also, data from the U.S. Census Bureau provided another a set of other
possible explanatory variables. Data for all 11 states for the years 1990 to 2004 were
collected on the following variables: industry revenue, state population, state per capita
income, total employment, state and local revenue, and average earnings. Also included
were changes in both state and local revenues as well as selected industries. A complete
list of the explanatory variables is presented in table 1.2.
The original approach was to use a regression framework to determine how industry
employment was affected by the introduction of casino gambling in a particular state
by using gambling data only for that state. However, it became clear that gambling is a
regional as opposed to a discrete state economic activity. For example, riverboat casinos
in Illinois compete with casinos in Missouri and Indiana and, to a lesser extent, with
casinos in Nevada and Atlantic City. Subsequent regression models for each industry
were therefore constructed using a panel of state data.

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10
casinos
Table 1.2 Independent Variables
Variable Name
Explanation
NSM
Total number of slot machines in the state in a particular year
Year
A time trend to reﬂect exogenous growth
CMR
Year-to-year change in manufacturing industry revenue of a state
CSLR
Year-to-year change in state and local revenue of a state
CP
Year-to-year change in population of a state
TNT
Total number of gambling tables in a state in a particular year
WPA
Win per admissions in gaming in a state in a particular year
CGR
Year-to-year change in gaming revenue of a state
CDR
Year-to-year change in depository and non-depository revenue of a state
CCR
Year-to-year change in construction revenue of a state
TSFA
Total square footage of casinos present in a state in that year
NA
Total number of admissions into casinos in a particular state in that year
CFDSR
Year-to-year change in food and drinking services revenue of a state
CPCPI
Year-to-year change in per capita personal income of a state
The ﬁrst set of preliminary regressions suffered from low Durbin-Watson (DW)
values (0.2–0.5) due to auto correlation between the independent and dependent vari-
ables. In an attempt to correct the problem year-to-year changes in the variables were
used. This speciﬁcation increased the DW statistic to about 1 but reduced the R2 value
signiﬁcantly. Next, other independent variables, such as per capita personal income
and state and local revenues, were introduced. Also, the speciﬁcation of the dependent
variables was revised to measure the change in the ratio of employment in each indus-
try to total employment in the state. This allowed the model to capture the resulting
change in the composition of state employment rather than the absolute change and
made it easier to isolate the effect of changes in the independent variables. With these
changes the test statistics for the regressions improved; however, the DW statistic still
indicated the existence of serial correlation.
Various alternative approaches and speciﬁcations were used in an attempt to correct
this problem (i.e., taking the ratio of two variables or taking the ﬁrst difference and
dividingitbyanothervariable). Aftersometrialanderror,theGeneralizedLeastSquares
(GLS) produced the best results. No doubt there are other methodological issues, relat-
ing to stationarity of the data. However, this issue is complicated by the profound effect
that technology played in restructuring certain segments of the economy over this time
period. To capture some of this effect a technology variable proxy (personal computers
per capita) was included, as suggested by David Card and John DiNardo (2003).
The GLS method can be performed in one of two methods: Prais-Winstein
or Cochrane-Orcutt. Prais-Winstein is preferred over Cochrane-Orcutt because it
provides greater ﬂexibility to reduce serial correlation by allowing weights to be assigned
to the independent variables. Using this method the dependent and the independent

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the employment impact of casino gambling in the u.s.
11
variables were modiﬁed according to the following equations:
Y ∗= Yt −ρ × Yt−1
X∗= Xt −k × Xt−1
Where ρ and κ are assigned weights depending on the degree of serial correlation in
the model. The Prais-Winstein method involved taking the ratio in dependent variable
(industry sector employment in the state (EIJ) to (TJ), the total employment in the
state.) Then the regression model becomes:
EIJt
TJ

t
−ρ ×
EIJt
TJ

t−1

= (Xt −k × Xt−1) × β + εt
=>
EIJ
TJ
∗
t
= X∗
t × β + εt
Where Xt is vector of independent variables.
This speciﬁcation produced an acceptable Durbin-Watson. However, by using the
Prais-Winstein method the ﬁrst observation is lost, which reduces the R2 value. To
recover this observation the ﬁrst observation was weighted by 1/

1 −p2 for dependent
variables and by for independent variables. Then the regression model becomes
X∗=
⎡
⎣

1 −ρ2

1 −ρ2x11

1 −ρ2x21
1 −ρ
x12 −ρx11
x22 −ρx21
1 −ρ
x13 −ρx12
x23 −ρx22
⎤
⎦
EIJ
TJ
∗
=
⎡
⎢⎢⎢⎣

1 −ρ2
 eij
tj

1
 eij
tj

2 −ρ
 eij
tj

1
( eij
tj )3 −ρ
 eij
tj

2
⎤
⎥⎥⎥⎦
EIJ
TJ
∗
t
= X∗
t B + εt
Results
.............................................................................................................................................................................
This speciﬁcation produced acceptable results for all eight industries. Table 1.3 presents
the results, including T-statistics, R2 values, and level of statistical signiﬁcance. The
R2 statistic ranges from .625 to .295, indicating that the model accounts for up to
two-thirds of the variation in industry sector employment changes. This is acceptable
given the data limitations and the fact that only a small number of states had complete
time series for these industries. The results indicate that some of the gambling variables
(i.e., number of machines, numbers of tables, and gambling revenue) are positively
correlated with changes in employment for some sectors, such as employment in food

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Table 1.3 Regression Results
Dependent
Variable
Independent
Variable GLS
in Parentheses
(A)
Change in
Ratio of
Science and
Technology
Employment
to Total
Employment
(B)
Change in
Ratio of
Management
Employment
to Total
Employment
(C)
Change in
Ratio of Credit
Employment
to Total
Employment
(D)
Change in
Ratio of
Construction
Employment
to Total
Employment
(E)
Change in
Ratio of Arts
Employment
to Total
Employment
(F)
Change in
Ratio of
Gambling
Employment
to Total
Employment
(G)
Change in
Ratio of
Accommoda-
tion
Employment
to Total
Employment
(H)
Change in
Ratio of Food
and Drinking
Places
Employment
to Total
Employment
Constant
−1280.935
(−3.194)∗∗
−1257.983
(−3.004)∗∗
−0.082
(−0.201)
1.604
(3.039)∗∗
−1074.43
(−2.360)∗
613.541
(2.443)∗
−446.923
(−1.423)
1.245
(1.454)
No. of slot
machines (NSM)
(0.95)++
−0.000432
(−2.889)∗∗
–
–
–
0.00001
(1.980)∗
–
–
–
Year (Y )
(1)++
0.641
(3.195)∗∗
0.634
(3.016)∗∗
–
–
0.536
(2.354)∗
−0.308
(−2.446)∗
0.224
(1.823)
–
Change in state
and local
revenue (CSLR)
(0.92)++
−0.0000288
(−1.729)
–
–
−0.000367
(−3.198)∗∗
–
0.002133
(2.440)∗
−0.000414
(−3.523)∗∗
–
Change in
population (CP)
(0.9)++
0.116
(3.883)∗∗
–
−0.032
(−2.948)∗∗
0.03722
(2.903)∗∗
0.05138
(3.192)∗∗
−0.021
(−1.516)
0.08399
(4.401)∗∗
0.02673
(2.323)∗
Total number of
tables (TNT)
(1)++
–
–
–
–
0.006178
(1.813)
–
–
–

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## Page 34

Win per
admission (WPA)
(1)++
–
−0.037
(−1.977)∗
–
–
–
–
–
–
Change in
Gaming Revenue
(CGR)
(1)++
–
-0.003
(2.543)∗
0.0229
(1.974)∗
–
0.006438
(2.544)∗
0.08096
(4.786)∗∗
0.01186
(5.362)∗∗
0.036786
(2.394)∗
Number of
admissions (NA)
(1)++
–
–
–
−0.000275
(−1.984)∗
–
–
–
–
R2
0.625
0.558
0.295
0.314
0.350
0.393
0.541
0.314
Standard Error
4.433
1.548
1.980
1.382
3.206
2.635
3.546
2.572
Durbin-Watson
1.475
1.926
1.743
1.635
2.017
1.622
1.587
1.456
DF
72
64
83
58
58api
67
74
74
∗(T -statistic) ∗at 95% conﬁdence level, ∗∗at the 99% conﬁdence level.
++ Auto Correlation factor for each variable used in the Prais-Winstein method.

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14
casinos
and drinking establishments and accommodations, and arts industries, but negatively
correlated with employment changes in other sectors, such as science and technology,
and management.
An examination of the relationships among variables reveals some interesting trends.
First, an obvious demographic change involving an aging population of baby boomers
has played a strong role in the growth of recreation industries that is reﬂected in the
growth in hotel and restaurant employment. Second, beginning in the early 1990s,
an economic contraction and increased global competition led companies to down-
size their workforce. Related to this were reductions in the number of managerial and
supervisory positions. Third, changes in technology and the use of personal comput-
ers resulted in negative employment trends in such industries as banking and credit
intermediation. Thus increases in state population had a strong positive effect on
employment in most industries except those experiencing structural changes. Finally,
changes in state and local government revenues are positively correlated with the change
in gambling employment but negatively correlated with employment changes in science
and technology, construction, and accommodations industries. It is not obvious why
this is the case because the results appear to be counterintuitive, but previous gambling
research indicates that revenue displacement may have affected state revenues to some
degree. Additional research is needed to examine this issue more carefully.
Conclusions
.............................................................................................................................................................................
This chapter attempts to shed light on the impact of casinos on state economies. Many
of the economic impact studies written to support the adoption of casinos use expen-
diture and employment multipliers, which demonstrate that casinos beneﬁt regional
economics through direct purchases and employment or through indirect multiplier
effects (Rose 2001). The prevailing wisdom is that the induced impacts associated with
gambling employment stimulate the creation of additional jobs in related industries.
Given that employees in the casinos and related businesses pay state income taxes and
sales taxes on their purchases of goods and services, states are expected to beneﬁt from
additional tax revenue. Thus the total ﬁscal impact of casinos is often thought to be
positive. Although limited by data availability, these preliminary ﬁnding suggest that the
expansion of commercial and tribal casinos may have a positive local employment effect
in some sectors, but taken regionally where states have legalized competing gambling
venues, the overall employment effect for other sectors is quite possibility negative. The
evidence suggests that casinos may not have as signiﬁcant a positive effect on higher
paying jobs (e.g., jobs in science and technology, and management) due to the types of
jobs created by casino expansion and possible job losses that occur from competition
with other sectors of the economy.
The literature indicates that there are several factors that signiﬁcantly increase or
reduce the positive impacts of casinos. First, to a certain extent, the economic beneﬁts

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the employment impact of casino gambling in the u.s.
15
of casinos depend on whether gambling is exported to residents of other states or
whether opening local casinos encourages residents not to gamble in other jurisdictions
(import substitution). For maximum beneﬁt local economy casinos should bring in
new money rather than displace existing consumer expenditures. For example, when
Mississippi legalized riverboat casinos, the state captured some of the gambling revenue
that would have been spent by its residents in Louisiana. Likewise, Mississippi gamblers
now substitute gambling at local casinos for trips to Las Vegas or Atlantic City, and this
increases the economic contribution to the state. But as more and more states adopt
casino gambling the opportunities for import substitution decrease, and the only way
that growth can occur is through increasing the amount gambled per visit or increasing
the number of gamblers.
A major unresolved issue is the nature of source of money spent in casinos . If some
portion of the gaming dollars comes from savings, or substitutions from other types
of expenditures, the displacement effect would be smaller. At this time there is not
enough speciﬁc household information on gambling behavior to draw conclusions.
The existing literature does, however, suggest that a large segment of the gambling
market is from lower income households where the marginal propensity to consume is
high and saving is conversely low (Borg, Mason, and Shaprio 1990).
Given the favorable public attitude toward legalized gambling, I anticipate continued
expansion in new markets (Anders 2003). In calculating the net economic impact of
gambling, policy makers should take into consideration the reductions taking place in
the proportion of higher paying jobs that are lost against the economic value of lower
wage jobs generated in the entertainment, hotel, and food and beverage sectors. Further
expansion of casino gambling also raises the possibility of market saturation. Unless the
growth of gambling casinos is met with an increase in the demand for gambling, then
as with other industries, there could be overcapitalization and eventually reduced prof-
itability (Eadington 2007). Furthermore, on-line gambling presents a new competitive
alternative that could signiﬁcantly affect the demand for casino gaming. Internet gam-
bling is already estimated at over $50 billion worldwide and is growing rapidly. Given
the ease and convenience of this form of on-line gambling it is certain to become a seri-
ous competitor to casinos. It will be interesting to see how this phenomenon, which is
quite popular among younger gamblers, will offset current employment trends caused
by the increased demand for recreation and tourism by an aging population of baby
boomers.
Notes
∗The author wishes to acknowledge the research assistance of Sandeep Kumar Somavarapu
and the helpful comments of Donald Siegel and William Eadington.
1. For a discussion: Kurlantzick (2007).
2. Some of the largest and most proﬁtable casinos are tribally owned and located in areas that
may have had only pari-mutuel gambling or state lotteries.

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16
casinos
3. In 1989 Colorado and South Dakota legalized historical limited stakes casinos. Starting
in the early 1990s Illinois, Indiana, Iowa, Louisiana, Missouri, and Mississippi legalized
riverboat casinos. Other states have legalized racetrack casinos.
4. Because the Indian Gaming Regulatory Act speciﬁcally exempts tribes from the Freedom
of Information Act, it is not possible to acquire data on tribal gambling revenues unless a
tribe makes that information available.
5. Gambling industry data are collected from issues of Christiansen Capital Advisors’ Inter-
national Gaming & Wagering Business, Bear Stearns’North American Gaming Almanac, and
gambling websites for various states.
References
American Gaming Association. 2011. State of states: The AGA survey of casino entertain-
ment. Washington, D.C.: American Gaming Association; http://www.americangaming.org/
newsroom/op-eds/state-states-2011-turning-corner.
Anders, Gary C. 2003. Reconsidering the economic impact of Indian casino gambling. In
The Economics of Gambling, edited by Leighton Vaughan Williams. London: Routledge,
204–223.
Anders, Gary C., Donald Siegel, and Munther Yacoub. 1998. Does Indian casino gam-
bling reduce state revenues? Evidence from Arizona. Contemporary Economic Policy 16(3):
347–355.
ArthurAndersen. May1997. Economicimpactsof casinogamblingintheUnitedStates,Volume2:
Micro Study. Study conducted for the American Gaming Association. Las Vegas, Nev.:
Arthur Andersen.
Brattle Group. 2011. Beyond the casino ﬂoor: Economic impacts of the commercial casino
industry. Study conducted for the American Gaming Association.
Bear Stearns. 2002–2003. North American gaming almanac. Las Vegas, Nev: Huntington Press.
Beyond the casino ﬂoor: Economic impacts of the commercial casino industry. Study
conducted for the American Gaming Association.
Borg, Mary, Paul Mason, and Stephen Shapiro 1990. “An economic comparison of gambling
behaviour in Atlantic City and Las Vegas.” Public Finance Quarterly, 18(3): 291–312.
Card, David, and John E. DiNardo. 2003. Technology and U.S. wage inequalities: A brief
look. In Technology, growth, and the labor market, edited by Donna Ginther and Madeline
Zavodny. Boston: Kluwer Academic Publishers, 131–160.
Eadington, William R. 1998. Contributions of casino-style gambling to local economies.
Annals of the American Academy of Political and Social Science 556:53–65.
——. 1999. The economics of casino gambling. Journal of Economic Perspectives 13(3):
173–192.
——. 2007. “Trends in commercial gaming industries globally: Issues that might interest
economists.” Paper presented at the conference The Growth of Gambling and Prediction
Markets: Economic and Financial Implications, University of California Riverside, Desert
Palms, May 21.
Felsenstein, Daniel, Laura Littlepage, and Drew Klacik. 1999. Casino gambling as local growth
generation: Playing the economic development game in reverse? Journal of Urban Affairs
21(4):409–421.
Garrett, Thomas A. 2003. Casino gambling in America and its economic impacts. St. Louis, Mo.:
Federal Reserve Bank of St. Louis.

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the employment impact of casino gambling in the u.s.
17
Grinols, Earl L. 1994. Incentives explain gambling’s growth. Forum for Applied Research and
Public Policy 11(2):119–124.
——. 1996. Who loses when casinos win? Illinois Business Review 53(1):7–11.
——. 2004. Gambling in America. Cambridge: Cambridge University Press.
Grinols, Earl L., and David B. Mustard. 2001. Business proﬁtability versus social proﬁtabil-
ity: Evaluating industries with externalities, the case of casinos. Managerial and Decision
Economics 22:143–162.
——. 2006. Casinos, crime, and community costs. Review of Economics and Statistics 88(1):
28–45.
Kurlantzick, Joshua. 2007. Raising the stakes. Foreign Policy, May/June.
National Gambling Impact Study Commission (NGISC). 1999. National Gambling Impact
Study Commission ﬁnal report. Washington, D.C.: NGISC; http://govinfo.library.unt.edu/
ngisc.
National Indian Gaming Commission.
2011.
National Indian Gaming Commission
announces 2010 industry gross gaming revenue; Indian gaming revenues remain stable.
Press release No. 175 07-2011. Washington, D.C. National Indian Gaming Commis-
sion,July18; http://www.nigc.gov/Media/Press_Releases/2011_Press_Releases/PR-175_07–
2011.aspx.
Popp, Anthony V., and Charles Stehwien. 2002. Indian casino gambling and state revenue:
Some further evidence. Public Finance Review 30(4):320–330.
Rose, Adam Z. 2001. The regional economic impacts of casino gambling. In Regional science
perspectives in economic analysis,edited by Michael L Lahr and Ronald E. Miller. Amsterdam:
Elsevier, 345–378.
Siegel, Donald, and Gary Anders. 1999. Public policy and the displacement effects of casinos:
A case study of riverboat gambling in Missouri. Journal of Gambling Studies 15(2):105–121.
——. 2001. The impact of Indian casinos on state lotteries: A case study of Arizona. Public
Finance Review 29(2):139–147.
Simmons, Louise. 2000. High stakes casinos and controversies. Journal of Community Practice
7(2):47–69.
Thompson, William N., Ricardo Gazel, and Dan Rickman. 2000. Social cost of gambling: A
comparative study of nutmeg and cheese state gamblers. UNLV Gaming Research & Review
Journal 5(1):1–15.
Walker, Douglas M. 2003. Methodological issues in the social cost of gambling. Journal of
Gambling Studies 19(2):149–18.
——. 2007. The economics of casino gambling. New York: Springer.
Walker, Douglas M., and John J. Jackson. 1998. New goods and economic growth: Evidence
from legalized gambling. Review of Regional Studies 28(2):47–69.
——. 2007. Do casinos cause economic growth? American Journal of Economics and Sociology
66(3):593–607.

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## Page 39

chapter 2
........................................................................................................
THE ECONOMICS OF
CASINO TAXATION
........................................................................................................
john e. anderson
1 Introduction
.............................................................................................................................................................................
In this chapter, I analyze the various ways that governments tax casino gambling around
the world and consider the economic effects of that taxation. In the ﬁrst section, I
examine the types of casinos and casino gambling that takes place along with the forms
of taxation that governments apply to casino operations, including wagering taxes,
admissions taxes, fees, and other taxes. In section 2 I examine the economics of casino
taxation, including market analysis of a casino game, efﬁciency effects of casino game
taxation, equity impacts or the incidence of casino taxation, and optimal government
tax policy regarding casinos. Section 3 provides a summary of the forms of taxation used
around the world, highlighting major gambling locations, such as Las Vegas, Macau
(Macao), and Singapore, among others.
2 Economic Analysis of Casino Taxation
.............................................................................................................................................................................
In order to analyze casino taxation, the tax base, or that which is taxed, must ﬁrst be
identiﬁed so that the tax rate(s) and any exemptions, deductions, or credits can be
considered. For general background on economic analysis of casino gambling, see Suits
(1979b), Eadington (1999), Walther (2002), Benar and Jenkins (2008), and Hoffman et
al. (1999).
The most common form of casino taxation around the world is a wagering tax,
based on the adjusted gross receipts (AGR) collected by casinos on all forms of games
that they offer (table games, roulette, slot machines, etc.). AGR is generally deﬁned
as gross gambling receipts minus payouts for prizes. Some governments also subject

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the economics of casino taxation
19
casinos to admissions taxes and fees of various sorts. Admissions taxes are imposed by
several states that permit casinos in the United States, as indicated in Anderson (2005),
although these taxes are not frequently used in the rest of the world. Fees are often
charged to support social purposes in the jurisdictions where casinos are permitted, as
in Macau, for example, where two fees are levied for social and economic purposes.
2.1 Market Analysis of a Casino Game
Following the analysis in Anderson (2005), we can consider basic market analysis of a
casino game. A unique terminology is used in the world of gambling, but the economic
analysis of casino game taxation is relatively straightforward. Bettors place wagers on
a game, with the total amount wagered called the handle H, and the casino withholds
a fraction, w, of the handle. That fraction is called the takeout rate, and it determines
the price of the casino game. The total amount of prizes paid out to bettors P can be
written as P = H −wH = (1 −w)H. Then, if we solve this equation for the takeout
rate w, we obtain w = 1 −P/H. Hence, the takeout rate is one minus the ratio of total
prizes paid to bettors divided by the total amount wagered, or, the handle.
Consider how the relationship between the total amount of prizes awarded and
the handle affect the takeout rate. At one extreme, suppose the casino was entirely
benevolent and paid out all the money wagered in prizes. In that case, P = H and the
takeout rate is w = 0. At the other extreme, suppose the casino pays out no prizes, so
P = 0 and the takeout rate is unity: w = 1. In general, the derivative of the takeout
rate w with respect to the prize amount P is, ∂w
∂p = −1
H , indicating that as the prize
amount rises the takeout rate falls in inverse proportion to the total amount wagered
H. Consequently, the price of the casino game varies inversely with the prize amount.
The demand for casino gambling is inversely related to prices of the casino games.
At lower (higher) relative prices, other things being equal, we expect a larger (smaller)
quantity demanded. In this regard, there is nothing different about the demand for
casino gaming as compared to other goods and services. With full information, a
fundamental requirement of a well-functioning market, casino gamblers will have well-
behaved demand curves. The demand for a casino game can be written as H(w), where
H ′(w) < 0, reﬂecting the usual situation where the higher the price, measured by the
takeout rate applied by the casino, the smaller the amount wagered (handle). We cannot
assume that gamblers are perfectly informed about the price of each game they play,
but there is evidence that the price is generally well known by gamblers. For example,
there is empirical evidence in the lottery literature reported by Victor Matheson and
Kent Grote (2004) indicating that lottery ticket purchasers exhibit a high degree of
rationality as the effective price of a lottery ticket changes with the size of the jackpot. It
should be noted, however, that there is also evidence of non-rational lottery play, such
as overuse of birthday numbers (1–31), as in Anderson and Schmidt 2002.
The market for a casino game is illustrated in Figure 2.1, where the price or the
takeout rate w is measured on the vertical axis and the total quantity of bets or handle

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20
casinos
Supply
Demand
Supply with tax on AGR
Price (take-out rate w)
w0
w1
w1(1-t)
Quantity wagered (handle H)
H0
figure 2.1 Market analysis of a casino game with a tax on AGR
H is measured on the horizontal axis. The demand function is downward sloping and
can written as H(w) where H ′(w) < 0. On the supply side, we assume that there is
an upward sloping supply. As the price of the casino game rises, the quantity supplied
increases. Becausethemarketforcasinogamesishighlyregulatedinmostgovernmental
jurisdictions,often with limits on the number of games and gaming outlets,we illustrate
the supply curve as relatively inelastic. The interaction of market supply and demand
determines the equilibrium price (takeout ratio) w0 and quantity (handle) H0.
The precise nature of the demand curve deserves further attention. While some
individuals gamble purely as a form of entertainment and can readily walk away from
a casino after a gambling session regardless of their winnings or losses, pathologi-
cal gamblers cannot. Hence, the overall demand for casino gambling may comprise
two quite different groups of gamblers, each with distinct demand characteristics.
Pathological and problem gamblers, not being very responsive to price given their
addictions and compulsions, may have very inelastic demand. Other gamblers with-
out such addictions and compulsions may have much more elastic demand. Evidence
reported in Grinols 2004 indicates that in areas near casinos, pathological gamblers
constitute one or two percent of the population, with problem gamblers making
up another two or three percent. Of course these problem and pathological gam-
blers may constitute a much larger share of the population of gamblers who enter a
casino. When the demands of the two groups are aggregated to obtain total market
demand for a casino game, the overall demand will reﬂect the shares of the market
demand that come from the two groups. The overall sensitivity of demand to price
will reﬂect the dominant group of gamblers. Dean Gerstein et al. (1999) provide an
overview of gambling impacts and human behavior, and the General Accounting Ofﬁce
(2000) provides insight on measurement of both economic effects and social effects of
gambling.

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the economics of casino taxation
21
There is some evidence that slot machines take in nearly 60 percent of their revenue
from problem and pathological gamblers. There is also evidence that a typical casino
derives about 80 percent of its revenue from slot machines. Consequently, nearly half
of the casino revenue may be derived from problem and pathological gamblers. As a
result, the demand for casino gaming is relatively inelastic. This is especially so if the
casino has a local geographic monopoly due to restrictive regulations. If this is the
case, the demand curve will be relatively inelastic, and so will the supply curve. In the
extreme case of a local monopoly, the supply curve will be vertical and the demand
curve will be relatively steep, both of which will have an impact on the incidence of
taxation.
2.2 Effects of a Tax on Adjusted Gross Receipts (AGR)
Now consider the effect of introducing a tax on this casino game. The most common
form of tax applied to casino games deﬁnes the tax base as the adjusted gross receipts
(AGR) of the game. Tax revenue T generated by the tax determined by the product
of the nominal marginal tax rate tand the tax base AGR: T = tAGR. Recognizing
that the tax base AGR is the product of the handle and the takeout rate, AGR = wH,
we can write the tax revenue as, T = twH. This expression reveals that the effective
marginal tax rate applied to the handle is tw, the product of the nominal tax rate t
and the takeout rate w. The higher the takeout rate the larger the effective tax rate.
The supply curve shifts upward in a non-parallel manner. The reason for the non-
parallel shift is due to the form of the tax. The tax revenue T is obtained by multiplying
the marginal tax rate t times the AGR: T = tAGR. Because the AGR is the product
of the handle and the takeout rate, AGR = wH, we can rewrite the tax as T = twH.
This expression indicates that the marginal tax rate applied to the handle H is ∂T
∂H =
tw. Julie Smith (1999) and Jim Johnson (1985) identify three potential measures of
the effective tax rate, depending on the deﬁnition of the tax base that is used in the
computation.
A tax is applied to the casino’s AGR, but we can analyze the market effects in terms of
the handle H. The tax shifts the supply curve upward as indicated and results in a higher
equilibrium takeout rate w1 and lower equilibrium handle H1. A tax of tw on handle
H1 raises the price paid by gamblers from w0 to w1 and lowers the price received by the
casino from the original takeout rate w0 to the new rate w1(1 −t). Revenue generated
by the tax is tw1H1. Of that amount, the gamblers bear a tax burden of (w1 −w0)H1
while the casino bears the remaining burden of [(w0 −w1(1 −t)]H1.
The incidence of the tax can be analyzed in terms of the changes in takeout rate
w and handle H. The tax shifts the supply curve upward as illustrated, resulting in a
higher equilibrium price for the casino game w1 and a smaller equilibrium quantity
H1. The tax raises the price paid by gamblers from w0 to w1 and lowers the price
that the casino receives from w0 to (1 −t)w1. The tax generates revenue of tw1H1,
of which the gambler bears the burden (w1 −w0)H1 and the casino bears the burden

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22
casinos
[(w0 −w1)(1 −t)]H1. As is typical of tax incidence analysis, the tax has a statutory
incidence falling entirely on the casino, but market forces result in economic incidence
that differs from that. As usual, the economic agent with the less elastic behavior bears
the greater share of the economic incidence of the tax. A regulatory environment that
limits the supply of casino games causes the elasticity of supply to be relatively inelastic
in relation to the elasticity of demand, thereby causing the incidence of the casino
game tax to fall primarily on the casino. In fact, if the government jurisdiction has legal
limits on the number of casinos, slot machines, or table games, then as those limits
are reached the supply curve turns vertical. In the extreme with a vertical supply curve,
the incidence of the tax falls entirely on the casino. With the proliferation of gam-
ing opportunities in recent years, however, the supply curve is becoming increasingly
elastic.
The tax causes a welfare loss illustrated as the shaded triangle. This is the reduction
in total welfare over and above the tax revenue collected by the tax, or the excess burden
of the tax. As usual, the size of this excess burden depends on the magnitude of the
tax rate and elasticities of demand and supply. The greater the tax rate or either of
the elasticities, the larger the excess burden. Figure 2.1 illustrates the excess burden as
the usual shaded triangle with height t and base width H0 −H1. The magnitude of
the excess burden of the tax depends on the tax rate as well as on the compensated
elasticities of demand and supply. In the typical case of linear demand and supply, the
excess burden rises with the square of the tax rate. Doubling the tax rate quadruples
the excess burden, for example.
What do we know about the elasticity of demand? In a classic study of gambling,
Daniel Suits (1979a) estimated elasticities of demand for several types of gambling.
He found price elasticities substantially in excess of unity for legal bookmaking estab-
lishments in Nevada and also for wagering at thoroughbred racetracks. More recently,
David Paton, Donald Siegel, and Leighton Vaughan Williams (2004) conﬁrmed that
the demand for bookmaking is price elastic in the United Kingdom. They used recent
changes in U.K. tax policy with regard to bookmakers in order to estimate the elasticity.
Both of these studies indicate elastic demand. David Forrest, David Gulley, and Robert
Simmons (2000) estimated the elasticity of demand for U.K. national lottery tickets
during the ﬁrst three years of that lottery’s existence and found that their estimated
elasticity of −1.03 was not signiﬁcantly different from -1, indicating unitary elastic
demand. Richard Thalheimer and Mukhtar Ali (2003) have provided evidence on the
demand for gaming at riverboat and racetrack casinos in the United States, ﬁnding that
the demand for slot machine gaming was price elastic at the beginning of their study
period (1991–1998) but that it declined to be approximately unitary elastic at the end
of that period. They also found that demand for table games and slot machines are
substitutes. Paton, Siegel, and Vaughan Williams (2003) provide a review of studies on
the demand for gambling.
These estimates raise several important policy issues. First, high-price elasticities
limit the effectiveness of gambling taxes, in terms of providing additional revenue for
governments. Tax revenue is maximized at the unitary elastic point on the demand

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the economics of casino taxation
23
curve (where marginal revenue is zero). A monopolist will operate above that point
on the demand curve where the price elasticity of demand exceeds unity (in absolute
value). As a consequence, any tax rate increase that raises the price will reduce revenue.
If governments have already set tax rates on casinos to maximize revenue, any further
tax rate increases will reduce revenues. Beyond that, the ﬁnding of relatively high-price
elasticities likely points to the availability of illegal gambling alternatives. That being the
case, any further tax increase may simply drive gambling activity out of the legal casino
sector into the illegal gambling sector. While these two studies do not estimate price
elasticities for casino gambling as such, they do suggest that gambler responsiveness in
general may be elastic.
2.3 Optimal Takeout Rate
Charles Clotfelter and Philip Cook (1987) were the ﬁrst to consider the question of
the optimal takeout rate in the context of state-run lotteries in the United States. More
recently Herbert Walther (2004) examined the issue of optimal taxation of several
forms of gambling, with a primary focus on lotteries, within an inter-temporal, state-
dependent expected utility model. Using that type of model, he demonstrates that
(1) optimal tax rates are higher for larger lotto communities, (2) jackpots induce
overshooting bubbles, and (3) taxes on lotto and ﬁx-prize gambles are regressive.
Paton, Siegel, and Vaughan Williams (2001) provide a helpful note in which they
analyze the difference between a tax on stakes (the quantity wagered) and a general
goods and services tax (GST) applied to the net revenue earned from gambling activity.
They rightly indicate that a tax on stakes/wagers is the equivalent of an excise tax while
the GST is ad valorem in its nature. Consequently, a policy change from an existing tax
on stakes to a GST will potentially have efﬁciency gains.
2.4 Incidence of Casino Taxes
In popular discussion of casino taxation, it is often assumed that the tax burden falls
entirely on the gambler, but that is not necessarily true unless the gambler’s demand is
price inelastic—that is, the gambler is completely unresponsive to price. Such is unlikely
to be true except for the most pathological problem gambler. Consequently, we expect
the tax burden to be shared by the gambler and the casino.
Taxes on gambling have generally been found to be regressive with respect to income.
The seminal study ﬁnding this result is Suits 1977, which analyzed survey data on horse
tracks, state lotteries, casino games, numbers, sports cards, off-track betting, and
sportsbooks. Suits’s estimates indicate that overall gambling taxes are somewhat more
regressive than general state sales taxes (the most regressive of major state revenue
sources). His early ﬁndings for Nevada casino gambling, in particular, were progres-
sive. However, at that time casino gambling was limited to isolated locations, such as

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24
casinos
Las Vegas, where the time cost of travel plus the out-of-pocket expense meant that
only relatively high-income gamblers could afford to travel to Vegas to gamble. Since
then, casinos have multiplied all over the United States, making it possible for gamblers
to travel to a casino at a much lower cost. Consequently, more recent studies have
found that casino taxes are regressive. For example, Paul Mason, Stephen Shapiro,
and Mary Borg (1989) studied three groups of Las Vegas gamblers and found gaming
taxes to be regressive for all three groups but especially so for local residents as com-
pared to other Nevada residents and non-Nevada residents. A later study (Borg, Mason,
and Shapiro 1991) also found regressive incidence. William Rivenbark (1998) found
regressive incidence for casino gamblers in Mississippi as well.
Another aspect of casino tax incidence is obtained if we view these taxes as taxes
on the economic rents earned by casino operators. In most cases, the casino oper-
ators have been granted a franchise by way of restrictive government regulations on
casino gambling. Government legalization of casino gambling, when combined with
restrictions on the number of casinos, table games, and slot machines, results in eco-
nomic rents for the casino operators. The casino taxes, to the extent they fall on the
owners and operators of casinos, may then be progressive. The casino taxes are paired
with the liberalized regulations permitting casinos to operate. States grant the casino
franchise then tax away part of the economic rents generated by the regulations they
create.
2.5 Taxation of Casinos in Relation to other
forms of Gambling
Casinosarenottheonlyformof gamblingthatgovernmentstax. Consequently,wemust
consider the ways in which taxation of casinos may affect other forms of gambling
and the revenue derived from them. Lisa Farrell and David Forrest (2008) draw an
important distinction in this regard. Their review of the literature on the relationship
between alternative forms of gambling points out that the concepts of substitutes and
complements are often misapplied. To be correct, the precise question is whether the
cross-priceelasticitiesforalternativeformsof gamblingarenegativeorpositive. Authors
in the gambling literature tend to be more interested in the question of whether a new
form of gambling reduces sales from existing forms of gambling—a distinctly different,
although important, issue.
Farrell and Forrest (2008) examined whether the introduction of casinos in Australia
caused a change in lottery sales, displacing those sales. Using state-level panel data to
analyze intra-state differences in the portfolio of games available, the authors report
mixed results. The introduction of new super casinos appears to have reinforced lot-
tery sales, while the addition of more slot machines in the network of local gaming
venues appears to have diverted sales away from lottery games. The evidence provided
in Paton, Siegel, and Vaughan Williams 2004 indicates that the demand for bookmaker
gambling in the United Kingdom is highly sensitive to the tax rate principally because

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the economics of casino taxation
25
that form of gambling is a strong substitute for lottery and other forms of gambling.
Forrest, Gulley, and Simmons (2010) found evidence from Britain that bettors substi-
tute away from horse race, soccer, and numbers betting as the price of lottery tickets is
unusually low.
2.6 Monopoly Regulatory and Pricing Rules
There are several aspects of the monopoly position often granted to casinos by gov-
ernments that deserve more attention in the literature. For example, in cases where
the government applies both an admissions tax and a wagering tax, as is common in
the United States, the question is why both taxes are applied. This combination may
entail an optimal two-part tariff, as is often implemented in rate-of-return regulatory
contexts. Or it may reﬂect risk sharing on the part of the state government and the
casino operator, with the state receiving a certain return for each gambler and the
casino operator receiving a return based on performance.
Pursuing a monopoly regulatory point of view, we could consider how the govern-
ment may regulate a monopoly casino that has been granted an exclusive franchise
to operate in a given geographic area. The government could set the takeout rate to
extract the monopoly rent earned by the monopoly casino. The casino would maximize
its AGR net of its cost of operation: AGR −C(H), where C(H) is the casino’s total cost
of operation at the handle amount H. We can assume a concave cost function, with
C′(H) > 0,C′′(H) < 0. The usual monopoly pricing solution yields the optimal take-
out rate wm = C′(Hm)

sd
(1+sd)

, where the marginal cost at the monopolist’s optimal
handle C′(Hm) is multiplied by the ratio of the elasticity of demand divided by one
plus that elasticity. Then the government could allow the casino to retain a share of the
handle equal to C(Hm)
Hm
and take the remaining share, w −C(Hm)
Hm .
The former monopoly position of casinos being granted exclusive rights to operate in
isolated geographic markets has in recent years given way to a more competitive situa-
tion, however. At present there is more competition as more markets have been opened
with liberalized gaming regulations. Furthermore, the market is more contestable than
ever with a growing international market and computer-based means of gaming. Ray-
mond Sauer (2001) examined the industry structure of gambling markets in the United
States and how they have changed as government regulations have been altered in
response to political and economic conditions. He used the interest group model to
explain how government regulations have changed and become more liberalized. Smith
(2000) examines the general issue of the government’s stake in the gaming industry.
2.7 Multiple Taxes and the Second Best
The introduction of casino gambling in a region yields a new source of tax revenue, but
that revenue is not entirely new. There are important interactions among the various

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26
casinos
preexisting taxes that are collected by state and local governments. Thomas Garrett
(2003) has studied casino start-ups and warns that the new tax revenue a new casino
generates cannot be considered as new money to the region in which it is located.
His review of the evidence on revenue interactions indicates that the effects of casino
revenue on other state revenue sources have to be examined carefully with particular
attention paid to local conditions. Charles Leven and Donald Phares (1998) estimated
the spending displacement caused by casinos introduced in the State of Missouri (USA).
Their evidence indicates that spending on casino gaming comes at the expense of
reduced spending on other goods and services, including other forms of gambling (dog
and horse racetracks in the Missouri context), as well as from reduced savings. Since
the displaced spending may have also been taxable, the net revenue gains to the state
and local governments are smaller than they ﬁrst appear.
It is important to disentangle the signiﬁcant revenue interactions in order to get
an accurate picture of the net revenue generated by new casinos. Mason and Harriet
Stranahan (1996) modeled several channels by which tax revenue substitution may
occur. One channel is through direct substitution of various forms of gambling. Suits
(1977) originally provided evidence that other forms of gambling are substitutes for
casino gambling, not complements. If that is the case, then a new gambling opportunity
will substitute for existing gambling, with the result that the new casino revenue will
in part displace existing tax revenue. The other channels of revenue substitution run
through sectoral changes in the local economy that occur with the opening of a new
casino. Adjustments in income and employment in the regional economy are impor-
tant to consider. Furthermore, there are effects on the tourism industry. Suits (1982)
provides an example of such an analysis for the City of Detroit.
Gary Anders, Donald Siegel, and Munther Yacoub (1998) examined whether the
introduction of Native American casinos in Arizona (USA) in 1993 caused a struc-
tural shift in state tax revenue sources. They used data for the transaction privilege,
use, and severance tax (TPT) collected in Maricopa County (the largest county in
the state and the location of the state’s largest city, Phoenix). The authors report
that the new Native American casinos diverted spending from taxable to nontaxable
sectors of the regional economy. Gamblers substituted expenditure on nontaxable
Indian gaming for other taxable consumption expenditures. The TPT tax base was
reduced as a result. They found that the spending displacement occurred primar-
ily in retail trade, restaurants and bars, hotels and motels, and amusements. Siegel
and Anders (2001) also examined the impact of Native American casinos, but their
study considered the effect on state lottery revenue in Arizona. They used monthly
time series data to estimate a model of lottery game sales. Their estimates indicate
that a 10 percent increase in the number of slot machines due to the introduction
of new casinos resulted in a 3.8 percent reduction in general lottery revenue and a
4.2 percent reduction in lotto revenue. In addition, Siegel and Anders (1999) esti-
mated the economic displacement effects of riverboat casinos in Missouri (USA)
using industry-level, time series data for the eleven counties where the casinos were
introduced. Among the various effects they found, the strongest source of economic

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the economics of casino taxation
27
displacement was between casino spending and spending on entertainment and
amusements.
There is limited direct evidence on how net revenue generated by casinos affects
other tax collections. A study that examined this issue was conducted by Anthony
Popp and Charles Stehwien (2002), who used county-level data for the State of New
Mexico (USA) to examine whether Native American tribal casinos had an effect on
total taxable gross receipts (TGR), a main source of business tax revenue in that state.
Their evidence indicates that the ﬁrst casino introduced in a county reduces TGR by a
small but signiﬁcant amount. A second casino introduced in a county decreases TGR
by approximately 6 percent, reﬂecting substitution of spending on gambling relative to
other taxable goods and services. They further found that the presence of a casino in
a county reduces the TGR in contiguous counties, revealing spillover revenue effects.
Shonkwiler (1993) examined the impact of newAtlantic City casinos on Nevada gaming
revenues. Donald Elliott and John Navin (2002) examined how licensing of new casinos
in Missouri (USA) cannibalized revenues from the state lottery. Their conclusion is that
the state lottery lost $0.83 in net revenue for each dollar of additional casino tax revenue.
In the lottery literature there is ample evidence that increased lottery revenue comes at
the expense of reductions in other tax revenue sources. See, for example, Fink, Marco,
and Rork (2004) and Haas, Heidt, and Lockwood (2000).
The excess burden of a set of taxes on k forms of gambling, all of which are subject
to taxation, would be written as −1
2
k
i=1
k
j=1 titjSij. Arnold Harberger (1974, 37)
provided this expression as a general description of the measurement of the welfare
cost of a system of excise taxes on several goods. In this expression the ti/j terms are
the taxes on each form of gambling and the Si/j terms are the pure substitution effects:
Sij = ∂Xi/∂Pj (using compensated demands, with no income effects). Analysts wishing
to estimate the welfare effects of gambling taxes can use this approach and the above
expression, to derive empirical estimates of substitution effects. These provide a more
accurate measure than would be obtained from a partial analysis, which considers only
the casino tax.
2.8 Second-Best Taxation
Suppose that a casino tax tc is introduced in the presence of an existing tax on lottery
tickets tl. The existing tax on lottery tickets creates an existing excess burden of taxation
illustrated in the dark blue triangle in the right-hand panel of Figure 2.2. The introduc-
tion of a casino tax creates an excess burden in that market illustrated by the dark blue
triangle in the left-hand panel of Figure 2.2. But it is necessary to consider the further
effects of the introduction of the casino tax in the market for lottery tickets. Assuming
that casino gambling and lottery ticket purchases are substitutes, the new tax on casino
games causes the demand curve for lottery tickets to shift rightward. That rightward
shift creates a social welfare gain of the amount of the shaded rectangle, including both
the existing excess burden triangle and the additional area illustrated. The reason for

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## Page 49

28
casinos
Excess burden of casino tax
Welfare gain in lottery market
w(l+tc)
pl(l+tl)
pl
w
H1
D
Casino Market
Lottery Market
H0
D2
L1
L0 L2
D1
D1
figure 2.2 Effect of a casino tax with a preexisting lottery
this social welfare gain is that the amount that lottery ticket purchasers pay, pl (1 + tl),
for each of the additional L2–L1 tickets they buy exceeds the cost of providing those
tickets, pl. Hence, there is a social gain of the amount of the shaded rectangle with
height pltl and base L2–L1. The net social cost of the new casino tax is then the excess
burden triangle in the casino market minus the social welfare gain rectangle in the
lottery market. The casino tax introduction in the presence of a preexisting lottery tax
is actually less costly in terms of social welfare loss than would have been the case in
isolation. In fact, if the welfare gain in the lottery market is sufﬁciently large, the net
cost of the casino tax may actually be negative, or, a welfare gain. This is the standard
result from the second-best literature where a policy that may have been inefﬁcient in
isolation can be efﬁcient in the face of a preexisting distortion.
The literature to date on casino taxation has not taken a second-best approach to
estimating the net excess burden of taxation. Certainly, to examine the social welfare
implications of the introduction of a casino tax it is necessary to take into consideration
the preexisting distortions in other gaming markets. If that is not done, the estimates
of the excess burden of casino taxes will be biased upward. The extent of that bias will
depend crucially on the degree of substitutability of the alternate form of gambling.
The stronger (weaker) the degree of substitution, the greater (smaller) the extent of
the bias.
2.9 Optimal Commodity Taxation (Ramsey Rule)
The classic Ramsey Rule for optimal commodity taxation requires that the tax rates be
inversely proportional to the compensated elasticities of demand for the goods being
taxed: ti/tj = ϑj/ϑi. Alternatively, the Ramsey Rule requires that the taxes applied to
the goods reduce the demand for each good in the same proportion. Walther (2004)

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the economics of casino taxation
29
examines the issue of optimal taxation of gambling and lotteries, although his analysis
emphasizes lottery games and is conﬁned to optimality for a single form of gambling.
Xinhua Gu and Guoqiang Li (2009) consider the factors that may explain why tax rates
differ across gaming markets.
2.10 Pigouvian Tax to Correct for Externalities
Concern for the social costs created by casinos has generated proposals to implement
corrective taxes. In the tradition of economist A. C. Pigou, who ﬁrst suggested that a
tax (subsidy) can be used to correct for negative (positive) externality, corrective taxes
have been suggested as a means of reducing casino gambling and thereby also reducing
the spillover or social costs created by casinos. For example, Earl Grinols (2004) has
suggested that if a Pigouvian tax were designed to correct for the negative externalities
generated by casinos, a tax of 45 to 70 percent of gross casino revenues would be needed.
Those estimates do not take into account the excess burden of casino taxation. Douglas
Walker (2007) reviewed the social costs of casinos and argued that many of the alleged
social costs are inappropriately included or are overestimated. Even so, he does not
include the excess burden of taxation in his review or suggest any ways to include this
legitimate social cost of casinos.
2.11 Fungibility of Casino Tax Revenue Use
On the expenditure side of the budget, there is the issue of earmarking of gambling rev-
enue and its impact on government budgets. While there is no apparent research on this
topic in the literature to date for casinos, experience with lotteries is highly instructive.
Garrett (2001) has analyzed the issue of earmarked lottery revenue and found it to be
highly fungible. Just because the revenue from a particular source of gambling revenue,
including casino games, is dedicated for a particular spending purpose (problem gam-
bler assistance, public education, environmental protection, etc.) does not mean that
net spending on that budget category will rise. Borg and Mason (1990) also found that
earmarked lottery revenues do not generally beneﬁt the statutory recipients. Charles
Spindler (1995) has found that earmarked lottery funds for education in particular are
highly fungible.
3 Casino Taxation around the World
.............................................................................................................................................................................
Casino gambling has grown substantially in recent years in many parts of the world.
While an exhaustive review of the current state of global casino gaming and that growth

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30
casinos
is beyond the scope of this chapter, it is useful to highlight the forms of taxation used
in selected major global casino markets. For a useful overview of casinos around the
world, see Thompson 1998. The following section reviews casino taxation in the United
States, Singapore, and Macau.
3.1 United States
In the United States casino gambling was ﬁrst permitted legally in the State of Nevada
in 1931 and in New Jersey in 1976. Since those two pioneering states legalized casinos,
a number of other states have legalized casino gambling in various forms (riverboat,
land-based, and racetrack casinos). Over the very active period 1989–1996 nine states
legalized casinos (Colorado, Illinois, Indiana, Iowa, Louisiana, Michigan, Mississippi,
Missouri, and South Dakota). Native American casinos operate in 28 states on land
sovereignly controlled by the tribes, regardless of state laws regarding the legality of
casinos. William Evans and Julie Topoleski (2002) provide a useful overview of the
growth of Native American gaming, in particular. The American Gaming Associa-
tion (AGA) (2011) reports that in 2011 casinos were operating in 38 states, including
438 land-based or riverboat casinos in 15 states, 45 racetrack casinos in 12 states,
and 456 tribal casinos in 28 states. The AGA survey also indicates that casinos paid
a total of $34.6 billion in taxes in 2010, of which $7.59 billion was paid in direct
gaming taxes to state and local governments. For a comprehensive review of casino
taxation in the United States, see Anderson 2005. The most recent 50-state review of
casino gambling in the United States is provided by the National Conference of State
Legislatures (2010).
States apply wagering taxes to casinos along with other taxes on admissions and/or
license fees. The most important tax revenue source is the wagering tax. The tax base is
someformof adjustedgrossreceipts(AGR)withsomevariationintheprecisedeﬁnition
across states. In 2011 rates applied to the AGR base varied from a low of 4 percent to a
high of 50 percent. Rate structures are ﬂat in some states and graduated in others.
Other than wagering taxes, casinos in the United States may also be subject to other
forms of taxation. Riverboat casinos are typically required to charge an admission tax
of each gambler. Tax rates generally range from a low of $2 per admission to a high of
$5 per admission. In some states, the admissions tax varies with the casino’s patronage
or the size of the casino facility. In other cases, the admissions tax varies across local
government units, as proscribed by the state. Ranjana Madhusudhan (1996, 1999) was
the ﬁrst to document the emerging importance of all forms of gaming revenue among
state and local government units in the United States.
Other taxes and fees also may be charged, depending on state statutes. Riverboat
casino states, for example, typically impose a licensing fee based on the capacity of the
riverboat or a local government licensing fee based on AGR. States permitting land-
based casinos have more extensive systems of fees and taxes imposed by both state
and local government units. Nevada, home of Las Vegas, has a system of license fees

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the economics of casino taxation
31
imposed by county governments and a separate slot machine tax. New Jersey, home
of Atlantic City, imposes an annual license fee per facility and a slot machine fee. In
addition, New Jersey imposes taxes on goods complementary with casino services (such
as entertainment, food, hotel rooms, and beverages) provided at reduced or no prices to
casino patrons,a tax on gross revenues of companies operating multi-casino progressive
slot machines, and a tax on alternative investments applied to casino licenses.
3.2 Singapore
The rise of Singapore as a casino center is a recent phenomenon worthy of attention
and analysis. The Inland Revenue Authority of Singapore (2011) reports that casinos
are taxed by way of two integrated resorts (IRs): Marina Bay Sands and Resorts World
Sentosa. The tax applied to casinos is based on gross gaming revenue (GGR), deﬁned
as the difference between the “aggregate of the amount of net wins received on all
games conducted within the casino premises of the casino operator” and the goods
and services tax (GST) “chargeable to the casino from all gaming supplies made by the
casino operator.”
Net wins is computed as the total of all bets received by the casino operator on a
game minus the amount paid out by the casino operator as winnings on that game.
Two tax rates are applied to GGR, depending on the class of players from whom the
GGR was generated. A percent tax rate is applied to GGR obtained from premium
players, while a 15 percent tax rate is charged from all other players. Premium players
are deﬁned as those who maintain a deposit account of at least $100,000 prior to the
start of playing any game at the casino. As The Economist (2011) reports,“Thanks to low
taxes—roughly 17% compared with Macao’s 39%—Singapore’s casinos are fabulously
proﬁtable.”
3.3 Macau
Macau (also spelled Macao) is currently the largest casino gambling jurisdiction in the
world (Center for Gaming Research 2011). Once a Portuguese colony off the coast of
China,it is now a SpecialAdministrative Region (SAR) of the People’s Republic of China
(PRC), with exclusive rights to have casino gambling, which is illegal in the rest of the
PRC. The current gaming regime began in 2002 with an oligopoly of three gaming com-
panies and/or consortia serving the market. Gu and Pui Sun Tam (2011) indicate that
the sources of gaming proﬁts in Macau stem from (1) rising demand for gaming oppor-
tunities among Chinese consumers, (2) Macau’s monopoly position with regard to casi-
nos in China, and (3) the oligopolistic market structure of the casino industry in Macau.
Casinos are taxed using a two-part mechanism in Macau. A variable tax component
is based on the gross gaming revenue of the casino, which is taxed at a 35 percent
rate. In addition, there are other variable tax components based on GGR requiring 2

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32
casinos
and 3 percent contributions for social and economic purposes, respectively. A ﬁxed tax
component also is charged of casinos together with a charge per VIP table and other
tables and slot machines in the casino. Furthermore, gaming promoters are required to
pay taxes on the commissions they receive. In total, the variable tax rate on GGR can
be as high as 40 percent.
The UNLV Center for Gaming Research (2011) reports that the effective rate of
taxation is 38 to 39 percent. The total effective rate comprises a 35 percent base rate
plus a 1.6 percent contribution to the Macau foundation and a 1.4 percent contribution
required of SJM casinos (a division of the former monopoly entity permitted to operate
casinos in Macau, Societdade de Turismo e Diversões de Macao—STDM) or 2.4 percent
required of other casinos. Revenues generated from casinos in Macau were estimated
to have been over $15 billion in 2011, with the primary game source being baccarat
games (both from VIP players, the major source, and other players). Gu and Zhicheng
Gao (2006) have chronicled the rise of Macau as a major gaming center and provided a
critique of the development of the gaming industry in that location. Their major policy
recommendation is for diversiﬁcation of the casino industry, relying less on table games
and more on other services. Gu and Tam (2011) provide analysis of casino taxation in
Macau, with an emphasis on the structure of the industry and its implications for tax
policy. William Thompson and Christopher Stream (2006) provide lessons for Asian
policy makers based on the American experience with casinos.
4 Summary and Conclusions
.............................................................................................................................................................................
In this chapter I have examined the variety of ways that governments around the world
tax casino gambling and considered the economic effects of such taxation. The most
common form of casino taxation is a wagering tax whose base is the adjusted gross
receipts (AGR) collected by the casino. In some cases, governments also apply a casino
entry fee. Both efﬁciency and equity aspects of this form of taxation are considered in
theory in this chapter, and empirical evidence from the literature on the elasticities of
demand and supply has been presented to provide insights on the economic effects of
casino taxation. On the supply side, a regulatory environment that limits the supply of
casino games causes the supply to be relatively inelastic, making a casino tax reason-
ably efﬁcient and causing the incidence of the tax to fall primarily on the casino, not
gamblers. But, with the more recent proliferation of gaming opportunities in general,
and casinos in particular, the supply is becoming increasingly elastic, which may be
altering these initial indications. On the demand side, the evidence reviewed indicates
relatively price elastic behavior by gamblers, but as the industry matures this too may
be changing with some evidence indicating that casinos may be moving to the unitary
elastic point of their demand curve.
This review suggests ﬁve areas where more research is needed in order to inform
policy decisions regarding casinos. First, the apparent high price elasticities of demand

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the economics of casino taxation
33
may limit the effectiveness of additional gambling taxes as a source of revenue for
governments. If casinos are operating at the unitary elastic point on the demand any
taxrateincreasethatraisesthepricewillreducetaxrevenue. If governmentshavealready
set tax rates on casinos to generate maximal revenues any further rate increases will
reduce revenues. More research is required to know deﬁnitively whether the maturing
of the casino industry in various countries together with the regulatory and taxing
environment has led to both maximal casino and tax revenue. Second, the evidence of
relatively high price elasticities points to the availability of illegal gambling alternatives.
With that, further tax increases may simply drive gambling activity out of the legal
casino sector into the illegal gambling sector. Further research is needed on the general
equilibrium effects of taxation in the legal casino industry. Third, the issue of optimal
casino taxation is deserving of further attention. To date, efforts to consider optimal
gaming taxation have been limited primarily to lottery games. Fourth, the gaming
taxation literature to date has not taken a second-best approach to estimating the net
excess burden of taxation, recognizing that a casino tax may be adopted in the presence
of existing gaming taxes (e.g. lottery tax). Fifth, viewing a casino tax as a Pigouvian tax
to correct for externalities, more research is needed to accurately estimate the size of
the externalities involved and design optimal corrective taxes.
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chapter 3
........................................................................................................
THE ELASTICITY OF
CASINO GAMBLING
........................................................................................................
mark w. nichols and mehmet serkan tosun
Introduction
.............................................................................................................................................................................
Casino gambling, once an industry dominated by Las Vegas, Nevada, is now available
in many developed countries around the world. Indicative of this transformation is
the recent surpassing of Las Vegas as the world’s largest gambling market, measured by
total gross revenue, by Macau (Macao). Singapore, which ﬁrst opened casinos in 2006,
is the world’s third largest market, just behind Las Vegas.
A primary factor driving the expansion of gambling is its ability to raise tax revenue.
While casino gambling is now legal in many parts of the world, it is frequently restricted
tocertainlocationsandaﬁxednumberof licenses. Therestrictiononcasinosisgenerally
justiﬁed on grounds of limiting the public’s exposure to gambling, but it also generates
economic rents due to the associated market power. Thus, as with any industry where
competition is restricted, prices may higher than those that exist in a more competitive
market.
However, while competition within a particular location may be restricted, competi-
tion among locations has grown more intensive as gambling has expanded. Indeed, one
justiﬁcation for casino legalization and expansion is competition from nearby locations
as jurisdictions attempt to attract gamblers from out of the region or prevent their own
citizens from travelling elsewhere to gamble.
The efﬁcacy of casino gambling, in terms of generating tax revenue, depends on
many factors, including the size of the market, market structure and the competitive
environment, quality of the product offered, and the industry’s growth potential over
time. One commonality that impacts all of these factors is the price elasticity of demand.
Size, market structure, and quality of the product all will impact this elasticity Price
elasticity will inﬂuence a jurisdiction’s ability to generate tax revenue by changing tax

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## Page 59

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casinos
rates. Similarly, the long-term growth of the industry and its ability to contribute tax
revenue over time will depend on its growth relative to the economy as a whole, that is,
the income elasticity of demand. Of course the behavior of individual gamblers, the size
of consumer surplus, and the impact of, and effect on, competing forms of gambling
also will depend on these factors. A knowledge of the price, cross, and income elasticity
of demand for gambling therefore has important implications for the debate about the
economic and social impact of casinos.
This review examines the price, cross, and income elasticity of demand for casino
gambling. The focus is speciﬁcally on casino gambling as opposed to other forms of
gambling, such as lottery or pari-mutuel wagering. Nevertheless, in the case of price
elasticity, comparisons with other forms of gambling are made to provide a context for
the reader. Similarly, in the case of income elasticity comparisons are made between
casino revenue versus income and sales tax revenue. As will become clear, despite the
importance of elasticity to our knowledge about the revenue generating capacity of
casino gambling, gambler behavior, and casino gambling’s impact on other forms of
gambling and vice versa, very few empirical studies have calculated elasticity estimates
for casino gambling. One notable reason for this is the unavailability of accurate data
on the quantity and price of casino gambling. Reasons for this and existing studies are
reviewed here and recommendations for future research are made.
Price Elasticity of Demand
.............................................................................................................................................................................
Walkintoanyretaillocationandpricesarenearlyalwayspublishedoravailablebyasking
a sales clerk. Pay that price and you will have purchased the product. Walk into any
casino and what you will see is denominations reported on electronic gaming devices
(EGD) such as slot, fruit, or video poker machines equal to, for example, $1,25c/, or £1.
Table games may similarly provide information on minimum and maximum allowable
wagers. Pay the monetary unit necessary to play the EGD or bet on a number or color in
roulette and you may walk away with nothing or more than your initial wager. Clearly,
then, the information posted on a slot machine or table game is not the price. So what
is the price of casino gambling?
The Price of Casino Gambling
The price of casino gambling is known as the house advantage (Eadington 1999) or
equivalently as one minus the expected value of a wager (Gulley and Scott 1993; Forest,
Gulley, and Simmons 2000; Paton, Siegel, and Vaughan Williams 2004). This is what
a customer can expect to lose on average over the long run. The house advantage can
vary by numerous factors, including the type of game, player skill, rules of the game,

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## Page 60

the elasticity of casino gambling
39
and type of wager being made. The house advantage can vary also between casinos or
even between games within a particular casino. Ask a casino dealer the house advantage
for placing a numbers bet on roulette and the dealer may tell you it is 2.70 percent for
single zero and 5.26 percent for double zero. Ask the same question at a blackjack table
and you will likely be told it depends on your knowledge of basic strategy or, less likely,
your ability to count cards. Ask what the house advantage is for a particular EGD and
it is almost guaranteed that the employee will not know or be unwilling to tell you.
Many casino games are what are known as ﬁxed-odds or pure chance games, where
both the outcome and payoff are predetermined or beyond the control of the gambler.
Slot machines, one of the most popular EGDs, are an excellent and popular form of
ﬁxed-odds games. Once the spin or play button is pushed a computer generates a ran-
dom number that determines the outcome, which in turn corresponds to a ﬁxed payoff
to the gambler. This cannot be manipulated by the gambler and neither can the payout
percentage programed into the computer chip. Roulette and craps, where the outcome
depends on the spin of a wheel or roll of the dice and payoffs are predetermined, also
are ﬁxed-odds games.
Games such as blackjack and EGDs such as video poker are a mix of ﬁxed-odds or
pure chance and skill. In these instances players can alter the outcome or change the
amount of their wagers as the game progresses. For example, a player dealt two eights
in blackjack could keep that hand and stay, take another card, or split the hand, thereby
playing two hands and placing a wager on both. Actions taken by the gambler in this
case will inﬂuence what the player can expect to lose in the long run and hence the price
of the game.
Complicating matters further is the fact that the house advantage, while frequently
unknown, is almost certain to differ from the amount gamblers lose in the short run.
The total amount wagered is known as handle or turnover.1 The total amount of money
lost by the player, or alternatively won by the casino, is known as win or gross revenue.
Win as a percentage of handle is frequently used as a measure of the price of gambling,
particularly for EGDs, but clearly may not equal the house advantage. Complicating
matters even further is the fact that handle is unknown for table games. Rather, what
is known is the total amount of money exchanged for chips at the table, known in the
industry as drop. For example, if a gambler purchases $20 worth of chips at a black jack
table, makes and loses four wagers of $5 and decides to stop playing, the drop from that
gambler will equal $20, as will handle. If however, the gambler wins a few hands and it
takes, say, eight hands to lose the initial $20, drop will still equal $20, but handle will
have been $40 (8 hands × $5 bet per hand). Thus, drop will differ from handle, and
clearly hold percentage, deﬁned as the percent of the drop won by the casino, also will
differ from the house advantage.
Table 3.1, taken from Eadington (1999), demonstrates the house advantage for
selected games as well as the standard deviation from that advantage after 1,000 wagers.
For example, after 1,000 number wagers on European roulette a player, on average,
should be down 27 units (0.027∗1000), but the standard deviation is 182.1. Thus, after
1,000 wagers there is a 95 percent probability that the player will be somewhere between

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40
casinos
391 units down and 337 units up (−27+/−2∗182.1). For a typical slot machine hold-
ing 5 percent, a player, on average, would be down 50 units after 100 wagers but might
be as many as 720 units down or 670 units ahead.
When measuring price in a casino, the researcher is unlikely to have data on the
true price. The price of EGDs, determined by a computer chip, is unknown to both
researcher and gambler. Similarly, the price of such games as blackjack varies by player
skill and rules of the game. What generally is available to the researcher is information
on total win (revenue won by the casino or lost by the gambler) and handle (total
wagers made), although for table games only drop rather than handle is known. Using
this information, the researcher is able to estimate price for game j at time t using the
following simple formula:
Pricej,t = Revenuej,t/Handlej,t
(3.1)
For EGDs the data on both revenue and handle will be accurate as these are accounted
for by computer. For table games, as demonstrated in the example above, it is unlikely
that handle, which is a function of the number of bets made and the amount wagered
during each of those bets, will be known. Moreover, as demonstrated in table 3.1, there
is signiﬁcant variation around the true price (house advantage) in the short run. While
in the long run price should converge to the house advantage, at any point in time
the estimation of price is potentially quite noisy. Moreover, it is difﬁcult to determine
Table 3.1 Statistical Properties of Select Casino Games and Devices (1 Unit Wager)
Game
House
Advantaged
Standard Deviation
(1 Wager)d
Standard Deviation
(1,000 Wagers)d
Standard Deviation
(House Advantage
after 1,000 Wagers)d
Crapsa
1.41%
1.0
31.6
3.16%
Blackjackb
0.50%
1.1
34.8
3.48%
Roulette (American)c
5.26%
5.7
179.8
17.98%
Roulette (European)c
2.70%
5.8
182.1
18.21%
Baccarata
1.25%
1.0
31.6
3.16%
Pai Gow Pokerb
2.50%
1.0
31.6
3.16%
Video Pokerb,e
2%
2.3
73.7
7.37%
Slot Machinese
5%
10.6
335.2
33.52%
Keno
28%
42.3
1336.3
133.63%
a Standard wager.
b Assuming player plays optimal strategy with typical house rules.
c Single number wager.
d Approximate.
e Typical values. Slot machine and video poker house advantages vary by many factors, including
denomination, location, and competition, among others.
Source: Eadington (1999).

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## Page 62

the elasticity of casino gambling
41
whether changes in price over time are due to changes in the house advantage due to
new computer chips, new games with different house advantages, differences in player
luck, changes in the competitive environment, or variation in the types of games played
by gamblers. Higher denomination games generally have lower hold percentages, so if
more wagers were made on high denomination machines in one time period relative
to another, price may appear lower, even though no changes in actual price took place.
In summary, unlike most other products or services, the posted nominal denomina-
tion of the game is not the price of that game. Rather, the price is equal to the house
advantage. For some games, particularly EGDs, this price is unknown to the gambler
or researcher. For other games, blackjack and video poker, for example, it will vary
with player skill. Estimates of the price are nevertheless available using equation (3.1)
above. However, it is only an estimate and will vary over time for reasons other than
changes in the house advantage. Thus the seemingly simple issue of the price elasticity
of casino gambling is in practice rather difﬁcult in large part because price is measured
noisily. In cases where it is known, for example, roulette, price may not vary over time
or the quantity of bets, that is, handle, is likely unknown. Nevertheless, several studies
have estimated the price elasticity of EGDs using the price approximation given by
equation (3.1). Those are now reviewed.
Methodology and Estimates of Price Elasticity
There are relatively few studies that estimate the price elasticity of demand for casino
gambling, in no small part due to limitations on the availability of price and quantity
data described above. The few studies that have estimated the price elasticity of demand
have generally limited their investigation to EGDs. To estimate elasticity, variations on
the following simple demand equation are estimated:
Qj,t = β0 + β1Pj,t + β2INCr,t +

βkPk,t +

θcXc,t + εj,t
(3.2)
where Qj,t represents the quantity of gambling, usually handle, or the natural log of
handle, for unit j at time t. This could be estimated for an individual game or casino,
or such geographic areas as states or countries. Pj,t is the price, generally measured as
win percentage, or the natural log of win percentage, as given in equation (3.1) for unit
j at time t. INCr,t is a measure of income at time t corresponding to the country, state,
or market area where the casino is located. Pk,t is price of alternative goods and could
include, for example, the price of lottery games, pari-mutuel wagering, or even alcohol
and cigarettes, which often are thought of as complements to casino gambling. Xc,t
is a vector of various other characteristics that researchers frequently include, such as
variablestoaccountforoperatingtimes,regulatorystructure,competitiveenvironment,
and so on.
Duetothedifﬁcultyobtainingpricedatadescribedabove,thereisapaucityof studies,
particularly academically refereed papers, that examine the price elasticity of demand.

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42
casinos
Table 3.2 Price Elasticity Estimates for Various Forms of Gambling
Author(s)
Location(s)
Elasticity Estimate(s)
Casino (EGDs)
Thalheimer and Ali 2003
Iowa, Illinois, Missouri
(USA)
−1.5 (1991); −0.90 (1998)
Landers 2008
Iowa, Illinois, Missouri,
Indiana (USA)
−0.75 to −0.87
BERL 1997
New Zealand
−0.85
Swan 1992
New South Wales
(Australia)
−1.9
Lottery
Gulley and Scott 1993
Kentucky, Massachusetts,
Ohio (USA)
−1.15, −1.92, −1.20
Farrell et al. 1999
United Kingdom
−1.05 (short run); −1.55 (long run)
Forrest et al. 2000
United Kingdom
−1.03
Beenstock and Haitovsky 2001
Israel
−0.65
Lin and Lai 2006
Taiwan
−0.142
Yu 2008
Canada
−0.672
Horse Racing
Suits 1979
Nevada (USA)
−1.59
Morgan and Vasche 1982
California (USA)
−1.30
Thalhiemerand Ali 1995
Ohio, Kentucky (USA)
−2.85, −3.06, −3.09
Betting Shops
Paton et al. 2004
United Kingdom
−1.59, −1.62
Table 3.2 provides a summary of the few papers that exist, including some prepared
by private consultants. Richard Thalheimer and Mukhtar Ali (2003) were among the
ﬁrst to provide estimates of the price elasticity of demand. Due to the unavailability
of handle for table games, Thalheimer and Ali restricted their analysis to slot machine
handle. They examined the slot machine demand for riverboat casinos in three states
in the United States, Iowa, Illinois, and Missouri, for the period 1991–1998. In addition
to price (win percent), they also included per capita income, number of slot machines,
number of table games, days of operation, government restrictions (betting limits, loss
limits, and boarding restrictions2), and market conditions (access to customers and
customer access to competitors).
Thalheimer and Ali reported that price decreased over their sample period from
0.4 percent in 1991 to 6.1 percent in 1998. At the sample average of 7 percent, the price
elasticity of demand was found to be unitary. Given the reduction in price over time,
they found that price became less elastic over their sample period, from −1.5 in 1991
to −0.9 in 1998.
Jim Landers (2008) employed a similar methodology to estimate a ﬁxed effects panel
model for 50 casinos operating in Illinois, Indiana, Iowa, and Missouri between 1991

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## Page 64

the elasticity of casino gambling
43
and 2005. As with Thalheimer and Ali 2003, handle was measured as per capita slot
machine handle, price as win percent. Landers also included data on per capita income,
days of operation, number of table games, number of slot machines, loss limits, and
cruising requirements.
Win percentage in Landers’s sample averaged 6.99 percent, ranging from a low of
4.71 percent to a high of 12. percent. Estimating numerous double log models, Landers
found price elasticity of demand ranging from −0.75 to −0.87. Neither estimate, how-
ever, is statistically different from unitary elasticity at the 10 percent level. Similarly, by
including lags of price, Landers found a long-run elasticity of −1.0. Unlike Thalheimer
and Ali, Landers, interacting the price variable with a time trend, did not ﬁnd that
elasticity changes over time.
Few others have estimated the price elasticity of demand. Business and Economic
Research Limited (BERL) (1997) derived a price elasticity estimate of −0.85 for elec-
tronic gaming machines and casino gambling in New Zealand, while Peter Swan (1993)
estimated a price elasticity of −1.7 for poker machines and −1.9 for casino gambling
in New South Wales, Australia.
Generally, the above studies suggest that the demand for EGDs is either unitary
or slightly inelastic. Thalheimer and Ali found demand to be slightly elastic initially
but later falling to slightly inelastic. This is plausible as competition in those states
increased over their sample period and casinos reduced their price, as demonstrated by
John Navin and Timothy Sullivan (2007), in the St. Louis, Missouri metropolitan area.
Moreover, the fact that consumers are not aware of the true price and frequently are
loyal to certain products or casinos also supports a slightly inelastic demand (Paton,
Siegel, and Vaughan Williams 2003). Indeed, most casinos have loyalty programs that
reward gamblers with comps, generally in the form of free entertainment, food, or
lodging. In addition to creating loyalty, this also may reduce the perceived price for the
gambler.
In addition to the problems due to the unavailability and uncertainty of price and
quantity of casino gambling, there are other problems that potentially arise with esti-
mation of price elasticity. Price in equation (3.2) above, as with any demand equation,
is endogenous, leading to potentially biased estimates of its coefﬁcient. Moreover,
given the deﬁnition of price in equation (3.1), if handle is measured inaccurately,
equation (3.2) will also suffer from division bias (Borjas 1980).
Another obstacle to obtaining accurate estimates of the price elasticity of demand is
the aggregate nature of the data collected. Handle and price are generally averages across
multiple casinos in different jurisdictions with different competitive environments.
Economic theory predicts that a casino with a linear demand curve operating as a
local monopoly will have higher prices and elasticity than will casinos operating in
more competitive environments. Aggregation hides this variation. Moreover, handle
and price are aggregated across machines of different denominations. The elasticity of
demand for a $1 machine may be different from that for a $5 machine. One solution,
of course, is to analyze individual markets or players, making more precise estimates
possible.

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44
casinos
Access to individual data, however, is difﬁcult due to its proprietary nature. Sridhar
Narayanan and Puneet Manchanda (2008) conducted the only study of which we
are aware that examines individual gambling behavior using data from a U.S. casino
operating in the southwestern United States.3 The data are from the casino operator’s
player reward program, and Narayanan and Manchanda have data for 198,223 gamblers
over the period January 2004 through December 2005. Using a random sample of 2,000
gamblers comprising 15,632 gambling trips, Narayanan and Manchanda have a very
richdatasetconsistingof dataontotaltimespentgambling,ahistoryof allwagersmade,
cumulative win, as well as comps awarded by the casino. However, while Narayanan and
Manchanda provide elasticity estimates with respect to comps (0.14), last bet (−0.28),
last loss (0.133), last win (−0.020), cumulative loss (−0.245), and cumulative win
(0.030), they do not provide any estimates of price elasticity.
Cross-Price Elasticity Studies
.............................................................................................................................................................................
Around the world, governments have turned to various forms of gambling as a means of
increasing tax revenue, including lotteries, casino gambling, and to a lesser extent pari-
mutuel wagering. However, does the introduction of one form of gambling substitute
for the other? Governments need to know if this is the case if they are going to maximize
tax revenue.
In the United States, pari-mutuel wagering, both horse and dog racing, has experi-
enced a prolonged and signiﬁcant decline. One response has been to allow slot machines
or video lottery terminals at racetracks. These racinos, as they are commonly known,
are intended, in part, to increase demand for racing by using revenue from the casino to
subsidize purses, under the assumption that larger purses should attract better horses
and more wagers.
Thalheimer (1998, 2008) estimated demand equations for pari-mutuel gambling
and found that video lottery terminals are strong substitutes for pari-mutuel wagering.
An increase in the number of video lottery terminals is associated with a substantial
reduction in pari-mutuel handle. For example, relaxing government restrictions on
the number, location, and maximum allowable bets on video lottery terminals was
estimated to reduce pari-mutuel handle in the long run by 49 percent at Mountaineer
Park in West Virginia. Moreover, both Thalheimer (2008) and Ali and Thalheimer
(2002) found low elasticities of handle with respect to purse size, 0.08 and 0.15, respec-
tively. Thus even if EGDs enable larger purses, the impact on total wagering handle
is small.4
Studies on the degree of substitution between lottery and casino gambling are more
numerous and varied but generally ﬁnd casino gambling and lotteries to be substitute
forms of gambling. For example, Donald Elliott and John Navin (2002) found that
for every additional dollar of per capita revenue from riverboat gambling, state lottery

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## Page 66

the elasticity of casino gambling
45
per capita revenues decline by $1.38. Based on average tax rates, this equates to a loss
of $0.83 in net lottery revenue. Stephen Fink and Jonathan Rork (2003) also found a
substitution effect between lottery and casino gambling, with each additional dollar
of casino gambling tax revenue reducing net lottery proceeds by $0.56. On the other
hand, Mehmet Tosun and Mark Skidmore (2004) found a complementarity between
video lottery terminals and lottery games in West Virginia border counties. However,
in the interior West Virginia counties, video lottery was still a substitute for lottery
games.
Donald Siegel and Gary Anders (2001) found that a 10 percent increase in slot
machines at Indian casinos is associated with a 3.8 percent decline in lottery revenue
and a 4.2 percent decline in lotto revenue, with seasonally adjusted ﬁgures equaling
2.8 percent and 3.7 percent, respectively. David Giacopassi, Mark Nichols, and Grant
Stitt (2006) found that lottery play in Shelby County (Memphis), Tennessee, which is
adjacent to a large number of casinos in Tunica County, Mississippi, is approximately
$10 lower per month per eligible gambler (over 18 years of age) relative to other
counties in Tennessee. Craig Landry and Michael Price (2007) also found that casino
gambling is a substitute for lottery, with states that earmark lottery revenues seeing a
3 percent reduction in per capita lottery expenditures due to casino legalization versus
a 17 percent reduction for general fund lottery states.
The substitutability of different forms of gambling has also been done within casinos.
Thalheimer and Ali (2008a) found that an increased number of table games on river-
boat casinos reduce slot machine revenues but that total casino revenue increases. Ina
Levitzky, Djeto Assane, and William Robinson (2000), in contrast, estimated a model
of gambling revenue in Las Vegas and found that the introduction of more table games
reduces total gambling revenue.
Recently the issues of smoking and alcohol consumption and their complementar-
ity to casino gambling have been explored. Chad Cotti and Douglas Walker (2010),
using data from all counties in the United States, found that the introduction of casino
gambling increases the number of alcohol-related fatal car crashes, but this increase is
restricted to rural counties, with more urban counties experiencing a decrease. Thal-
heimer and Ali (2008b) found that the smoking ban implemented in Delaware resulted
in a 15.9 percent reduction in handle. Similarly, Thomas Garrett and Michael Pakko
(2010) showed that the ban on smoking in casinos in Illinois reduced gambling revenue
by 20 percent and attendance by 10 percent, suggesting that gamblers made both fewer
visits and gambled less.
The above studies demonstrate that casino gambling and lottery as well as casino
gambling and pari-mutuel wagering are substitutes. Smoking and alcohol consump-
tion, in contrast, are complements to casino gambling. None of the above studies,
however, provide traditional cross-price elasticity estimates. Of the studies reviewed
above, only Thalheimer and Ali 2008b used handle as the dependent variable. All
others analyzed casino revenue. No studies examined changes in the price of lottery,
pari-mutuel wagering, cigarettes, or alcohol that would yield traditional cross-price
elasticity estimates.

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casinos
Income Elasticity Studies
.............................................................................................................................................................................
While there is a small literature on the income elasticity of casino gambling, those
studies follow a larger literature on the income elasticity of state and local taxes. One
of the ﬁrst such papers, by Harold Groves and Harry Kahn (1952), used double-
log OLS speciﬁcation to estimate long-run income elasticity of various state taxes
using annual tax revenue data. Thomas Cargill and William Eadington (1978) and
David Babbel and Kim Staking (1983) followed this by examining income elasticity of
gambling, although only Cargill and Eadington examined casino gambling speciﬁcally
using California personal income to show the responsiveness of gambling revenue
in Nevada to regional income changes.5 In addition, Thalheimer and Ali (2003) and
Landers (2008) examined how casino demand has responded to changes in market and
state income in the riverboat states of Iowa, Illinois, Missouri, and Indiana.
More recent studies of the income elasticity of state taxes distinguish between growth
and variability of tax bases by separately estimating long-run and short-run elasticities.6
Nichols and Tosun (2008) built on this broader literature to estimate the short- and
long-run income elasticities of casino gambling but made several improvements and
contributions. First, they used quarterly data, as in Fox and Campbell (1984), but
expanded the analysis to a number of states (Colorado, Connecticut, Illinois, Indiana,
Iowa, Louisiana, Mississippi, Missouri, Nevada, New Jersey, and South Dakota) instead
of just one. Second, they used data on the actual tax base for the ﬁrst time in the
literature, thus removing the potential error inherent in previous studies that used
proxies. Third, they added a new estimate of the income elasticity of gross casino
gambling revenues to the list of past elasticity estimates on such state taxes as the
individual income tax, general sales tax, corporate income tax, motor fuel tax, tobacco
tax, and alcohol tax. Finally, they also examined the responsiveness of the tax base to
changes in regional income in the vicinity of the state and changes in national income.
This is important because casino gambling revenues might be quite sensitive to visitors
from the state’s region or even from the entire nation, as in the case of Nevada.
Methodology and Income Elasticity Estimates
Long-Run Elasticity
The basic model used to estimate the long-run elasticity of demand is given by
Rj,t = β0 + β1INCj,t + εj,t,
(3.3)
where Rj,tis the natural log of gross casino gambling revenue for country or state
j at time t and INCj,t is a measure of income, such as the natural log of personal
income, for country or state j at time t. The coefﬁcient on INCj,t provides the income
elasticity of demand, thereby predicting the long-run responsiveness of the tax base to

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## Page 68

the elasticity of casino gambling
47
income. Nichols and Tosun (2008) further used the dynamic OLS (DOLS) estimator
with heteroskedasticity and autocorrelation consistent (HAC) standard errors, and
estimated the following equation with Newey-West (1987) standard errors:
Rj,t = β0 + β1INCj,t + β2SLOTSj,t−2 + β3TABLESj,t−2 + β4St +
n

t=−m
	INCj,t + εj,t,
(3.4)
where SLOTSj,t−2 is the natural log of the number of slot machines in state j at time
t −2, that is, lagged two quarters; TABLESj,t−2 is the natural log of the number of tables
games in state j at time t −2; St represents seasonal dummies for spring, summer, and
fall to account for potential seasonal variation in gambling revenue; and 	INCj,t is
the change in the natural log of income with the number of lags and leads determined
using the Bayesian Information Criterion (Stock and Watson 2007). SLOTSj,t−2 and
TABLESj,t−2 are included to ensure that the impacts on the tax base from relaxing
regulatory constraints, such as a new or expanded casino, or a change in the mix of
slots versus tables, are not attributed to a change in income.
Short-Run Elasticity
Nichols and Tosun (2008) followed Bruce, Fox, and Tuttle (2006) to derive short-run
elasticity estimates using an Error-Correction Model (ECM) allowing for asymmet-
ric income elasticity and adjustment to equilibrium. In the short-run, changes to
the tax base may come from changes in income or an adjustment toward the long-
run co-integrating relationship derived from equation (3.4) above, both of which
may differ depending on whether the actual tax base is above or below the long-
run value. Hence they estimated short-run elasticities estimated using the following
model:
	Rj,t = β0 + β1	INCj,t + β2	SLOTSj,t−2 + β3	TABLESj,t−2 + β4St
+ β5(Dj,t ∗	INCj,t) + β6εj,t−1 + β7(Dj,t−1∗εj,t−1) + μj,t
(3.5)
where variables are described as above and Dj,t = 1 if εj,t > 0 in equation (3.4). εj,t−1 is
the error correction term and β6 captures the adjustment in period t to the disequilib-
rium in period t −1, that is, the difference between the last period’s actual tax base and
the long-run co-integrating relationship predicted by equation (3.4). The inclusion of
the interaction term, Dj,t−1∗εj,t−1, allows for this adjustment to differ depending on
whether the actual tax base is above or below its long-run value.
Cargill and Eadington (1978) analyzed seasonally adjusted data for the period 1960–
1974 and found that the long-run income elasticity of gross gambling revenue is fairly
elastic with signiﬁcant variation across three regions in Nevada. The highest is in the
Las Vegas region (1.75), followed by the Lake Tahoe (1.25) and the Reno-Sparks (1.05)

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## Page 69

Table 3.3 Long-Run State, Regional, and National Income Elasticity Estimates for
Casino Revenue, Short-Run Regional Income Elasticity and Long-Run State Income
Elasticity for Sales and Income Tax
State
Income
Regional
Income
National
Income
Short-Run
Regional
Elasticity
Adjustment
to Long-Run
Equilibrium
Sales Taxa Income Taxa
Destination Resorts
Nevada
(1983:q2:2006:q2)
0.30∗∗∗
(0.035)
0.44∗∗∗
(0.075)
0.50∗∗∗
(0.080)
0.56
(0.42)
−0.46∗∗∗
(0.10)
0.78∗∗
1.03∗∗∗
New Jersey
(1985:q1:2006:q2)
0.38∗∗∗
(0.05)
0.46∗∗∗
(0.06)
0.35∗∗∗
(0.05)
0.76∗∗
(0.32)
−0.41∗∗∗
(0.09)
1.05∗∗
2.01∗∗
Mississippi
(1994:q4–2005:q2)
2.05∗∗∗
(0.57)
1.15∗∗∗
(0.40)
1.53∗∗∗
(0.35)
−0.64
(1.14)
−0.28∗∗
(0.11)
0.48∗∗
1.91∗∗
Riverboat Casinos
Iowa
(1995:q3–2006:q2)
1.28∗∗∗
(0.36)
1.49∗∗∗
(0.20)
1.05∗∗∗
(0.21)
2.92∗∗∗
(0.66)
−0.97∗∗∗
(0.04)
0.37∗∗
2.35∗∗
Illinois
(1995:q3–2006:q2)
1.72∗∗
(0.83)
2.10∗∗∗
(0.70)
1.85∗∗∗
(0.66)
0.66
(1.11)
−0.15∗
(0.07)
0.87∗∗
1.56∗∗
Missouri
(1995:q1–2006:q2)
2.37∗∗∗
(0.33)
2.32∗∗∗
(0.26)
1.85∗∗∗
(0.23)
1.19
(0.81)
−0.34∗∗
(0.13)
0.64∗∗
2.29∗∗
Louisiana
(1995:q3–2005:q2)
1.36∗∗∗
(0.17)
0.66∗∗
(0.25)
0.69∗∗
(0.29)
2.04
(2.40)
−0.54
(0.44)
0.51∗∗
2.27∗∗
Indiana
(1997:q1–2006:q2)
0.53
(0.47)
0.02
(0.66)
−0.30
(0.26)
1.71∗∗
(0.92)
−0.67∗∗∗
(0.15)
0.47∗∗∗
2.43∗∗
Mining Towns
Colorado
(1993:q2–2006:q2)
1.27∗∗∗
(0.16)
1.42∗∗∗
(0.22)
1.58∗∗∗
(0.32)
1.01∗∗
(0.57)
−0.33∗∗∗
(0.09)
0.78∗∗
1.26∗∗
South Dakota
(1990:q2–2006:q2)
1.25∗∗∗
(0.14)
1.43∗∗∗
(0.19)
1.31∗∗∗
(0.15)
0.22
(1.03)
−0.47∗∗∗
(0.10)
1.15∗∗
1.03∗∗∗
Indian Casinos
Connecticut
(1995:q3–2006:q2)
1.36∗∗∗
(0.25)
1.28∗∗∗
(0.24)
0.96∗∗
(0.43)
1.18
(0.87)
−0.20
(0.12)
1.24∗∗
0.96∗∗∗
(1) Fixed Effects
(AR1, no slots or
table games)
1.18∗∗∗
(0.17)
(2) Fixed Effects
(AR1, with slots
& table games)
0.76∗∗∗
(0.23)
Note: Newey-West standard errors in parentheses. All time series regressions, except for Louisiana and New Jersey,
include number of slot machines and table games as control variables. For Louisiana and New Jersey data on the
number of slot machines were not available. For those states signiﬁcant regulatory changes are controlled with
dummy variables. Data on table games were not available for Colorado and Connecticut.
a Income and sales tax elasticities are taken from Tuttle, Bruce, Fox, and Tuttle 2006 and Holcombe and Sobel
1997. Elasticities from Holcombe and Sobel 1997 are used for Indiana (sales tax) and Nevada, South Dakota, and
Connecticut (income tax).
b Regression (1) does not include number of slots or number of table games and is run with data on ten states
excluding only Nevada. Regression (2) includes number of slots and number of table games but is run with data
on six states, excluding New Jersey, Colorado, Connecticut, and Louisiana, for which there no slots and/or table
games data are available. In regression (2) we used number of slots and table games lagged two quarters to be
consistent with time series regressions.
∗, ∗∗, and ∗∗∗represent signiﬁcance from zero at the 10, 5, and 1% level, respectively.
Source: Nichols and Tosun (2008).

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## Page 70

the elasticity of casino gambling
49
regions. Thalheimer and Ali (2003) did not explicitly estimate income elasticity but
noted that the percentage change in handle decreases up to real per capita income of
$16,500 (which is greater than the mean of $15,000), then increases. They also note
that a greater proportion of income is wagered at both low and high levels of income
relative to the middle. Landers (2008) found elasticity estimates ranging from 1.4 to
1.9, although none were statistically different from unity.
Long-run and short-run income elasticity estimates from Nichols and Tosun 2008
are shown in table 3.3. Results for states are grouped under four types of industry
structures for casinos: destination resort casinos (Nevada, New Jersey, and Mississippi),
riverboat casinos (Iowa, Illinois, Missouri, Louisiana, and Indiana), mining town casi-
nos (Colorado and South Dakota), and Indian casinos (Connecticut). The table also
presents separate state elasticity estimates based on time series regressions and over-
all long-run elasticity estimates from panel regressions. Finally, the long-run income
elasticity estimates for casino gambling are compared to long-run income elasticity esti-
mates for two major state revenue sources, the personal income tax and the sales tax.
The overall long-run income elasticity estimates from the ﬁxed effects regressions are
1.18 and 0.76 depending on whether slots and tables are included as control variables in
equation (3.4). Both estimates are statistically equal to unity and are consistent with the
earlier results of Cargill and Eadington (1978) and Landers (2008). However, estimates
do vary substantially across and within market structures. The main results can be sum-
marized as follows: (1) long-run income elasticities for casino gambling are relatively
high and more similar to the ones for the state personal income tax; (2) more mature
casino markets, such as Nevada and New Jersey, show signiﬁcantly lower long-run elas-
ticity estimates, which could indicate lower growth potential as casino programs age;
(3) Nevada’s casino gambling is more sensitive to national income changes, whereas
casino gambling in other states responds more to state and regional income changes; (4)
short-run income elasticity estimates are generally lower than long-run estimates, but
those estimates are signiﬁcantly higher when they are separated into below long-run
equilibrium and above long-run equilibrium of casino gambling revenue; and (5) there
appears to be a fairly rapid adjustment to long-run equilibrium of casino gambling
revenue.
Conclusions
.............................................................................................................................................................................
Casino gambling, much like the lottery, has greatly expanded over the last two decades.
This trend has been driven, in large part, by governments seeking new sources of tax
revenue. Gambling is somewhat unique in that governments generally tax a portion of
revenue rather than proﬁt. Therefore, governments would clearly prefer that operators
maximize revenue, a goal that may conﬂict with proﬁt maximization. Similarly, gov-
ernments prefer a stable and growing tax base over time. To understand whether these

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## Page 71

50
casinos
objectives can be achieved, policy makers require accurate estimates of the price and
income elasticity of casino gambling.
Despite the important policy implications of these ﬁgures, there are few academic
studies that provide estimates of the elasticity of casino gambling. The estimates of
price elasticity from Thalheimer and Ali (2003) and Landers (2008) reviewed above,
in general converge on unity, suggesting that casinos are, on average, maximizing
revenue. While excellently done, both studies derive their estimates from riverboat
casino states in the United States. Do these estimates generalize to other jurisdictions?
Are there signiﬁcant differences in price elasticity between government owned (e.g.,
Canada, Holland) and privately owned casinos? How do elasticity estimates vary by
type of game, game denomination, competitive environment, and industry structure
(e.g., tourist oriented versus locals oriented)? How do they vary by speciﬁc income and
demographic groups? What are the consequences of continued casino expansion and
the expansion of on-line gambling?
Similarly,the income elasticity estimates reviewed here also tend to be unity or higher,
except for the mature markets of Nevada (casinos legalized in 1931) and Atlantic City,
New Jersey (casinos legalized in 1976 and operating in 1978), where the estimates are
signiﬁcantly lower. Does the growth in casino revenue slow as markets mature? What is
the potential for revenue growth in the face of new competition from other jurisdictions
and the Internet? How does casino revenue behave over the business cycle, and how has
it responded to the most recent recession, the most severe recession since many casinos
have been legalized?
These are several important policy questions that academics should explore. Par-
ticularly interesting would be micro-oriented studies that analyze data on individual
gamblers. This could best be accomplished by acquiring data from player loyalty pro-
grams offered by many casinos. While anonymity would have to be preserved, such
data would allow differences in elasticity by volume of play, type of game, gender, and
ethnicity, to name only a few, to be estimated. Alternatively, researchers may be able
to generate data by conducting experiments. This would be a very effective way to
overcome the unavailability of handle data for table games and to observe how it varies
with price. To date, Walls and Harvey (2005) is the only study of which we are aware
that conducts such an experiment, changing price and observing betting patterns in an
experimental roulette game.
Finally, there is need for more study on competition among various forms of gam-
bling. Does the introduction of casino gambling impact lottery sales, and does this
impact vary over time as, perhaps, the price of casino gambling declines? As Inter-
net gambling grows in popularity how will traditional casinos be impacted, and how
will they respond? How does the introduction of casino gambling by one jurisdiction
impact another, and how does it impact the potential for revenue generation? While the
European Union has allowed each country to retain its own unique gambling policy,
similar to individual states in the United States, would a broader regional or national
approach to gambling result in a more efﬁcient use of resources and an increase in
revenue?

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the elasticity of casino gambling
51
The academic community has only recently begun to undertake the study of casino
gambling as it would any industry. The lack of a studies estimating elasticity is evidence
of this. Further research is critical if we are to understand gambler behavior and the
revenue-generating potential of an activity that, while newly legalized, has been around
perhaps as long as humankind. It is an industry that poses many fascinating academic
and public policy questions and is deserving of continuing academic inquiry.
Notes
1. In the United States the term handle is used for total wagers, whereas in many other parts
of the world, for example, Australia and South Africa, the term turnover is used.
2. Riverboat casinos were often required to “cruise.” In Iowa and Illinois the boats would
take a two-hour excursion, after which they would return to the dock in order to allow
new customers to board and existing customers to exit if they chose. Existing customers
were allowed to remain for another cruise if they chose but had to pay another admission
fee (generally $2). In Missouri boats that were on rivers had the same restrictions. Others,
denoted as“boats in moats,”were on land next to the river. They had water that surrounded
them and had to mimic cruising. Customers were given a certain time to enter the casino
but during the next two hours were prohibited from entering the casino. Customers could,
however, leave whenever they chose. Over time states dropped these restrictions. For a
history and analysis of these and other restrictions see Nichols 1998.
3. The name and precise location of the casino are conﬁdential. Narayanan and Manchanda
(2008) describe the casino as a local monopoly with the nearest competitor 30 miles away.
4. Thalheimer (2008) notes that the larger purses did allow the racetrack to sell the simulcasts
of its live races. The elasticity estimates above refer only to handle from live races at the
racetrack.
5. On the other hand, there is a much broader literature on the income elasticity of lottery
expenditures. One of the earlier studies by Babbel and Staking (1983) ﬁnds that lotteries
have close to unitary income elasticity. Other studies ﬁnd very different elasticity estimates,
including negative income elasticity for West Virginia in Garrett and Coughlin 2009. See
Babbel and Staking 1983, Mikesell 1989, 1994, Garrett and Coughlin 2009, and Coughlin
and Garrett 2009 for examples of those different income elasticity estimates for lotteries.
6. See Fox and Campbell 1984, Dye and McGuire 1991, Sobel and Holcombe 1996, Holcombe
and Sobel 1997, Dye 2004, and Bruce, Fox, and Tuttle 2006 for examples of those studies.
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chapter 4
........................................................................................................
THE ECONOMICS OF ASIAN CASINO
GAMING AND GAMBLING
........................................................................................................
ricardo chi sen siu
The chief factor in the gambling habit is the belief in luck; and this belief is
apparently traceable, at least in its elements, to a stage in human evolution
antedating the predatory culture.
(Veblen 1899)
... the Chinese are a nation of gamblers... they hope for a miracle, a
streak of luck, a big win.
(Blanchard2002)
Introduction and Approach
.............................................................................................................................................................................
Rapid growth in the Asian casino gaming markets since the last quarter of the twentieth
century has evidently drawn the interest of academics in the ﬁeld. Despite a number of
socially and politically controversial issues, the evolution and organization of the casino
industry with regard to the contextual settings in Asia deserve extensive exploration.
Introduction
While gambling is a common activity for humans, the demand for various types of
games and related gaming services is not identical across different regions. Given the
differences in social, political, and economic factors, such as culture, education, public
administrative structure, regulatory system, income, and so on among different coun-
tries in the world, the organization and market performance of casino gaming and
gambling in Asia are unique. For example, while the markets in America are largely

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56
casinos
dominated by gaming machines, it is well-known that Asia is a table-game market (see,
e.g., Siu and Eadington 2009). In addition, while most casino ﬁrms in the world are
competing for patrons from the mass gaming market whereby lower operating risk and
higher proﬁt margins are expected, Asian casinos are more inclined to pursue VIP (or
premium) players with a considerable volume of turnover but higher liquidity risk and
lower proﬁt margins (see, e.g., Siu 2009a).
In Asia, the composition of the casino gaming markets is largely driven by the par-
ticular desires of players for various games. Nevertheless, given the ﬁxed odds of casino
games, the role of non-price factors in exploring the demand-side issues presents an
interesting topic for study. Besides that, given the unique features of this industry
in that its practice may easily be correlated with socially and ethically controversial
underground economic activities (e.g., crime, drugs, commercial sex, money laun-
dering, etc.), a free market approach may be inappropriate. Indeed, institutions and
institutional changes have exerted signiﬁcant inﬂuences in the recent progress and orga-
nization of this industry, hence leading to differences in performance across various
Asian casino jurisdictions.
In the early decades of the twenty-ﬁrst century, it is commonly anticipated that
increasing income and wealth effects will accelerate the growth and development of
casino gaming in Asia. For example, as cited in “Gambling on Asia’s middle classes”
(GBGC 2011), theWorld Bank estimated that“the global middle class will increase from
$430 million in 2000 to 1.2 billion in 2030. China and India will account for two-third
of this expansion.” As the two most-populated countries in Asia (also in the world),
both China and India would undoubtedly expand the potential demand for casino
gaming should they experience a rapid increase in the numbers of people reaching
the middle classes. Accordingly, direct and indirect economic beneﬁts are appealing
to the host economies and related world investors. Nevertheless, taking into account
the underdeveloped social and public administrative systems of most Asian countries,
social costs and impacts associated with the potential expansion of casino gaming are
also imperative issues for the related parties.
This chapter explores the aforementioned topics. In particular, the determinants of
the Asian demand for casino gaming and factors responsible for the evolution and
organization of the casino industries will be examined. In addition to the market
fundamentals, the signiﬁcance of the unique features of the Asian culture and related
institutional structure of the gaming industrial performances will be uncovered. Lastly,
controversial debates over the social beneﬁts and costs of casino gaming in Asia will
also be evaluated.
Approach of This Study
Only a limited amount of literature is available as reference for a study of the economics
of casino gaming and gambling. That is because this is a relatively new area of study.
Research on gambling in Asia is particularly scarce. In congruence with the modern

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the economics of asian casino gaming and gambling
57
development of casino gaming in Las Vegas since the 1980s and the subsequent expan-
sion of this industry within North America, a few representational studies have been
devoted to explore the practice of casino gaming and its economic impacts, such as
taxation, social beneﬁts and costs, and economic growth (see, e.g., Walker and Barnett
1999; Eadington 1984, 1999; Garrett and Nichols 2005; Nichols and Serkan 2008; and
Walker 2007). Besides that, aware of the rapid expansion of casino gaming in East
Asia since the dawn of the twenty-ﬁrst century (e.g., the success of Macau (Macao)
in surpassing the reported gross gaming revenue (GGR) of Las Vegas since 2006 and
the approval of two casino licenses by the Singapore government in 2006), Ricardo
Siu (2006a and 2007a) and Guoqiang Li, Xinhua Gu, and Siu (2010) also embarked
on studies related to the organization of casino gaming and its impacts on economic
growth and development. To enhance our understanding in this area with a speciﬁc
focus on Asia, this chapter will ﬁrst develop adequate evidence sourced from various
contexts in Asia to support the pragmatic research work in the related topics.
In the process of consolidating and analyzing the evidence, related reasoning from
institutional economics will follow, especially in uncovering the evolutionary aspects
of casino gaming in Asia as well as the forces that drive the development of various
major casino jurisdictions. For example, the argument of a ceremonial-instrumental
dichotomy that was raised by ThorsteinVeblen (1899), with emphasis placed on uncov-
ering the opposing forces between tradition and technological progress in economic
changes. Besides that, the situation, structure, and performance (SSP) institutional
impact theory (Schmid 1987, 39–43) in revealing the interrelationship between the
rights structure in an economic society and its impacts on economic performance,
and the nature of path dependence in economic changes (North 1997), are found to
Industrial performance
and social impacts
practice of casino gaming and gambling in Asia
Public
choice
Social, cultural, political,
and economic factors
Institutions
Demand
Market structure and
industrial organization
Feedback
figure 4.1 A pragmatic approach in exploring Asian casino gaming and gambling topics

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## Page 79

58
casinos
provide the pragmatic grounds for this study. In principle, by following the institutional
economics approach, this study “does not attempt to build an all-embracing general
theory”(Hodgson 1998, 168) for casino gaming and gambling. This approach is instead
consistent with the argument of Robert Prasch (2008, 6–7), who indicated that “there
is no single ‘theory of the market’.” Instead, the inﬂuence exerted on industrial changes
and performance by particular “institutions, habits, rules, and their evolution” (Hodg-
son 1998, 168) will be emphasized. As a recap of the aforementioned, ﬁgure 4.1 depicts
the organization and ﬂow of this study.
Current Layouts of the Asian Casino
Gaming Markets
.............................................................................................................................................................................
In comparison with Europe, America, Oceania, and Africa, the evolution of land-
based casino gaming in Asia has its own process and hence holds unique features and
structure. For example, according to the level of modern development and organization
of businesses, the practice of this industry is evidently associated with duality features.
Given the unique situation present in various Asian societies, the structure employed
by the respective authorities and power groups, alongside the layouts and performance
of the related markets, are found to be quite different.
Composition of Land-Based Casino Jurisdictions in Asia
According to the United Nations, Asia is geographically composed of 30 legally
recognized independent countries, 1 de facto country (i.e., Taiwan) and 2 Special
Administrative Regions (SARs) (i.e., Hong Kong SAR and Macau SAR) of China1 (see
ﬁgure 4.2). At the end of 2011, casino gaming has been legalized in 19 of the 33 Asian
countries/regions (as labeled by “♠” and “♥” in ﬁgure 4.2). Of the other 14, 12 coun-
tries/regions have outlawed casino gaming and the governments also enforce related
laws to ban the business. For the remaining 2 countries (Indonesia and Uzbekistan,
which are labeled with “♦”), casino businesses are operated in the open, even though
casino gaming is banned by law. In Indonesia, around 3 to 4 casinos are currently in
operation; one is located in Surabaya, the country’s second largest city. In Uzbekistan,
although casinos have been formally banned since the beginning of the 1990s, at this
writing a casino is operating in Tashkent, the capital city.
During the process of reviewing and compiling related information to construct
ﬁgure 4.2, several particular features associated with the existing composition and
layouts of the Asian casino gaming markets were identiﬁed. First, religion was found to
be a major factor responsible for the lack of casino gaming in a country. For example,
casino gaming is outlawed in most Islamic countries in Central and West Asia, such as

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the economics of asian casino gaming and gambling
59
 (♠: legalized casino gaming, ♥: casino gaming is legalized, but no operating casinos yet, 
  ♦: casino gaming banned, but casinos openly operating)
Russia
Kazakhstan
Kazakhstan
Mongolia
Kyrgyzstan
Kyrgyzstan
Uzbekistan
Uzbekistan
Tajikistan
Tajikistan
Afghanistan
Afghanistan
Pakistsan
Pakistsan
India Bangladesh
Bangladesh
Bangladesh
Sri Lanka
Maldives
Burma
Cambodia
Cambodia
Indonesia
East Timor
Papua New Guinea
Malaysia
Singapore
Vietnam
Laos
Laos
Thailand
Thailand
Cambodia
Laos
Thailand
Nepal
Bhutan
China
Taiwan
Philippines
Macao
Macao
Macao
Hong Kong
Hong Kong
Hong Kong
North
Korea
South
Korea
Japan
Turkmenistan
Turkmenistan
Kazakhstan
Kyrgyzstan
Uzbekistan
Tajikistan
Afghanistan
Pakistsan
Turkmenistan
figure 4.2 Land-based casino jurisdictions in Asia (as of Dec. 31, 2011)
Legend: ♠= legalized casino gaming; ♥= casino gaming is legalized but no operating casinos
yet; ♦= casino gaming banned but casinos openly operating
Afghanistan, Pakistan, Tajikistan, and the Maldives. The same also applies to Indonesia.
In East Timor, the reasons for outlawing casino gaming are unclear even to foreigners,
but inasmuch as the majority in the country are dedicated Roman Catholics, religion
could possibly be a factor. In addition, moral and ethical concerns of other major Asian
religions, such as Hinduism, Buddhism, and Confucianism, also play essential roles
in inﬂuencing political interests and, hence, the public choice for the physical layouts
and magnitude of casino gaming in various countries. While social factors play a part
in determining the institutional context, scope, and scale of the related markets at the
outset, economic factors lead to the observed performance of the markets.
In the particular social context of Asia, it is recognized that the physical scale of casino
gaming in most of the jurisdictions in Central and South Asia are more traditional in
organization and small in scale. While casino industries in these countries are generally
represented by fewer than 10 ﬁrms, the largest casinos commonly located in hotels or

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60
casinos
hotel resorts are in the scale of around 20 to 40 tables and a few dozen to a few hundred
gaming machines. In contrast, the industries are much larger in scale and modern in
organization in East and Southeast Asia. Macau, as the world’s casino capital, has a
geographical area of less than 30 square kilometers, yet the industry comprises more
than 30 casinos (in 2011) and approximately 5,000 gaming tables and 14,000 slot
machines. The recent development of certain individual mega casino resort properties
in Malaysia, Singapore, South Korea, and the Philippines have also reached a scale and
organization comparable to those in Las Vegas.
Last but not least, another unique feature associated with the practice in Asian casino
gaming markets is the relatively high proportion of table games to gaming machines.
While the ratio of gaming tables to gaming machines in a typical North America casino
is around 30, it is less than 10 in an Asian casino (see, e.g., Siu and Eadington 2009,
45). In one extreme case, for example, there were only 16 tables and no equipped
gaming machines, as in the largest casino in Sri Lanka, the Ritz Club (International
Land Casinos Directory—Sri Lanka). This unique composition of gaming devices is
likely to persist in the Asian markets for the foreseeable future.
Duality of Markets
Broadly speaking, the term duality of markets refers to the existence of two non-parallel
segments (e.g., existing traditional sector versus newly developed modern sector) or
two opposing forces (e.g., local versus international business practices), which interact
with each other and produce the dynamics of market evolution. Indeed, this concept is
identical to the ceremonial-instrumental dichotomy described by Veblen (1899), which
provides the pragmatic grounds to examine the differences in the evolutionary paths
between various economies (or an industry in different economies).
Gambling activities have long been a part of the history and culture in Asia, especially
in China. However, related businesses are negatively perceived by the general public
and have a low social status. This is due to the fact that most Asian societies are less
developed. Thus, they lack an appropriate regulatory system to police the socially
undesirable activities associated with gambling businesses. Consequently, stereotypical
perceptions are derived from the concept of gambling dens instead of casinos or casino
resorts. The former is a common term used in the past in Asia to describe a casino-like
gaming venue. Indeed, gambling dens operate in the open and are suspected by many
as having been triad related or controlled throughout Asian history. Together with
underdeveloped regulatory systems in most of the countries, these gambling dens have
generated an adequate force to encapsulate the modern development of this industry.
On the other hand, following the rapid integration of Asia (especially East Asia) into
the global economy beginning in the last quarter of the twentieth century, improvement
of regulatory systems (including transparency and enforcement mechanisms) and
political reforms carried out by various Asian governments have opened a new chapter
in the development of casino gaming. In addition, triggered by the decision of the

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the economics of asian casino gaming and gambling
61
Macau SAR government to eliminate the casino monopoly in 2002, and the decision of
the Singapore government to legalize casino gaming in 2005, the casino jurisdictions
in East Asia have evidently entered into a phase that looks geared to improving the
industrial structure and organization. It is anticipated that the impacts of the related
instrumental changes may also be diffused to other countries in Asia. Nevertheless,
while the entertaining features of modern casino gaming are incorporated into casinos,
traditional components that are associated with less than desired activities continue to
take place. In addition, constrained by underdeveloped legal systems in many Asian
countries, casino gaming is to a large extent still being carried out in a gray area
somewhere between law and custom.
Structural Issues Associated with the Related Markets
With reference to the current layouts of the Asian casino gaming markets, it is possible
to pin down a number of structural issues that are associated with/confronted by the
industries and related policy makers. Among these issues, the role played by the public
sector deﬁnitely warrants careful examination. Since a large number of Asian coun-
tries have underdeveloped political and administrative systems, the current gaming
laws may be either insufﬁciently constructed or weakly enforced, or subject to inef-
fective changes due to social and political interests. The operations of this 24/7 type
of business, which involves a considerable amount of cash turnover, are difﬁcult to
regulate, and consequently it is difﬁcult to safeguard the interests of modern corporate
investors.
Given the particular concern around the public sector structure, the next prominent
issue is the corporate governance structure of the casino ﬁrms. Aside from Singapore
and Malaysia, South Korea, and probably the newly developed segment in Macau,
which have put forth the required layouts to balance business objectives and com-
munity interests, most other casinos in Asia do not seem to have a well-deﬁned
or efﬁcient internal governance structure. Pursuant to the current social, regula-
tory, and economic environments in many Asian countries, the corporate governance
structure of many casinos is either largely shaped (or restricted) by public interests
or loosely drawn due to underdeveloped regulatory frameworks and enforcement
mechanisms.
For example, it is well known that casino gaming is prohibited in Thailand. Conse-
quently,smallcasinosaremadeavailabletoThaipatronsineasilyaccessibleneighboring
countries, such as Cambodia, Laos, and Burma. These casinos would not be overly
keen to have in place a corporate governance structure that would balance business
turnovers and social impacts. Accordingly, crime, drugs, commercial sex, and other
socially and ethically controversial activities are found to be associated with the related
casino gaming businesses. Similarly, as casino gaming is prohibited in Mainland China,
legalized casinos that operate in the neighboring countries (e.g., North Korea, Viet-
nam, Burma, Kyrgyzstan, and Kazakhstan) widely publicize their services to Chinese

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casinos
patrons. Consequently, it has been the ongoing endeavor of the Chinese government to
detect cross-border gambling activities and to pressure these neighboring governments
to shut down casinos in locations that are easily accessible by the Chinese (e.g., Rank
2005; BBC News 2007).
On the basis of this evidence, it is obvious that the issues associated with revenue
(GGR) maximization and harm (social costs and impacts) minimization are of par-
ticular concern due to the unique social and administrative settings. Besides that, it is
clear also that excess demand on the existing industry in its current scale is a common
phenomenon.Inordertoadequatelypresenttheperspectivethatafreemarketapproach
may not be a desirable means of closing the gap in demand, the unique socioeconomic
factors that contribute to the Asian demand for casino gambling will be discussed in
the next section.
Unique Contributing Factors to the Asian
Demand for Casino Gambling
.............................................................................................................................................................................
Despite the conceptual robustness of the law of demand (Marshall [1890] 1997, ch. 3;
Samuelson and Nordhaus 1995, 24), it is evident that this concept is not necessarily
sufﬁcient to reveal the quantity demanded nor applicable enough to directly uncover
the demand behavior of casino gambling in practice (Siu 2007a and 2011). A major
issue associated with economic studies is that the unit price paid by individual patrons
to enjoy a casino game is unobservable. Indeed, once the odds of casino games are
ﬁxed, inﬂuences from a number of non-price factors (e.g., traits of a society in terms
of its culture, religion, political structure, education, etc., as well as income and
wealth) may contribute to the decision processes of individuals and endogenously
determine their choices (including various types of games and total amount of funds to
be spent).
A Socioeconomic Approach to Demand for Casino Gambling
To a large extent it cannot be argued that the contextual settings of a society shape the
ideology and value system of its members, hence inﬂuencing the representation of their
demand behavior for gambling. For example, it is of little dispute that the unique traits
of Chinese society contribute to a number of key attributes (especially inﬂuences from
Buddhism and Confucianism; see, e.g., Nepstad 2000) that induce a relatively higher
propensity of the population to gamble in comparison to people in other societies. As
a matter of fact,“gambling followed the development of the Chinese society every step
of the way and by 1000 B.C. it became as inseparable from Chinese culture” (Progress
Publishing Co. 2006).

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the economics of asian casino gaming and gambling
63
To account for social inﬂuence on the demand for casino gambling, the consumers’
utility function in a social environment as formulated by Gary Becker and Kevin
Murphy (2000, 9) provides relevant grounds for this effect.
U = U(x,y;S)
(4.1)
In equation (4.1), x and y denote the quantity of all kinds of economic goods and
services, and S represents the “social inﬂuences” on the utility function through the
stocks of “social capital” (e.g., social norms, religion, education, etc.). In principle,
“changes in social capital do not shift the utility function, but raise or lower the level of
utility with the stable function, U.” Thus, if x denotes the quantity of casino gambling
and y the quantity of all other economic commodities, one’s utility derived from casino
gaming (x) depends on whether one’s “friends and neighbors” choose to gamble in
casinos. In Backer and Murphy’s general argument, “x and S are complements so that
an increase in S raises the marginal utility from x, even when the increase in social
capital itself lowers utility.” It follows that changes in social capital stocks will alter
one’s marginal utility for casino gambling in the same direction, that is,
dx
dS > 0.
(4.2)
It is worth noting that, unlike in the traditional approach to demand theory, the price
of a casino game may not be directly expressed in the discussion of casino gambling.
Accordingly, the demand function for casino gambling of an individual in a social
environment is subject to the budget constraint of
G + pyy = I,
(4.3)
where gross expenditure spent on casino gambling is G = f (x). While x is determined
by different variables, such as the number of hands played, G is jointly determined by
x and other variables, such as the ﬁxed odds of a game and the average amount of bets.
With reference to the socioeconomic approach to demand for casino gambling, it
is evident that as stocks of social capital (S) are heterogeneous across societies and
nations, so too is the speciﬁc representation of behavioral demand for casino gam-
bling. In the case of Asia, the stocks of social capital are clearly inseparable from the
unique composition and traits of culture, religion, education, and so on across various
societies/nations.
Inﬂuence of Culture and Religion on the Demand
for Casino Gambling
As an essential component of social capital, culture incorporates a set of socially pre-
scribed behaviors (e.g., social norms and values, habits, etc.) and social cognition for

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casinos
people to interact with one another. In various societies, although the cultures are
not identical, they are determined by a number of factors that have resulted from
their respective paths of evolution. For example, geographical location, language, and
administrative structure traditionally adopted by different Asian societies may have
had substantial impacts on cultural traits. Among these factors, religion is probably the
most inﬂuential. According to Philip Wilkinson (2008, 14),“virtually every culture that
we know of has some kind of religion.” In societies,“religions provide a sense of moral
purpose.... Religion often occupies the centre of the world stage in politics, diplomacy,
and even war.... Despite the changing nature of our times, religion is still at the heart
of our lives” (10). Indeed, this social capital stock shapes beliefs about and the desire
for casino gambling.
In East and South Asia, the demand behavior for gambling is deeply linked to the
region’s unique cultures and religions (e.g., Buddhism and its factions, and Hinduism).
In addition to the commonly known Chinese culture of gambling (see, e.g., Nepstad
2000; Chien and Hsu 2006), it has also been recorded that“Indian culture adopted gam-
bling from the beginning of Indian civilization, which started 4000 years ago”(Progress
Publishing Co. 2006). Consequently, socially prescribed behavior for gambling allows
or even promotes the desire for casino gambling. In contrast to Western culture and
religion, superstition is the primary explanation for the cognitive preference (and illu-
sion of control) of the Chinese for games carried out by humans instead of machines.
This explains the phenomenon in which traditional Chinese patrons and a large pro-
portion of patrons from East Asia are more inclined to choose table games rather than
slot machines.
In contrast to East and South Asia, gambling is widely perceived as socially unaccept-
able behavior in the Muslim world and hence is prohibited (Binde 2005, 5; Wilkinson
2008, 137). Given that there is no endowment of related social capital, casino gam-
bling is obviously not a choice for religious Muslims. Besides that, social inﬂuences
may generate a negative utility (e.g., anticipated punishments) to individuals who ﬁnd
ways to gamble despite the legal ban. In other words, the utility function as stated in
equation (4.2) could be written as:
dx
dSR
≤0 for the Muslim world,
(4.4)
where SR denotes the religion of Islam.
Impacts from Education and Societal Modernization
From an evolutionary perspective,“culture is subject to a process of cumulative change.
Culture has ceremonial and technological aspects” (Hamilton 2004: 111). That is,
throughout the process of cultural change part of a society’s culture may be sustained
or reinforced while others may be altered or replaced. To a large extent, while religion

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the economics of asian casino gaming and gambling
65
is an aspect of culture that has ceremonial meaning, education and modernization
of a society over time generate technological changes that inﬂuence the value system,
patterns of life, and market behaviors. For example, in China and a number of Asian
countries public policies (including education) have been formulated to drive the com-
munity away from smoking. By the same token, education and societal modernization
also inﬂuence the traditional view on casino gambling but in a direction that differs
from that of smoking. While the majority of the views in various societies tend to
oppose smoking, casino gambling is increasingly perceived as a form of entertainment
rather than a sinful activity. This change well explains the phenomenon of rising Asian
demand for casino gaming.
Yet there is research that validates the impacts of changes in education on the demand
for casino gambling, with plenty of related studies that look at the demographical fea-
tures of problem gambling in North America and Australia (see, e.g., State Government
of Queensland 2005, ﬁgure 6; and Shinogle et al. 2011: table 4.20). The results suggest a
positive correlation between the education level of a community and the proportion of
its residents who have participated in gambling activities (including casino gambling).
Nevertheless,thereisnoconsistentpatternacrossdifferentcountries/regionsintermsof
whether education has an impact on the frequency of casino visits and amounts spent.
According to a 2005 study by the State Government of Queensland on a group of
people with normal behavior who gambled (i.e., classiﬁed as “recreational gambling”),
46 percent had an education level of 10 years or less; 32 percent, up to 12 years; and
19 percent, above 12 years. When the same study was applied to people with a higher
frequency of gambling (i.e., at “low risk” or “moderate risk” for gambling), the ratio to
education level of more than 12 years remarkably fell from the 19 percent to 9 percent
and 7 percent, respectively. Interesting in terms of the gambling group with the highest
risk (i.e., “problem gambling”), it was found that the ratio to education level of more
than 12 years increased all the way up to 22 percent.
On the other hand, with reference to an empirical study conducted by Daniel Lai
(2011) on “four ethno-cultural minority groups (i.e., Chinese, Filipinos, South Asians,
and Vietnamese) in Edmonton, Calgary, Toronto and Vancouver,” it was identiﬁed that
higher educated Asian groups in Canada are relatively less likely to become addicted to
gambling. In addition, other parameters used in this study also suggested that“cultural
differences in gambling (behavior) do exist.” Despite the fact that the ﬁndings reported
in most of the studies are not sourced from research intended to elucidate casino
gambling in Asia, the results are related enough to fairly verify the possible inﬂuence
of education level to demand by Asians for casino gambling. It is just a matter of the
degree of demand that varies across different Asian societies.
The Role of Income and Wealth Effects
Apart from cultural and social factors, income and wealth serve as the two most impor-
tant economic factors that directly enter into the decision-making process of individuals

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casinos
for casino gambling demand. Similar to the demand for such luxurious commodities as
tourism and recreation, the demand for casino gambling is regarded as income elastic.
For example, as measured by the GGRs, double-digit compound annual growth rates
(CAGRs) of spending in casino gambling were reported by major casino industries in
Asia (e.g., Macau, South Korea, the Philippines, Malaysia) in the ﬁrst decade of the
twenty-ﬁrst century, with the CAGRs generally being higher than GDP growth in the
region. Associated as part of economic development, income growth in Asia is widely
correlated with increases in the income of the working class and expansion of the
middle class, and this is especially true for China, India, and other emerging East and
Southeast Asian countries/regions.
In looking at the various major economic approaches recently employed to examine
gambling behavior, the Friedman-Savage utility function (Binde 2009, 26–28) provides
a reasonable framework for running analyses. In principle, the Friedman-Savage utility
function argues that as wealth of an individual increases“marginal utility ﬁrst decreases,
then increases, and ﬁnally decreases again” (27). As such, the “convex middle segment
of the (expected utility) curve represents the choices,.... of the upper stratum of
individuals belonging to a social group, for whom an increase in wealth will move
them up to a higher social group”; therefore, taking the risk of gambling may “allow a
working class man or woman to fulﬁll social aspirations of becoming middle class”(27).
Alternatively, while money lost on gambling “does not qualitatively lower a person’s
social status... the chance of winning substantial sums offers an opportunity for a
qualitative social advancement” (27), and therefore, a force is formed which promotes
demand for gambling.
Following the success of China’s economic reform and the rapid migration of labor-
intensive production sectors from East and Southeast Asia to South and Central Asia
since the end of the twentieth century, the income of the Asian working class and the
size of the middle income group have evidently expanded. For example, Benjamin
Chiang and Sherry Lee (2010), estimated that 100 million Chinese people in 2010
had an annual income of around USD20,000, while the annual disposable income
of another half a billion people was between USD1,600 and USD4,900.2 In addition,
it was perceived that “during periods of tremendous economic growth in India and
China, (the) household saving rate... increased nicely” (Hunkar 2009). As a propor-
tion of household disposal income, China’s household saving rate had increased from
around 14 percent in 1991 to 28 percent in 2008 while the same rate increased from
23 percent to 32 percent in India. Even though the household saving rate in some of
the Asian countries, such as South Korea, largely fell from over 20 percent to around
7 percent in 2008, it was still higher than that in the United States, which had a rate
below 4 percent. As instituted by particular Asian cultures and related social factors,
the increasing wealth of low-income to middle-income groups moving to the “con-
vex middle segment of the (expected utility) curve” has unarguably been expanding
over time.
Overall, non-price factors encapsulate the social choice of gambling in Asia, hence
providing indispensable and pragmatic grounds for individuals to consummate their

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the economics of asian casino gaming and gambling
67
desires for casino gambling. These factors have different degrees of inﬂuence across
Asian countries/regions, and these factors result in different patterns and degrees of
demand for casino gambling. In the foreseeable future, related traits from the demand
side will continue to differentiate Asian casino gambling behaviors from those in other
parts of the world.
Industrial Organization of Casino Gaming
in Asia: Same Principles but Different
Practices
.............................................................................................................................................................................
Since the dawn of the twenty-ﬁrst century, casino gaming as a modern industrial
sector has been noticeably expanding in the countries/regions of East and Southeast
Asia. Following the decision of the Macau government in 2002 to replace its casino
monopolywithanoligopolisticstructure,andthedecisionof theSingaporegovernment
in 2005 to legalize casino gaming, other jurisdictions, such as Malaysia, South Korea,
the Philippines, and Cambodia, also have taken measures to review and promote the
organization of their businesses. In addition, such small-scale casino jurisdictions as
Vietnam, India, and Sri Lanka, among others, have demonstrated interest in addressing
the expanding and excess demand for casino gambling in the markets. In view of the
differences in social, institutional, and economic settings, disparities exist even though
there are shared similarities in the industrial organization of casino gaming across
various Asian countries/regions.
Existing Scale and Structure of the Markets
Based on the number of casinos and reported GGRs, the scale of various Asian casino
jurisdictions is shown in ﬁgure 4.3.3 In 2010, the annual outputs (measured by GGR) of
most Asian casino jurisdictions are around or below USD1 billion, with the exception
of South Korea and the two outliners of Singapore and Macau. In addition, except for
Cambodia, Kazakhstan, the Philippines, South Korea, and Macau, other Asian casino
jurisdictions are built with around 10 or fewer casinos. Similar to most jurisdictions
in the world, entry into the market is highly restricted by the limited number of
licenses predetermined by the respective governments, which in turn, are inﬂuenced
by the interests of various social and political groups rather than pure market forces.
For example, while a monopoly structure is approved by the Malaysian government,
duopoly is deﬁnitely the choice of the Singapore government.
To a certain extent, the differences in the GGRs across various jurisdictions could
partially be explained by the variations in their respective physical and absolute

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casinos
Cambodia
Kazakhstan
Philippines
S Korea
Burma, India, Laos, Nepal,
Sri Lanka, Papua New Guiena,
Turkmenistan, Kyrgyzstan
Singapore
Malaysia
Vietnam
N Korea
10
20
30
Number of casinos
5
15
25
GGR
(bn USD)
Macao
figure 4.3 The scale of various Asian casino jurisdictions (around 2009 and 2010)
conﬁgurations (i.e., the scale of gaming devices, associated non-gaming hospitality
facilities, etc.).4 According to some related evidence as presented in table 4.1, it is
reasonable to infer that the business turnover of some of the Asian casino industries is
somewhat determined by their physical capacities. For example, it is interesting that the
physical scale of the industry in Singapore is around one-ﬁfth of that in Macau in 2011,
Table 4.1 Approximate Numbers of Gaming Tables and Machines in Some of the
East and Southeast Casino Jurisdictions (around 2009 and 2010)
Casino Jurisdiction
Number of
Gaming Tables
Number of
Gaming Machines
Source
Macau
~4,900
~14,000
http://www.dicj.gov.mo/web/en/
information/DadosEstat/2010/
content.html#n4
Singapore
~1,000
~3,000
Curtis, Cheung, and Dobson
(2011), 29
See also http://casinocity.sg/
South Korea
~700
~1,800
Kim and Matthew (2011), 15.
Malaysia
~400
~3,100
http://www.ildado.com/
land_casinos_malaysia.html
Philippines
~800
~5,200
http://www.ildado.com/
land_casinos_philippines.html;
http://www.casinocity.com/ph/
manila/allistar/
Note: In the same period of time, Las Vegas was equipped with around 3,000 gaming tables and 200,000
gaming machines.

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the economics of asian casino gaming and gambling
69
and this is close to the ratio of their reported GGRs. Nevertheless, the relationship
between physical conﬁguration and business turnover may not be general enough
to explain the differences in business performance across various jurisdictions (e.g.,
between Singapore and Philippines, South Korea and Malaysia, etc.). In terms of the
jurisdictions in Central and West Asia (e.g., India, Nepal, Kazakhstan, and Kyrgyzstan),
even though their absolute scales are generally smaller than those in East and Southeast
Asia,a general relationship between their physical scale and business turnover is difﬁcult
to see.5
As an industry that is a socially sensitive and exposed to public desire for exten-
sive government regulation and control, the casino industry is signiﬁcantly curbed
by various social and political inclinations instead of the interest of market partici-
pants (risk-seeking casino patrons and proﬁt-seeking casino ﬁrms). This simple and
unarguable principle for explaining the scale and structure of the casino industry is
indeed in line with the phenomenon seen in the Asian markets. Nevertheless, owing
to the normative nature of social costs and impacts in public policy discussions, the
determinants of the scale of the industry and structure in various jurisdictions vary
accordingly.
Changing Dynamics to the Organization of the Industry
Given that the modern progress of casino gaming in Las Vegas can be traced back
only to the 1970s (Schwartz 2003), many Asian jurisdictions were seen to be in their
developing stages or sporadic in development until the end of the twentieth century.
In the new millennium, we have witnessed a change in the organization of tradi-
tional gambling-based casino businesses toward the concept of casino resorts. Led by
Macau and Singapore, the modern development process of casino gaming in Asia has
accelerated.
Because casino gaming is a policy-based industry, the practice and business routines
of the industry are largely shaped by public interest and changes at the outset. The
dramatic success of Macau, for example, is highly accredited to the full support granted
by the Chinese government under its one country, two system policy. Indeed, not only
is Macau able to retain its existing casino industry despite the ban in Mainland China,
but it also is blessed with continuous support from the Chinese government. Since
the elimination of the casino monopoly in 2002, and the approval of new licenses to
world-class casino operators, the number of casinos almost tripled from 2002 to 2012.
In addition, the scale and organization of the industry as a whole have also undergone
signiﬁcant changes from their traditional layout.
Parallel to the increase in the ﬁxed capacity of the industry and the service quality
driven by competition, the number of visitor arrivals from both Mainland China and
outside the Mainland to Macau has signiﬁcantly increased. Under a special visa policy
approved by the Chinese government in the summer of 2003 allowing more Chinese
residents from wealthier cities in Mainland China to travel to Hong Kong and Macau,

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casinos
visitor arrivals from the Mainland to Macau dramatically increased (from around 2.3
million in 2000 to around 16.2 million in 2011).
Congruent with changing public interests and the expanding accessibility of the mar-
ket, the organization of the casino ﬁrms in Macau (both local and foreign) has evolved
over time. On the one hand, it is evident that foreign casino ﬁrms from North America
and Australia have been adjusting their business models to accommodate this Chinese-
based market (especially the composition of gaming devices as well as the practice of
competition, etc.). On the other hand, local casino ﬁrms have been improving the
content of their traditional and monotonic scope of gambling to ensure their compet-
itiveness. Consequently, as compared with other overseas jurisdictions, even though
casino gaming in Macau is still largely a table game market (which accounted for over
94 percent of the 2011 GGR in Macau), new aspects of its organization have come into
place and led to changes in the performance of this industry. As revealed in ﬁgures 4.4
and 4.5, while the number of slot machines has grown at a faster rate than that of
gaming tables since 2005, the proﬁtability per slot machine has risen much higher than
that of the gaming tables. Indeed, this evidence further veriﬁes the changing trend as
identiﬁed by Siu and Eadington (2009, 47–54) in that the casino industry in Macau
is in a transition stage and is moving toward becoming a high value–added service
sector.
Regardless of the differences in business scale, industrial structure, and organization,
some of the major Asian jurisdictions have also undergone changes that are similar
to those in Macau. In the Philippines, for example, casinos have long been regulated
and managed by a government-owned corporation, the Philippine Amusement and
Gaming Corporation (PAGCOR). To promote the efﬁciency and competitiveness of
Number of tables/slots
16,000
14,000
12,000
10,000
8,000
6,000
4,000
2,000
0
2005
1,388
3,421
6,546
13,267
11,856
14,363
14,050
13,787
4,375
4,017
4,770
4,791
4,853
Tables
Slots
2,762
2006
2007
2008
2009
2010
2011
Year
figure 4.4 Changes in the number of tables and slot machines in the casino industry of Macau,
SAR, China (2005.1q–2011.1q)

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the economics of asian casino gaming and gambling
71
Index
160
180
200
220
240
140
120
100
100
100
116
106
68
62
95
138
140
126
132
190
219
Slots
Tables
65
83
94
60
80
40
20
0
2005
2006
2007
2008
2009
2010
2011
Year
figure 4.5 Changes in the performance of table games and slot machines in the casino industry
of Macau, SAR, China (GGR index per table and slot machine: 2005.1q = 100)
this industry in the region, the Philippines congress amended the PAGCOR charter
in 2004 to allow the private sector (including local and foreign ﬁrms) to take part in
casino gaming. Consequently, the Malaysia-based Genting Club, which is well-known
in Asia, opened its world-class casino resort (Resorts World Manila) in the capital of
the Philippines in 2009. This single property added over 20 percent more to the total
number of gaming machines in the industry and more than 50 percent to the number of
gaming tables. Together with the enhancement of non-gaming facilities, casino gaming
in the Philippines has entered a new stage of development.
In addition, Kangwon Land, which opened in 2000 as South Korea’s largest casino
resort, is the only casino in the country allowed to receive local customers, and it
accounts for over 60 percent of casino revenues in the country. To further diversify,
and hence strengthen its competitiveness, Kangwon Land even took progressive steps
to improve its organization so that it would be similar to the Genting Highlands in
Malaysia and the new casino resorts in Macau. This included a major proposal to
further expand its property with luxury condominiums and a world-class water park
(Lee 2010b, 22). Indeed, led by Kangwon Land, other existing small- and medium-scale
casinos in the country are also improving the organization of their businesses.
Apparently the dynamics generated through the process of changes in organization
in major jurisdictions like Macau, the Philippines, and South Korea, as well as the
new force formed in Singapore, will further diffuse to other existing and emerging
jurisdictions in Asia. Indeed, changing trends in the organization of casino gaming as
a particular economic sector that provides entertainment services have emerged. The
related changes will continue to be extended to other Asian jurisdictions but at different
paces and in different forms subject to the social, political, and economic contexts of
the respective countries/regions.

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72
casinos
The Practice of Market Competition
That the theoretical prices of casino games are neither observable by patrons nor
directly responsive to changes in market conditions (see, e.g., Siu 2011), indicates that
the nature of casinos is to interact with their customers and compete in the markets
mainly through a set of non-price elements. Under the change in the organization of
casino gaming toward that of a modern economic sector which provides a package of
gaming and non-gaming entertainment experiences to customers, the differentiation
of services has become a common principle in competition. Nevertheless, owing to
the aforementioned differences in social, cultural, and political settings across coun-
tries/regions, the practice of product differentiation between casino ﬁrms as a form of
competition varies, and the degree of variation is largely inﬂuenced by public interests.
For example, the promotion of the gaming business is totally or partially prohibited
in some countries. Alternatively, non-gaming attractions (e.g., unique accommoda-
tion features such as those featured in the interior design of buildings and the service
quality, renowned restaurants and shops, particular types of entertainment and per-
formances/shows, etc.) are the focus of advertisements designed to bring customers to
these casinos.
With regard to industrial development stages, competition in the Asian casino mar-
kets could be broadly categorized into four different forms. First, there is oligopolistic
competition between a few large-scale casino ﬁrms within a jurisdiction (e.g., six
licensed world-class casino ﬁrms in Macau and two in Singapore). Second, one or
two major casinos enjoy a major share or a high reputation in the market, accompanied
by a number of small- and medium-scale casinos that run their businesses in different
locations/segments within the jurisdiction (e.g., South Korea, the Philippines). Third,
a number of small- and medium-scale casinos offer gaming opportunities in particular
locations and compete for potential patrons at a more modest level (e.g., Cambodia,
India, Nepal, Kazakhstan). Fourth and last, subject to the location of a jurisdiction,
casinos within the industry as a whole will compete for potential patrons on a geo-
graphical basis (e.g., competition between Malaysia and Singapore, Burma and Laos,
as well as Macau and other jurisdictions for Chinese patrons).
Regardless of the different forms of competition, their practices share some common
features. In the most modernized gaming corporations that are operating in the major
jurisdictions, such as Macau, Singapore, Malaysia, South Korea, and so on, casino
gaming has been packaged as part of a set of comprehensive entertainment and leisure
services supplied on individual properties as unique destinations. Under the guise of
the label “casino resorts,” however, differences in the facilities installed in the various
properties represent important measures to differentiate services from those of com-
petitors. For example, a casino gaming package that is bundled with particular features
and services provided by the Wynn Resorts are different from those provided by the
Venetian and MGM in Macau. In addition, in order for casinos to remain competitive
in various jurisdictions, non-gaming features adopted by the same casino ﬁrm also are
distinct. This could be veriﬁed by comparing the non-gaming features of the Venetian

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the economics of asian casino gaming and gambling
73
in Macau with those of Marina Bay Sands in Singapore, as both properties are owned
and operated by LasVegas Sands. It is also true when comparing the Genting Highlands
in Malaysia with the Resorts World Sentosa in Singapore and the Resorts World Manila
in the Philippines, all of the Genting Group.
In the Asian market it is especially interesting that a community network constitutes
the most important factor in promoting the casino business. Led by Macau, casinos
compete with one another by collaborating with a special type of junket operator who
provides a speciﬁc type of agency service for the casinos by underwriting signiﬁcant
amounts of nonnegotiable chips and directly or indirectly reselling them to patrons
for the purpose of earning a commission or sharing a certain percentage of the total
wins and losses from the businesses. Under this form of organization, casino ﬁrms
could secure “basic” turnovers by directing marketing efforts to the junket operators
(for more details about this business practice see Siu 2006a and 2007b). Due to the
dramatic success of Macau in terms of reported GGR, some Asian jurisdictions have
shown interest in embracing this business model. Nevertheless, concerns over low
transparency and legitimacy of certain business activities under legal frameworks in
different jurisdictions are obstacles to replicating this model. For example, related
business is highly controlled in Singapore.
Following the modern development and the dynamics of organizational changes of
Asian casino gaming industries, competition through effective amalgamation between
gaming and non-gaming facilities would evidently be an indispensable measure for
casinos to ensure their competitive edge. Nevertheless, as the regulatory framework
and the legal enforcement mechanism in many countries are yet to have sufﬁcient
capacity to monitor the related market activities, irregular forms of competitions are
likely to exist and persist in some markets, at least for the ﬁrst half of the twenty-ﬁrst
century.
The Role of Institutions and Their Changes
in the Process of Asian Market Progress
.............................................................................................................................................................................
In comparison with practices in other markets, the demand for casino gambling is
greatly inﬂuenced by social and cultural phenomena. Given the particular attributes of
the demand and supply of casino gaming, and public concerns over possible adverse
effects brought about by related activities, the structure (and organization) of this
industry in any one jurisdiction generally are chosen and outlined through the leg-
islative power of the government. In other words, the customs, legal system, and
their interactions and changes over time in a society contribute to the development
path and performance of a market. To explore the issues associated with the observed
performance and progress of the Asian markets, the SSP institutional impact theory by
A. Allan Schmid (1987, 39–41) will be followed.

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casinos
Choice of Industrial Structure and the Impacts on
Market Performance
According to the SSP institutional impact theory, while situational variables (i.e.,
“attributes of individuals, the community, and goods” [39] present in a market are
inherent in any given period of time, its rights structure (e.g., entry and exit conditions,
allowable actions, distribution of decision power, rules that govern/guide interactions
between market participants) “is a matter of human choice” (40). Consequently, mar-
ket performance (represented by the distribution of income among various competing
groups) “is a function of alternative rights given the situation” (ibid).\
In Asia, given the unique situational variables (i.e., the aforementioned demand-
and supply-side attributes), the changes in casino gaming is partially the consequence6
of the changing rights structure as chosen by the related power groups. Besides that,
the differences in the industrial structure and organization across various Asian juris-
dictions also explain the differences in development and performance. For example,
the impressive performance attained by Macau’s casino industry since the turn of the
twenty-ﬁrst century was triggered after a decision made by the government to replace
the industry monopoly with an oligopoly. In addition, the unexpected remarkable
growth in the industry’s GGR from the middle of the 2000s was palpable due to a
crucial (but controversial) decision by the Macau government (i.e., double the number
of legal entitlements shortly after three new licenses were granted in the beginning of
2002). Subsequently, the ﬁxed scale (both gaming and non-gaming hospitality capac-
ities) of the industry expanded by more than double the proposed scale of the three
original newly licensed casino ﬁrms. Moreover, the hands-off approach adopted by
the Macau government to cope with the practices of the casino gaming business has
tolerated increasing numbers of new casinos to attain increasingly higher volumes of
customer ﬂow and business turnovers. In parallel with the dramatic increase in the
industry’s GGR, and the surge in government taxation as well as income of the related
groups, questionable activities undertaken by casinos to win over their competition
(especially in the utilization of a business model that incorporates independent third-
party operated gambling rooms) have, however, concealed the real performance of the
market (see, e.g., Siu 2006b, 2009b, and 2010). After a decade of progress, even though
Macau has been crowned the world’s largest casino gaming jurisdiction in terms of
reported GGR, its ambition to become the world’s casino resort destination may still
be hindered by the irregular structure of the industry itself.
In contrast to Macau, the Singapore government perceives casino gaming as a new
segment to be integrated into its existing tourism and meetings, incentives, conferences
and exhibitions (MICE) industries (tagged“integrated”resort instead of “casino”resort
by the government). The primary purpose of legalizing casino gaming is to enhance
its competitiveness in the regional tourism market. In debates on granting approval
to casino gaming and formulating the structure of the business, the government has
clearly delivered a message to the community and potential operators in that casino

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the economics of asian casino gaming and gambling
75
gaming would be“a very small component of a much bigger whole”(Seneviratne 2005)
of the country’s economy. Besides that, casino gaming would be subjected to strict
regulations and highly controlled by the government. Thus, a transparent and effective
corporate governance structure to ensure the integrity of the industry, instead of simply
pursuing a high volume of GGR, had been formed at the outset. With proactive plans
enforced by the government to interact with the industry, Singapore’s casino gaming
is highly reputable and efﬁcient in a business sense. Consequently, in the ﬁrst full year
of its operation in 2011, Singapore’s casino GGR was larger than that of Las Vegas and
was crowned as the second large casino jurisdiction in the world.
Despite the impressive performances reported in Macau and Singapore, it is clear
that the underlying forces driving their achievements are quite different. To a large
extent, public choices, which fashion the structure and organization of industries, have
established the direction of development for casino ﬁrms,hence instituting their perfor-
mances. Indeed, differences in the performances across variousAsian jurisdictions (e.g.,
some related features are presented in ﬁgure 4.3 and table 4.1) could also be explained
with the same set of logic. For example, the relative outstanding performance of Kang-
won Land in South Korea was largely determined by public interests to develop a single
large-scale casino resort property as a measure to revitalize the declining economy in the
Gangwondo Province in the late 1990s. Consequently, the provincial government took
a dominant portion of the property’s shareholding, thereby supporting and inﬂuencing
its business organization. As outlined and supported by the related policies, Kangwon
Land outperformed other casinos in the country.
In contrast, most jurisdictions in Central and West Asia are composed of smaller-
scale casinos and casino hotels (there are few casino resorts) where traditional and low
value-added gaming services are provided. Despite the fact that the market size of casino
gaming in Central and West Asia is smaller, the structure and organization of the indi-
vidualindustriesasoutlinedbypublicinterestsinﬂuencetheirperformances. Forexam-
ple, legal requirements for the structure and organization of casino gaming in India
have long been a controversial topic among political and religious parties, which inhibit
progress of the industry. In an attempt to enhance tourism development in Goa, a num-
ber of offshore and onshore casinos recently were approved. Nevertheless, the GoaAnti-
Gambling Act allows protesters to restrict the industry by imposing additional licensing
requirements or banning local residents from entering into the casinos, and so on. Fur-
thermore, some licensed casinos may be intermittently forced to stop business, and
business turnover therefore becomes very difﬁcult to project for investment purposes
(see,e.g., Oberai 2011; Hand 2011; Yogonet Group 2011; Casinocitytimes.com 2008).
In other small West Asian jurisdictions adjacent to Muslim countries, structure and
organization as well as performance of the casino gaming markets are also restricted
by related social and political considerations. Alternatively speaking, in addition to
the attributes of demand and supply, differences in the institutional frameworks as a
determinant of the ways that the industries are structured and organized contribute as
indispensable factors to explain the differences in market performance across the Asian
jurisdictions.

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76
casinos
Inﬂuence of Institutions and Changes to
Their Business Routines
In institutional economics “a routine is regarded as automatic behavior, in contrast to
designed and implemented strategic plans,” which involves “the notion of procedural
memory, or recurrent interaction patterns and involving change driven by individuals”
(Lazaric 2011, 147). While it is commonly agreed that “management and authority
appear to be good candidates for the formulation of routines” (148), their actions in
practice are institutionalized by the legal and cultural environments of society. Owing
to this relationship, established routines are altered which would correspond to the
changes in the related institutions.
In terms of casino gaming in Asia, as long as a government deﬁnes an acceptable
middle ground for the interaction of casino ﬁrms and patrons, the market evolves
from thereon. Subsequently, decisions made by the management of casino ﬁrms would
then generate business routines. In a dynamic environment where institutions may
change due to discrete changes in public interest (hence altering the existing structure
of the industry), or changes in the situational variables after their interactions with an
approved structure, or both, business routines do evolve.
Indeed,the business model that incorporates independent third-party operated gam-
bling rooms as evolved in Macau from the beginning of the 1980s, and their changes
since the alteration of the market structure in 2002, constitute a typical case that reveals
a business routine and its evolution (Siu 2006 and 2007b; Chang 2007). Given the
unique social and political contexts of Macau in the 1980s and 1990s (Siu 2006a: 971–
974; Eadington and Siu 2007, 9–13), various evidence shows that while individual
governors were chasing short-term monetary beneﬁts before Macau’s handover back to
China in 1999, the primary interests of the family-run gaming monopoly was to retain
its monopoly position by means of increasing tax payments. Consequently, outsourc-
ing the casino business to certain independent third parties who could ensure contact
with big players and hence an ever increasing GGR became the “optimal choice” for
this monopoly. Following the initial success of this business arrangement, this evolved
into the norm in the Macau casino industry. Under this norm, all of the related parties
are bounded by a set of “informally” established rules.
As the ultimate beneﬁciary, the Macau government has traditionally taken a hands
off (or “silent”) approach toward the practice of this business model irrespective of
the presence of socially and administratively controversial activities in the market.
In the casino monopoly, this low amount of transparency was a business routine to
attract high GGRs from certain socially and ethically controversial business activities.
Indeed, evidence shows that VIP plays (the practice of gambling rooms was the main
contributor) had long represented over 60 or 70 percent of the industry’s reported
GGRs in Macau. To sustain a high turnover in this business, informal contracts between
casinos and a particular group of gaming agents had been established as the solution.
Since the termination of the gaming monopoly, changes in the business routines of

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the economics of asian casino gaming and gambling
77
casino ﬁrms have evidently taken place. Nevertheless, the hands-off nature of the
government continues, as it is bounded by its reliance on high gaming tax revenues,
which had hindered a number of its initial attempts to revise the industry’s business
routines toward those of a modern economic sector. Instead, evidence (see, e.g., Chang
2007) shows that although business routines do evolve, they are adjusted such that the
reliance of the industry’s GGR on the gambling room business model sustains or is
even reinforced.
Since the decision made by the Singapore government to legalize casino gaming,
a new model of business organization and routine for the practices in this industry
in Asia has evolved. In comparison with Macau, the social structure and legal system
(including its enforcement mechanism) in Singapore are much better developed. It is
commonly anticipated that the aforementioned business routines employed in Macau
will not be replicated in Singapore. Rather Singapore’s casinos have formulated a set of
their own business practices that accommodate its speciﬁc social and political contexts.
Indeed, the two contrasting and noticeable cases presented by Macau and Singapore
are undoubtedly “valuable reference points for other Asian casino jurisdictions” but
“should never be considered directly replicable” (Siu 2008, 21).
Dynamic Relationship between Institutional Changes
and Market Progress
Since the beginning of the twenty-ﬁrst century, changes in social perception in favor
of casino gaming as a modern entertainment sector, accompanied by reduction of
regulatory restrictions, have generated positive dynamics to further push the progress
of this industry. In other words, the recent changes in the formal rules and informal
constraints in the related Asian jurisdictions have expanded the boundary of their
markets, allowing the industry as a whole to enjoy the beneﬁts of increasing returns to
scale. In turn, the direct and indirect economic incomes generated during the process
of market growth may provide additional justiﬁcation for casino gaming to be legalized
or expanded further.
In addition to the cases of Macau and Singapore, the dynamic relationship between
institutional changes and market progress can be identiﬁed also in various major juris-
dictions as well as in the emerging markets in Central and West Asia. For example, after
its independence from the former Soviet Union bloc in 1991, the loosely formulated
and enforced legal system in Kazakhstan might unintentionally foster local enterprises
to chase after short-term monetary returns. However, it has been reported that “casi-
nos mushroomed across” the major cities of the country (Yogonet Group 2007), and
shady activities, including money laundering, were widely evident. As a measure to
counterreact to social pressure, the government instituted new policies to close down
most of the country’s casinos in 2007 and permitted only a few of them to continue
business in “two small resort towns” (ibid). As discipline of the market was restored
to a socially acceptable level, and potential economic beneﬁts derived from the casino

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78
casinos
industry once again caught the attention of the general public and the government, the
number of approvals granted to casinos was increased to 28 in 7 cities in 2009 (Angel
2009). During this process, the progress of casino gaming in Kazakhstan from the 1990s
was obviously inﬂuenced by changes in related regulations and public interests, given
the market demand.
In considering the unique attributes of casino gambling and gaming, as well as
the interrelated changes between social, political, and economic institutions in the
progress of the Asian jurisdictions, their ambitions to develop in a modern sense as
high value-added entertainment businesses have evidently accelerated. Other than any
signiﬁcant social and/or political conﬂicts as discussed, the existing development path
will continue, and the efﬁciency of their business routines will be evaluated.
Social Benefits and Costs Associated with
the Growth of the Markets
.............................................................................................................................................................................
On account of the rapid growth of the Asian economies, especially the dramatic income
and wealth effects that have arisen in China and the anticipated progress of India, the
growth in casino gaming would unarguably bring about business opportunities to
other related sectors as well as inﬂuence the social and economic welfares of local
communities. However, owing to the less developed social and political systems in
most Asian countries, drawbacks such as social moral values and regulatory systems
counteract the monetary beneﬁts derived (and potentially derived) from the growth in
casino gaming. By analyzing such from the interest of sustainable growth, a reasonable
(but not necessarily optimal) balance between the growth of the industry and its social
costs and impacts must be attained.
Direct and Indirect Social Beneﬁts Associated with
Growth in Casino Gaming
In line with the experiences of other nations throughout the world (see, e.g., Hall
and Hamon 1996; Nichols, Giacopassi, and Stitt 2002; Meister 2005; etc.), the recent
development of casino gaming in various Asian jurisdictions re-validates the argu-
ment that legalization and growth of this industry provide a considerable amount
of economic income, hence resources and opportunities for promoting tourism, and
urban development and re-development. In the process, investments made by related
ﬁrms further stimulate employment and income in the jurisdiction as well as busi-
ness opportunities for other hospitality-related businesses, such as hotels and retail
(i.e., the accelerator and multiplier effects7). To sustain the growth of this particular

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the economics of asian casino gaming and gambling
79
entertainment-based business, the provision of “fresh experiences” to complement
routine gambling activities has been a common and necessary tactic undertaken by the
industry. Thus periodical renovations and reinvestment in ﬁxtures not only maintain
the vigor of the industry; they also contribute to economic growth.
Returning to the example of Kangwon Land in South Korea, it is well documented
that “casino development as a strategy for economic rejuvenation of the county is
well recognized” (Cho 2002, 185). On top of the casino revenue generated by this
property, local employment is safeguarded. In addition, the success of Kangwon Land
also contributes a set of ﬁxtures that enhance the development of the county’s tourism
and social welfare. As pointed out by the CEO of Kangwon Land, 10 percent of the
property’s annual proﬁts since its opening in 2000“have been spent on various ventures
to support local communities” (Lee 2010a).
Similarly, monetary contributions to local communities made by the respectiveAsian
casino industries (e.g., Macau, the Philippines, Malaysia, etc.) in one form or another
also are unquestionable. Indeed, contributions are made either directly by the casino
ﬁrms to support various social and charity programs or indirectly through tax pay-
ments, which strengthen the ﬁscal position of the public sector to sponsor social welfare
and investment programs. For example, even though in the case of Malaysia where
casino gaming is highly restricted and only approved in a remote area of the country,
Genting Highlands organizes and supports various forms of charity concerts and sport
events as a measure to win social recognition.
Casino Gaming as a Threat to Social Harmony and
Economic Efﬁciency
Despite the explicit social beneﬁts, the social costs of casino gaming have long been
the most crucial aspect arguing against the legitimacy and progress of the industry.
Nevertheless, differentiation between social impacts and social costs, and measurability
of social costs in gambling studies are always controversial topics in economics (Walker
and Barnett [1999] conducted comprehensive review discussions on these topics). It
is pointed out that in gambling studies “most (non-economists) authors have adopted
an ad hoc approach—asserting that some activities constitute costs to society and then
quantifying the impact of those activities” (ibid, 183). Besides, from an economic per-
spective, not only have researchers inappropriately classiﬁed numerous consequences
of pathological gambling as “social costs”; they have also omitted several legitimate
social costs from their studies. Some of these costs are associated with government
restrictions and the legalization process” (204). Nevertheless, the arguments by Walker
and Barnett are still subject to continuous debate (see, e.g., Collins and Lapsley 2003).
Consistent with the arguments of Walker and Barnett (1999), and in view of the
particular social and political contexts in Asia, it is arguable that to a large extent
negative social impacts (e.g., adverse effects to social harmony) rather than social costs

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casinos
may pose major threats to the legalization and growth of casino gaming. Parallel to
the recent growth of casino gaming in Asia, and driven by the less developed social
structure in many of the jurisdictions, extra (instead of gross) amounts of economic
resources consumed by the non-casino sectors (including the public sector) to cope
with gambling problems could take place at the cost of other social and economic
sectors, in the form of forgoing better alternative uses of the same resources. Inasmuch
as most Asian economies have been in stages of development or transition since the
last quarter of the twentieth century, economic efﬁciency from alternative uses of
certain public resources to cope with negative spillover effects onto society could be
much higher. For example, economic returns derived from funding a job training
program (or an infrastructure project, etc.) could be much higher than a responsible
gambling program (or a pathological gambling center). Nevertheless, it is probably
more equitable to categorize the direct expenditures spent by casino ﬁrms on various
internal and external programs to grapple with or prevent negative spillover effects as
business costs rather than social costs.
Owing to high propensity of Asians to demand casino gambling, and the related
drawbacks in the regulatory systems of many jurisdictions, concerns over the negative
effects on social harmony are indeed much more profound than those over social costs.
Forexample,eventhoughtheSingaporegovernmentiswidelyaccreditedasbeinghighly
transparent as well as efﬁcient and proactive, there have been widespread debates and
concerns about casino legalization, in particular, that the business of casino gambling
may signiﬁcantly hinder social harmony in the country. Indeed, protesters of casino
gaming, such as Singapore’s National Council of Churches, have stressed that a“country
which may pride itself on having the best entertainment resort with gambling facilities
is unlikely to be a wholesome family-friendly society, which our government seeks to
advance” (Seneviratne 2005). In addition, surveys conducted by local organizations
have pointed out that “Singaporeans are more concerned about the proposed casino
eroding their value system rather than its social cost” (ibid).
In other socially and/or politically less developed Asian countries, widely reported
social problems linked to the practice of casino gaming have posed signiﬁcant threats
to social harmony. For example, crime, commercial sex, drugs, money laundering,
and so on have triggered many debates over the social impacts of casino gaming. It is
however necessary to carefully examine and gauge whether or not the gross amount
of expenditures spent to deal with related problems presumably brought about by
legalization and practice of casino gaming are straightforward social costs, given that a
large proportion of these monetary payments do not necessarily lower the net economic
efﬁciency.
Balance between Scale of Business and Social Costs/Impacts
Given the evidence illustrated so far in relation to the issues of Asian casino gambling
and gaming, it is clear that the development and growth of casino gaming in Asia are

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the economics of asian casino gaming and gambling
81
by no means cost-free. As a socially sensitive economic sector where such non-market
factors as culture and religion play essential roles in evaluating the overall social value,
negative social impacts may drive the focus of the community toward only the social
costs associated with casino gaming. Given that social acceptance, hence continuous
public approval of casino gaming, are preconditions for the industry to remain in
business, it becomes evident that a reasonable balance between the scale of business in
this industry and its social costs and impacts is a key challenge deemed to be addressed
by all related parties.
As summarized in ﬁgure 4.6, to sustain the growth of Asian casino gaming, each
jurisdiction should aspire to attaining growth at a reasonable scale by taking into
considerationthesocialbeneﬁtsandcosts. Inthisprocess,thefeasibilitymaybeadjusted
in accordance with the social and political perceptions on the social impacts of this
industry. Owing to the nature of such normative variables as culture, religion, political
interests, and the like, related institutions should recognize that a balance between the
scale of casino gaming and its social impacts could hardly be optimal, as are the eventual
social beneﬁts and costs observed by the general public.
In considering the variations in social values, political systems, economic struc-
tures, and stages of economic development, the necessary course of actions to realize
the principles as outlined in ﬁgure 4.6 to balance the scale of casino gaming and its
social costs and social impacts would never be identical across various Asian coun-
tries/regions. Indeed, it is a matter of the degree of public interest in a jurisdiction.
While culture and religion in some jurisdictions may play a dominant role, political par-
ties in other jurisdictions may be able to exert more inﬂuence in determining the scale
of this industry and the changes involved. Furthermore, in some other jurisdictions,
economic interests may take the lead in driving related decisions of the community and
government.
Social benefits and costs of casino gaming
Tourism
Casino
gaming
Economic
Social
impacts
Social benefits and
costs of institutions
Social value
Political system
Culture
Relegion
Legal system
Political interests
Social and political contexts in Asia
Education
efficiency and performance
Other
economic
sectors
figure 4.6 Social beneﬁts, costs and impacts of casino gaming in the Asian jurisdictions

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casinos
Conclusions and Remarks
.............................................................................................................................................................................
In a nutshell, the practices of casino gaming and gambling in Asia share many com-
mon features with those in world markets. Nevertheless, the unique attributes of the
demand in Asia for casino gambling, and the structure/organization of the individual
industries as outlined by public interests at the outset, differentiates its performance
from other jurisdictions in the world. Besides that, as excess demand is a common
phenomenon associated with the world casino gaming markets, and the scale of the
casino gaming industry is highly determined by public choice, they differ across vari-
ous Asian jurisdictions. These differences are largely explained by dissimilarities in (1)
culture, religion, level of education, stage of economic development, and hence the
income and wealth effects on the demand side; (2) industrial structure (including the
forms of competition), business organization and routines on the supply side; and (3)
legislative and regulatory systems, enforcement mechanisms, and dynamic interactions
between the power groups and the community on the institutional side. Despite dis-
similarities in scale and performance across various Asian casino markets, the gaming
industries share a common progression toward becoming a more modern and high
value-added entertainment economic sector instead of retaining a traditional business
form of gambling.
In considering the potential growth of casino gaming in Asia, which is supported by
the increasing income and wealth of the Asian economies and acceleration of interre-
gional and international ﬂows of population that have occurred since the end of the
twentieth century, proactive public policy measures undertaken by the related govern-
ments are necessary to sustain the growth of this industry and its real contributions
to the host jurisdictions. Indeed, evidence shows that for the sake of formulating an
effective institutional framework to balance the social, political, and economic interests
of the related parties, a free market approach or merely the replication of success stories
from one or a few jurisdictions may not serve the purpose. Instead, each jurisdiction
should cautiously examine both the positive and negative experiences of other juris-
dictions and refer to its own social, political, and economic contexts when approving
or altering the scale of the casino gaming industry and the related rules. In contrast
to the traditional economic sectors, other than economic interests, social and political
perceptions on the role of casino gaming exert signiﬁcant inﬂuence on the practice of
this industry.
Notes
1. According to the United Nations, Taiwan is classiﬁed as a de facto country instead of a
legally recognized independent country. Furthermore, in consideration of the particular
historical and political backgrounds of Hong Kong and Macau as the two SARs of China,
and for the purposes of this study, the term China in this study refers to Mainland China,

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the economics of asian casino gaming and gambling
83
where casino gaming is outlawed, but it has been legalized in both the Macau SAR and
Taiwan.
2. With reference to the living standards in China, this group is regarded as its middle income
class.
3. Given that the transparency of many casino jurisdictions in Asia is quite low, ofﬁcial data
which indicate the number of licensed casinos in related industries and their respective
GGRs are unavailable. Also, statistics displayed in various sources are occasionally found
to be inconsistent. Accordingly, only an approximation of the related scale instead of exact
numbers of the markets are indicated in the scatter chart (Figure 4.3). Nevertheless, the
data consolidated and presented in this chart fairly depict the existing scale of the related
industries.
4. Parallel to the number of licenses as predetermined by a jurisdiction’s government, the
physical conﬁguration of a casino industry is neither solely nor explicitly determined by
the markets. Instead, it is a matter of public choice largely inﬂuenced by the institutions in
a society and their dynamic changes over time.
5. Statistical veriﬁcation is constrained by the lack of data with regard to the many Asian
casino jurisdictions.
6. Emphasized in the role of institutions in this section, inﬂuences from both demand- and
supply-side factors and their attributes on the performance of casino gaming markets have
the same importance.
7. Due to the lack of related data, empirical testing on these two effects has never been
conducted. Nevertheless, the positive spillover effects from the growth of casino gaming
are widely acknowledged by related business sectors and the general public.
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chapter 5
........................................................................................................
HOW DOES IMPLEMENTATION
OF A SMOKING BAN AFFECT
GAMING?
........................................................................................................
john c. navin, timothy s. sullivan, and
warren d. richards
1 Introduction
.............................................................................................................................................................................
Basicmicroeconomictheorytellsusthatwhenconsumerchoiceisrestrictedconsumers
are made worse off. When faced with two alternatives, one that restricts choice and
one that does not, consumers prefer the unrestricted choice. Many state and local
governments have found that restricting consumer choice, as it relates to gaming, has
had such an impact. These restrictions have taken the form of restrictions on hours,
location, loss limits, and cruising requirements, for example. In the early days of
riverboat gaming, a number of restrictions were placed on access to the riverboats.
When Illinois opened its ﬁrst riverboat casino in 1991, a prohibition against any land-
based gaming was instituted. Boats would literally cruise the river while gaming took
place and then return to the dock. While Illinois was prohibiting land-based gaming,
Missouri found that it could set up“boats in moats.” These were small pools, or moats,
dug out next to the river and ﬁlled with river water. Barges were then ﬂoated in these
moats and casinos were built on top of them. These new casinos no longer made
patrons subject to the boarding, disembarking, and cruising requirements. According
to Bernard Goldstein, chairman and CEO of Isle of Capri Casinos, “bettors didn’t like
cruising. When they wanted to get on, they wanted to get on, and when they wanted
to get off, they wanted to get off.1” Similarly, both Missouri and Iowa placed loss limits
on their gamblers. The casinos and the state gaming commissions quickly realized that
restrictions on the amount people could wager and lose were costing them money.
A study by John McGowan and Muhammad Islam (2003) estimated that removal of
the loss limits would increase state and local tax revenue in Missouri by $50 million. In

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addition they estimated that $27 million in state and local tax revenue was being lost to
Illinois by patrons being able to simply drive into Illinois and not face the constraint of
a loss limit. Over time, restrictions on entry and spending have been removed, and the
casinos have seen an increase in both admissions and total handle.
As those restrictions on gaming have disappeared, new restrictions have appeared—
not limited to just riverboats,but to all establishments. These restrictions are manifested
in smoking restrictions, including total smoking bans.
Smoking bans have proliferated across the United States and the globe in recent years.
As shown in ﬁgure 5.1, as of 2011 roughly half of all U.S. states had banned smoking
in all public places. A handful of other states have banned smoking in most workplaces
and some hotels and restaurants. A number of cities and counties have implemented
local smoking bans where no statewide ban exists.
More recent bans have been implemented in response to growing health concerns
regarding second-hand smoke. Earlier bans focused mostly on the discomfort suf-
fered by nonsmokers and those (such as asthma patients) who are especially sensitive to
cigarette smoke. As such, most early bans required businesses to set aside smoking areas
ingovernmentbuildingsorrequiredrestaurantstodesignateaportionof theirseatingas
a nonsmoking area. However, as concerns have increased regarding the possible health
effects of second-hand smoke, state legislatures have focused on smoking as a poten-
tial workplace safety issue. The policy arguments that call for safety equipment and
ergonomic workspaces have been extended to the protection of workers from cigarette
smoke. Generally there are few exemptions to the smoking bans. In many areas the only
exemptions are hotels, long-term care facilities (which may, under certain restrictions,
designate smoking rooms), private residences, certain private clubs, and tobacco shops.
Smoking restrictions, such as these, raise objections from smokers’ groups and the
business community. Smokers, naturally, resent the inconvenience of being unable to
smoke or of being forced outside to smoke. Businesses, especially bars and restaurants
that rely on discretionary dollars, fear they will lose revenue if patrons are unable to
smoke (or are heavily inconvenienced). Patrons suffering such inconvenience may not
stay as long or may simply stay at home, where they can smoke more conveniently.
The gaming industry, and casinos especially, are quite unhappy with the smoking
restrictions. Anecdotal evidence suggests that a disproportionate number of casino
patrons smoke. Patrons forced to leave the casino to smoke may be less likely to return
to the table or may forgo visiting the casino altogether. This is a major concern for
establishments within a short distance of gaming establishments not subject to such
restrictions. For example, the Illinois riverboat casinos in Alton and East St. Louis,
as shown in ﬁgure 5.2, are within easy driving distance of four casinos in Missouri.
(All four are less than 30 miles away.) The Casino Queen in East St. Louis is directly
across the Mississippi River (approximately two miles) from both Lumiere Place and
the newly opened River City casino in south St. Louis and is a short (roughly 25-mile)
drive from the two casinos west of St. Louis. While the Illinois casinos are subject to the
smoking ban, gamblers wishing to smoke and gamble need only drive across the river
to Missouri, where no such restrictions exist.

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how does implementation of a smoking ban affect gaming?
89
This chapter reviews the current literature on the impact of restrictions on patron
smoking on gaming behavior. It also provides a brief case study of the riverboat gaming
market in Illinois and Missouri to highlight the issues associated with the imposition of
localized smoking restrictions. The case study uses thirteen years’ worth of data—two
and a half of which follow the smoking ban’s implementation—to evaluate whether the
smoking ban appears to have reduced the revenues of the casinos located in the Illinois
portion of the St. Louis Metropolitan area.2 We use monthly data on the amount
of money wagered at table games and slot machines at the casinos in the St. Louis
Metropolitan Area. These data are reported by the casinos to the respective state gaming
commissions and are published each month. Controlling for other factors, we will
attempt to isolate the impact of the smoking ban on the Illinois casinos.
The remainder of this chapter is organized as follows. Section 2 summarizes previous
studiesregardingtheimpactof smokingbans. Section3summarizesthedatausedinthe
study. Section 4 uses change-point analysis to examine the effect of the Illinois smoking
ban. Section 5 uses the Missouri casinos as a control group to examine the effect of the
ban on Illinois casinos. Section 6 uses regression methods to isolate the effect of the
ban. Section 7 provides a summary and discusses implications of the ﬁndings.
2 Research on Smoking and Gaming
.............................................................................................................................................................................
While the press is ﬁlled with speculation regarding the impact of smoking bans on
gaming, relatively few careful empirical studies have been conducted. Most press pieces
report year-to-year changes following a ban, with no attempt to control for other factors
that may be at work. Over the last few years, however, there has been an increase in
interest as to the impact of smoking bans—in part because they have a large impact on
tax revenues. This section examines the impact of smoking bans on various types of
gaming establishments.
There is a growing literature that examines the relationship between smoking and
gaming. Todd Harper (2003) found a number of interesting facts as they relate to gam-
blingandsmoking. BasedondatafromVictoria,Australia,hefoundthatsmokersspend,
on average, more than twice as much as nonsmokers at electronic gaming devices. D. S.
McGrath and S. P Barrett (2009) also found that smoking was correlated with a higher
rate of gaming. N. M. Petry and C. Oncken (2002) demonstrated that problem gam-
blers who smoke both gamble more often and spend more money than nonsmokers.
Smoking appears to be correlated also with problem gaming (see Grant et al. 2008 and
Rodda, Brown, and Phillips 2004 for example). This correlation has only worked to
reinforce the will of those looking to ban smoking in the presence of any type of gaming.
Delaware was the ﬁrst state to implement a statewide smoking ban that impacted
gaming establishments. Delaware legalized racinos in 1994. (A racino is a horseracing
track that also provides electronic gaming.) By the end of 1996, all three of Delaware’s

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casinos
racetracks permitted electronic gaming. Three studies have focused on the effect of
Delaware’s statewide ban. L. L. Mandel, B. C. Alamar and S. A. Glantz (2005) used data
from three racinos (Delaware Park, Dover Downs, and Harrington) to examine the
impact of the November 2002 statewide smoking ban on total gaming revenue at each
location as well as average revenue per machine at each location. Using ordinary least
squares and controlling for time, income, and seasonal effects, the authors found no
impact on either total revenue or average revenue per machine. Michael Pakko (2006a
and 2006b) also examined Delaware’s data. Using the same data as that used by Mandel,
Alamar, and Glantz and incorporating a slightly different estimation methodology,
Pakko found a clear adverse effect on revenue from gaming as a result of the smoking
ban. Richard Thalheimer and Mukhtar Ali (2008) used a different approach, estimating
separate demand functions for each of the three racinos. Using seemingly unrelated
regressions, and total handle, as opposed to total revenue, they found that the impact
of the smoking ban was signiﬁcant—accounting for almost a 16 percent decrease in
gaming demand. In later article Pakko (2008) found that those racinos which exhibited
the greatest loss in revenue were those that faced direct competition from gaming
establishments that did not restrict the ability of patrons to smoke.
As the proliferation of smoking bans, both local and national, has grown, the impact
on alternative forms of gaming has been investigated. M. K. Pyles and E. J. Hahn (2009)
examined the impact of local smoking bans on charitable gaming revenues. Using a
ﬁxed-effects model at the county level they found no measurable impact of the smoking
ban on charitable gaming. A recent report by the Minnesota Gambling Control Board
(2008) found a signiﬁcant negative impact on charitable gaming receipts after the
statewide smoking restriction was put in place. They found a reduction of between
7.5 and 8 percent of statewide gross receipts. Further they found that sites within 10
miles of the state border reported a loss in gross receipts of 17.7 percent post smoking
ban. In addition to simply being located near a border, the presence of tribal gaming
establishments (bingo halls, casinos, etc) also appears to impact venues that become
subjecttosmokingbans. Thestateof Washingtonimplementeditssmokingbanin2005,
and while it covered the state’s non-tribal casinos, Native-American establishments
were exempted. John Douglas (2008) reported a reduction in revenue of 13 percent
at Washington’s non-tribal establishments. S. A. Glantz and R. Wilson-Loots (2003)
examinedtheeffectof smokingrestrictionsonproﬁtsfrombingoandcharitablegaming
in Massachusetts. Using a liner regression model and establishing dummy variables to
indicate the presence of a complete ban on smoking in public areas, they found that
none of the smoking ban dummy variables were signiﬁcant. This study did ﬁnd a year-
to-year decline in those proﬁts over time but was unable to decipher the cause of the
year-to-year decline in proﬁts
A. Lal and M. Siahpush (2008) examined the effect of smoking bans on electronic
gaming expenditures in Victoria, Australia, as that effect compared to the rest of
Australia. Using data on monthly gaming expenditures from 1998 through 2005, they
found that the smoking ban resulted in a 14 percent reduction in expenditures on
electronic gaming devices.

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how does implementation of a smoking ban affect gaming?
91
Jonathan Macy and Erika Hernandez (2011) examined the impact of a local smoking
ban on an off-track betting (OTB) facility in Indiana. Using regression analysis to
compare per capita wagering at the OTB facility that banned smoking against two
facilities that did not, the authors found no difference in the longitudinal trend in
per capita wagering.
An additional area of focus has been the impact of a statewide smoking ban on
riverboat casinos. Riverboat casinos operate in a number of states (Indiana, Iowa,
Missouri, Illinois, Mississippi, and Louisiana), but only Illinois has banned smoking
on riverboat casinos. The focus of the remainder of this chapter is an examination of
the impact of the Illinois smoking ban. To date, three previous studies have examined
this ban. John Navin, Timothy Sullivan, and Warren Richards (2009) examined the
impact of the smoking ban on the two Illinois casinos (Casino Queen in East St.
Louis and the Argosy Casino in Alton) located in the St. Louis metropolitan area.
Using monthly data from 2000 through 2009, they found that Illinois casino revenue
dropped between 8 and 24 percent depending on the type of gamine device (tables
or electronic) and the method of estimation used. More recently Thomas Garrett and
Michael Pakko (2010) also examined the impact of the Illinois ban on both admissions
as well as revenue. Garrett and Pakko divided the Illinois gaming market into four areas:
Chicago, Southern (Metropolis, Ill.), Quad Cities, and St. Louis. Using a log-linear
model and data from 1997 through 2008, they found a decline in both admissions and
adjusted gross revenue (total handle less payouts). Their revenue estimates ranged from
a 10 percent to 30 percent decline for the Illinois casinos. Finally, Jenine Harris et al.
(2011) examined monthly casino admissions in Illinois and the surrounding states that
have non-tribal casino gaming (Missouri, Indiana, and Iowa) to test for the impact of
the smoking ban. Using a model that incorporates, time, location, and various measures
of economic activity, Harris et al. found that the decline in Illinois’ casino admissions
was not signiﬁcantly different from those of surrounding states. They further concluded
that the decline in Illinois’ casino revenue is not therefore due to the smoking ban but
rather is a result of slower economic activity.
As with much research surrounding smoking and gaming,both sides of the debate are
quick to dismiss studies by the proponents of the other side. The studies described above
that found no impact due to a smoking ban were all published in Tobacco Control, a
journal that is seen as a critic of the tobacco industry. Such studies are roundly criticized
by smokers’ rights groups, which offer up opposing studies arguing that smoking bans
hurt business.
While no single study can hope to end the debate, the data set we use for this chapter’s
study is somewhat unique, and we hope it will work to highlight some of the issues
discussed above as they relate to smoking bans. While this study looks speciﬁcally at
the riverboat gaming issue, the results obtained here are generalizable to other forms
of gaming where local substitutes not subject to the same form of consumer restriction
exist. We used data for a single metropolitan area that (at the time) hosted ﬁve casinos
within a 30-mile radius. We found that two of the casinos were affected by a smoking
ban implemented on one date; three were not. This data set thus provides an excellent

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casinos
opportunity to isolate the impact of the smoking ban from that of other factors. In
addition we have expanded on our earlier work by adding an additional 18 months of
data following the implementation of the Illinois ban.
3 Data and Methodology
.............................................................................................................................................................................
The Illinois smoking ban went into effect on January 1, 2008, and, in theory, examining
the impact of the smoking ban should be as simple as examining the Illinois casinos
for signs of a structural break in activity. If the smoking ban had an important negative
effect on the Illinois casinos near the Missouri border, we should expect to see a siz-
able drop in two data series collected by the Illinois gaming commission—table drop
(the amount collected at table games, such as blackjack) and slot handle (the amount
deposited into slot machines).
As shown in ﬁgures 5.3 and 5.4, there was a substantial drop in activity at the
Alton (Ill.) casino in January 2008. Table drop fell by nearly a quarter—from just over
$3 million per month throughout most of 2006–2007 to levels near $2.5 million each
month during 2008. Slot handle meanwhile fell by about a third—from levels near $150
million to levels close to $100 million.
Figures 5.5 and 5.6 show a similar drop in activity at the East St. Louis (Ill.) casino.
Compared with the corresponding month of 2007, table drop at the East St. Louis
casino plunged by about one-fourth in the second half of 2008. Similarly monthly slot
handle totals fell by about one fourth in the second half of 2008.
In isolation, while interesting, this evidence of drops can’t necessarily be attributed to
the smoking ban. The drops could reﬂect the economic downturn, new entertainment
alternatives in the St. Louis area, or changes in gamblers’ tastes.
A further important complication in the analysis is the opening of Lumiere Place, a
major St. Louis (Mo.) casino, on December 19, 2007. Lumiere Place immediately took a
position near the top of the St. Louis area casinos in terms of revenue. Furthermore, as
might be expected, its opening corresponded with an aggressive marketing campaign.
Because Lumiere Place opened less than two full weeks before the Illinois smoking
ban went into effect, it is extremely difﬁcult to disentangle the two effects on Illinois
casinos. In fact, because it opened in mid-December, we do not have even one complete
month’s worth of data with Lumiere Place in the region prior to the smoking ban’s
implementation.
We pursued three strategies to disentangle the results. First we used a change-point
test to see if a change point was detected and, if so, whether a December or January
change point dominated. Second, we treated the three Missouri casinos (other than
Lumiere Place), which were impacted by Lumiere Place but not the smoking ban, as a
control group for isolating the effect of Lumiere Place. Finally, we used a time series
regression analysis.

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how does implementation of a smoking ban affect gaming?
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4 Change-Point Analysis
.............................................................................................................................................................................
Change-point analysis is a collection of methods used to look for structural change in
a time series. The simplest case considers whether the population mean differs before
and after some point in time (the change point). Other analyses may be concerned
with changes in other parameters, such as the median or variance. Non-parametric
tests consider whether the underlying distribution has changed (without specifying a
parameter).
Not surprisingly, given the patterns found in ﬁgures 5.3 through 5.6, a simple test of
difference in means indicates that both the Alton and the East St. Louis casinos have
statistically different means for the periods before and after the smoking ban. As shown
in table 5.1, the Alton casino’s monthly average table drop fell from over $4 million to
just over $2 million. Its slot handle fell from a monthly average of over $140 million
to just under $100 million. Similarly, as shown in table 5.2, the East St. Louis casino’s
table drop fell from a monthly mean of about $12 million to an average of about $10
million. Its monthly average slot handle fell from about $212 million to just over $190
million. All of these decreases are statistically signiﬁcant, using a standard difference in
means test.
An important shortcoming of these difference-in-means tests is that they cannot
identify a unique change point. As previously discussed, the lower average during this
30-month period might reﬂect the opening of Lumiere Place in December 2007. As
shown in tables 5.1 and 5.2, similar drops are found when testing for a difference in
means beginning in December 2007. The standard difference-in-means test has no
method for determining which bifurcation dominates.
The tests described by A. N. Pettit (1979), however, can test the relative importance
of the breakpoints. Pettit provides a framework for using the Mann-Whitney-Wilcox U
test for a difference in distributions to test for a change point. In addition, Pettit suggests
a method for using the magnitude of the U statistic to select from different potential
change points.
Pettit’s method provides mixed results. U test statistics for the Alton casino indicate
that the opening of Lumiere was slightly more important than the smoking ban for
table drop, while for slot handle the two events are equal in terms of providing a break
point. For the East St. Louis casino, the implementation of the smoking ban appears
to be a stronger break point than the opening of Lumiere. However, as a reminder,
Lumiere Place was open for less than half of December 2007, meaning that the full
impact of the opening may not be reﬂected in the December 2007 data. This would
have the effect of biasing the results against a December 2007 change point.
While the change point results indicate that the January 2008 change point (imple-
mentation of the smoking ban) is important, it leaves open the possibility that two
separate change points occurred. It is entirely possible that the Illinois casinos were hit
with a double punch—ﬁrst the opening of Lumiere Place and then the implementation

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94
casinos
of the smoking ban. The struggling economy during the past year is likely a third fac-
tor. The next section attempts to control for these other effects by using the Missouri
casinos as a control group.
5 Comparison with the Missouri Casinos
.............................................................................................................................................................................
While the evidence presented in previous sections of this chapter indicates that the
Illinois casinos in the St. Louis Metropolitan Area saw sizable drops in gaming revenue
following the implementation of the smoking ban, they are far from deﬁnitive. They
leave open the possibility that the entrance of a new competitor drove the results (and
in fact one piece of evidence in section 4 indicates that the new competitor was a more
important factor). In addition the general downturn in the U.S. economy coincided
(roughly) with the implementation of the smoking ban.
Fortunately, a ready control group is available for the analysis—the three casinos in
the Missouri portion of the St. Louis Metropolitan Area that existed prior to December
2007. As shown in ﬁgure 5.2, the President Casino in St. Louis is less than two miles
away from the new Lumiere Place (much like the Casino Queen, located in East St.
Louis). Similarly, the two casinos west of St. Louis—Harrah’s in Maryland Heights and
Ameristar in St. Charles—are both about 20 miles from Lumiere Place (much like the
Argosy in Alton). The effect of the new casino on these three casinos should be similar
to the effects on the Illinois casinos. Furthermore, as all of the casinos are located in the
same metropolitan area (within a 30-mile diameter) prevailing economic conditions
should be very similar.
As shown in table 5.3, from 2007 to 2008 the two Illinois casinos saw a drop in
their combined slot handle that was higher in both absolute and percentage terms
than that of the three preexisting casinos in Missouri. The two Illinois casinos saw
a combined decrease of about 24 percent ($1.2 billion), compared with a decrease of
about 11 percent ($0.8 billion) at the three Missouri casinos. Lumiere Place’s slot handle
during 2008 was about $1.6 billion, indicating that it could not have single-handedly
accounted for the combined decrease at the ﬁve older casinos.
As shown in table 5.4, from 2007 to 2008 the two Illinois casinos saw a decrease in
table drop that was lower in dollar terms but higher in percentage terms than that of the
three preexisting casinos in Missouri. The two Illinois casinos saw a combined decrease
of about 16 percent ($31 million), compared with a decrease of about 13 percent ($40
million) at the three Missouri casinos. Lumiere Place’s table drop during 2008 was
about $108 million, indicating that it could have accounted for the combined decrease
at the ﬁve older casinos.
These results suggest that the smoking ban may have had an important effect on the
casinos in the Illinois portion of the St. Louis Metropolitan Area. If we are willing to
accept that the year-to-year decreases at the three preexisting Missouri casinos represent

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how does implementation of a smoking ban affect gaming?
95
the combined effects of Lumiere Place and the poor economy, the excess decrease at the
Illinois casinos would represent the effect of the smoking ban.
We formalized this analysis by examining the percent of revenue at the ﬁve preexisting
casinos that can be accounted for by the two Illinois casinos. The logic of this analysis
is straightforward: changes in the economy and the opening of Lumiere Place would
affect the size of the St. Louis market to be distributed across these ﬁve casinos but (to
the extent that the ﬁve casinos operate within the same market) would not affect the
distribution between Illinois and Missouri.
As seen in table 5.5, among the ﬁve preexisting casinos, there was a shift in gam-
ing revenue from the Illinois side to the Missouri side following the smoking ban.
Between July 1997 and the implementation of the smoking ban, the two Illinois casi-
nos accounted for (on average) 40 percent of the table drop and 41 percent of the
slot handle. Following the smoking ban, these percentages dropped to 34 percent and
36 percent, respectively. Not only did the gaming pie shrink (due to the economy and
the opening of Lumiere Place), but the percent of the pie going to Illinois got smaller
as well.
6 Regression Analysis
.............................................................................................................................................................................
Finally we estimated two regression models. The ﬁrst regression examines the Illinois
casinos individually. The second regression combines the two Illinois casinos.
The ﬁrst method utilized was to run individual regression models for the two Illinois
casinos including variables for the St. Louis area’s unemployment rate, the opening
of Lumiere Place, and the implementation of the smoking ban. This is essentially a
multivariate version of the difference-in-means tests examined in section 4, and it
allowed us to simultaneously examine the three effects. In particular, we estimated the
model as
REVit = αi + πiUEt + λiLUMIEREt + βiSMOKEBANt + εit,
where REV it is the revenue (either slot handle or table drop, either in levels or log form)
at casino-i (Alton or East St. Louis) during month-t; UEt is the St. Louis Metropolitan
Statistical Area unemployment rate during the month; LUMIEREt is a dummy variable,
equal to one-half in December 2007 and one starting in January 2008 (to represent the
fact that Lumiere Place was only open for part of the December 2007); SMOKEBAN t
is a dummy variable, equal to one starting in January 2008; and εit is a zero-mean,
homoskedastic error term assumed to follow a ﬁrst-degree autoregressive process. Also
included (but not shown in the above equation) is a set of month dummies to account
for seasonality.
Table 5.6 indicates that the Alton (Ill.) casino’s revenues were sizably lower after the
smoking ban. The estimated coefﬁcients indicate that (controlling for other factors)

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96
casinos
the casino’s monthly slot handle dropped by about $23 million due to the implemen-
tation of the smoking ban. The semi-log model estimates a 20 percent decrease in the
slot handle due to the smoking ban. The effect on monthly table drop is statistically
insigniﬁcant in the linear model, but the semi-log model estimates a 23 percent negative
impact.
Table 5.7 indicates that the East St. Louis casino’s slot handle was lower following the
smoking ban but ﬁnds little evidence that the table drop was affected. The linear model
estimates indicate that (controlling for other factors) monthly slot handle revenues
decreased almost $50 million due to the smoking ban. The semi-log model estimates a
23 percent decrease. Neither model ﬁnds a statistically signiﬁcant impact on table drop.
ThesecondmethodutilizedwastosumthetwoIllinoiscasinos’revenuesandestimate
that
REVt = α + πUEt + λLUMIEREt + βSMOKEBANt + εt,
where REV it (either in levels or its log) is the combined revenue (either slot handle
or table drop) at the Illinois casinos (Alton and East St. Louis) during month-t. UEt,
LUMIEREt, and SMOKEBAN t are as deﬁned earlier.
Table 5.8 indicates that most of the drop in Illinois casino revenues can be attributed
to the smoking ban. All else being constant, the implementation of the smoking ban
corresponds to a drop of 26 percent (or $86 million per month) in slot handle and
a decrease of 22 percent (or $3 million) in table drop. Both effects are statistically
signiﬁcant.
7 Conclusion
.............................................................................................................................................................................
The proliferation of legalized gambling in the United States over the past half century
has been dramatic. In a fairly short period of time state lotteries have become legal and
ubiquitous. Casinos in their various forms—standalone, riverboats, and those attached
to other enterprises—have left their previous conﬁnes of Las Vegas, Atlantic City, and
Native-American reservations. They now dot the landscape, in some cases as sizable
tourist attractions.
As legalized gaming expanded, it has become an important source of revenue for state
and local governments. For example, many states earmark lottery money for education.
In addition, casinos often pay sizable boarding fees and taxes to states, counties, and
cities. In many cases tax revenues from the gaming industry are the difference between
balanced budgets and sizable cuts to public services.
Public ofﬁcials have struggled to balance the economic and ﬁnancial importance
of the gaming industry with general efforts to limit access to gaming. In the United
States these limits start with restrictions on a casino’s location. These range from typical
zoning regulations that affect all businesses to gaming-speciﬁc rules that limit gaming

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how does implementation of a smoking ban affect gaming?
97
to boats and Native-American reservations. Additional regulations include loss limits
(that place an upper bound on the amount of money that a gambler may lose in one
day) and limits on times that gamers may enter the casino. Prior research (discussed
in the introduction of this chapter) indicates that such limits reduce the amount of
wagering that takes place at casinos.
This chapter examined the effect of indoor smoking bans in the state of Illinois. While
the bans are not directed speciﬁcally at casinos, the bans have a disproportionate effect
on casinos (as well as bars and some restaurants). Using a variety of methodologies, the
results indicate that, as expected, the Illinois smoking ban appears to have encouraged
a sizable number of gamers to travel across the border to Missouri.
This chapter does not attempt to provide a societal cost-beneﬁt analysis to smoking
bans. Aside from the inconvenience to the smokers, the ban appears to reduce casino
revenues, which indirectly reduces state and local tax revenues. These must be balanced
against the beneﬁts of the ban, which might include the public health beneﬁts of
potentially lower smoking rates and the reduction in second-hand smoke exposure
for the casino employees. Inconvenience caused by the ban that discourages problem
gambling and its potential side effects would be an additional potential beneﬁt. Since
most of these issues are nearly impossible to quantify, we do not attempt to pass
judgment on the ban.
Appendix
.............................................................................................................................................................................
figure 5.1 Statewide smoking bans in the United States
Source: U.S. States Smoking Bans. Wikipedia; http://en.wikipedia.org/wiki/File:US_states_smoking_bans.svg.

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## Page 119

98
casinos
Banned in
restaurants
Banned in
non-hospitality
workplaces
Banned in
bars
No
statewide
ban
figure 5.1 (Continued)
Illinois
Missouri
Mississippi River
Missouri 
River
N
W
River City 
Casino St.
Louis, MO
Casino Queen
East St. Louis, IL
Argosy
Alton, IL
Harrah’s
Maryland Heights,
MO
Ameristar
St. Charles, MO
S
E
Lumiere Place 
St. Louis, MO
figure 5.2 Casinos in the St. Louis metropolitan area

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how does implementation of a smoking ban affect gaming?
99
8,000
7,000
6,000
5,000
4,000
$1,000s
3,000
2,000
1,000
Jul-97
Jul-99
Jul-01
Jul-03
Month
Jul-05
Jul-07
Jul-09
-
figure 5.3 Table drop, Alton Casino
Source: Illinois Gaming Commission
200,000
150,000
100,000
$1,000s
50,000
Jul-97
Jul-99
Jul-01
Jul-03
Month
Jul-05
Jul-07
Jul-09
-
figure 5.4 Slot handle, Alton Casino
Source: Illinois Gaming Commission

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## Page 121

100
casinos
18,000
16,000
14,000
12,000
10,000
8,000
$1,000s
6,000
4,000
2,000
Jul-97
Jul-99
Jul-01
Jul-03
Month
Jul-05
Jul-07
Jul-09
-
figure 5.5 Table drop, East St. Louis
Source: Illinois Gaming Commission
Jul-09
Jul-07
Jul-05
Jul-03
Month
Jul-01
Jul-99
Jul-97
350,000
300,000
250,000
200,000
150,000
$1,000s
100,000
50,000
-
figure 5.6 Slot handle, East St. Louis
Source: Illinois Gaming Commission

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how does implementation of a smoking ban affect gaming?
101
Table 5.1 Change-Point Tests for Alton Casino (Ill.)
Time Period
Table Drop
Slot Handle
July 1997–Dec 2007
Mean
4,244
140,640
n
126
126
Jan 2008–June 2010
Mean
2,313
99,102
n
30
30
z−statistic
20.3∗∗∗
12.0∗∗∗
U−statistic
72∗∗∗
36∗∗∗
July 1997–Nov 2007
Mean
4,252
140,678
n
125
125
Dec 2007–June 2010
Mean
2,342
100,290
n
31
31
z−statistic
19.3∗∗∗
11.1∗∗∗
U−statistic
73∗∗∗
36∗∗∗
Z-statistic is from a test of the null hypothesis that the means are equal,
versus the alternative that the means are different. Test allows for unequal
variances.
U-statistic is from the Wilcoxon Rank-sum test of equivalent distributions.
Means are reported in $1,000s.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.
Table 5.2 Change-Point Tests for East St. Louis Casino (Ill.)
Time Period
Table Drop
Slot Handle
July 1997–Dec 2007
Mean
12,075
211,873
N
126
126
Jan 2008–June 2010
Mean
9,959
190,169
N
30
30
z−statistic
6.2∗∗∗
5.2∗∗∗
U−statistic
28∗∗∗
20∗∗∗
July 1997–Nov 2007
Mean
12,062
211,545
N
125
125
(Continued)

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102
casinos
Table 5.2 (Continued)
Dec 2007–June 2010
Mean
10,081
192,192
N
31
31
z−statistic
5.6∗∗
4.2∗∗∗
U−statistic
25∗∗∗
17∗∗∗
Z-statistic is from a test of the null hypothesis that the means are equal,
versus the alternative that the means are different. Test allows for unequal
variances.
U-statistic is from the Wilcoxon Rank-sum test of equivalent distributions.
Means are reported in $1,000s.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.
∗∗indicates statistical signiﬁcance at the 0.05 level.
Table 5.3 Annual Slot Handle Sums ($1,000s)
Years
Illinois Casinos (2)
Missouri Casinos (3)
Lumiere
1997
1,282,420∗
1,712,296∗
1998
2,937,803
3,791,442
1999
3,516,918
4,260,818
2000
4,381,272
5,525,907
2001
4,367,535
6,507,868
2002
4,561,257
6,808,298
2003
4,314,689
7,142,920
2004
4,546,957
7,659,987
2005
4,652,003
7,655,842
2006
4,783,087
7,514,346
2007
4,894,994
7,044,033
58,019∗
2008
3,735,450
6,245,286
1,589,262
2009
3,394,179
6,132,851
1,844,438
2010∗
1,548,519∗
2,878,366∗
840,416∗
Sources: Missouri and Illinois gaming commissions. Lumiere opened
December 19, 2007. For all casinos, 1997 data include July through
December and 2010 data include January through June.

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how does implementation of a smoking ban affect gaming?
103
Table 5.4 Annual Table Drop Sums ($1,000s)
Years
Illinois Casinos (2)
Missouri Casinos (3)
Lumiere
1997
94,244∗
125,868∗
1998
177,774
242,532
1999
195,454
254,161
2000
196,092
288,825
2001
189,121
302,829
2002
199,281
306,637
2003
193,239
305,695
2004
205,976
322,645
2005
206,394
308,410
2006
198,233
315,975
2007
200,453
304,219
4,794∗
2008
169,306
263,750
108,826
2009
138,576
312,626
169,600
2010∗
60,275∗
153,357∗
75,216∗
Sources: Missouri and Illinois gaming commissions. Lumiere opened
December 19, 2007. For all casinos, 1997 data include July through
December and 2010 data include January through June.
Table 5.5 Percentage in Illinois
Time Period
Table Drop
Slot Handle
July 1997–Dec 2007
Mean
40.1
40.8
N
126
126
Jan 2008–June 2010
Mean
33.6
36.2
N
30
30
z−statistic
6.5∗∗∗
12.1∗∗∗
U−statistic
24∗∗∗
53∗∗∗
Thevariablemeasuresthepercentageofrevenueattheﬁvepreexisting
casinos that is accounted for by the two Illinois casinos.
Z-statistic is from a test of the null hypothesis that the means are
equal, versus the alternative that the means are different. Test allows
for unequal variances.
U-statistic is from the Wilcoxon Rank-sum test of equivalent
distributions.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.

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104
casinos
Table 5.6 Coefﬁcient Estimates for Alton (Ill.) Casino
Slot Handle
Ln (Slot Handle)
Table Drop
Ln (Table Drop)
UE
−1,136
(1,887)
−0.004
(0.01)
−227∗∗∗
(51)
−0.05∗∗∗
(0.02)
LUMIERE
−13,632
(13,387)
−0.09
(0.10)
−517
(670)
−0.17
(0.14)
SMOKEBAN
−22,863∗∗
(9,954)
−0.20∗∗∗
(0.08)
−559
(549)
−0.23∗∗
(0.12)
R2
0.96
0.97
0.92
0.95
N
156
156
156
156
Sample is July 1997 through June 2010.
Standard errors are given in parentheses.
Slot handle and table drop are measured in $1,000s. UE is measured in percentage points.
The model also includes month dummies. Estimated correcting for AR(1) errors.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.
∗∗indicates statistical signiﬁcance at the 0.05 level.
∗∗indicates statistical signiﬁcance at the 0.10 level.
Table 5.7 Coefﬁcient Estimates for East St. Louis (Ill.) Casino
Slot Handle
Ln (Slot Handle)
Table Drop
Ln (Table Drop)
UE
7,502∗∗
(3,386)
0.04∗∗
(0.02)
214
(183)
0.02
(0.02)
LUMIERE
−9,313
(27,269)
−0.06
(0.15)
−1,829
(1,467)
−0.16
(0.13)
SMOKEBAN
−49,918∗∗
(22,005)
−0.23∗
(0.12)
−1,538
(1,178)
−0.13
(0.10)
R2
0.83
0.81
0.84
0.85
N
156
156
156
156
Sample is July 1997 through June 2010.
Standard errors are given in parentheses.
Slot handle and table drop are measured in $1,000s. UE is measured in percentage points.
The model also includes month dummies. Estimated correcting for AR(1) errors.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.
∗∗indicates statistical signiﬁcance at the 0.05 level.
∗∗indicates statistical signiﬁcance at the 0.10 level.

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how does implementation of a smoking ban affect gaming?
105
Table 5.8 Coefﬁcient Estimates for Combined Illinois Casinos
Slot Handle
Ln (Slot Handle)
Table Drop
Ln (Table Drop)
UE
6,407
(4,733)
0.02
(0.01)
−87
(177)
−0.01
(0.01)
LUMIERE
−14,045
(17,483)
−0.04
(0.05)
−920
(841)
−0.06
(0.06)
SMOKEBAN
−86,053∗∗∗
(17,400)
−0.26∗∗∗
(0.05)
−3,114∗∗∗
(845)
−0.22∗∗∗
(0.06)
R2
0.93
0.93
0.85
0.87
N
156
156
156
156
Sample is July 1997 through June 2010.
Standard errors are given in parentheses.
Slot handle and table drop are measured in $1,000s. UE is measured in percentage points.
The model also includes month dummies. Estimated correcting for AR(1) errors.
∗∗∗indicates statistical signiﬁcance at the 0.01 level.
∗∗indicates statistical signiﬁcance at the 0.05 level.
∗∗indicates statistical signiﬁcance at the 0.10 level.
Table 5.9 Summary of Results
Strategies
Slot Handle
Table Drop
Change Point
Alton
no impact
no impact
East St. Louis
negative
negative
Missouri Control Group
Combined
negative
negative
Regression
Alton
negative
negative
East St. Louis
negative
no impact
Combined
negative
negative
Notes
1. Brunker, Mike. “Riverboat Casinos Going Nowhere Fast,” msnbc.com, Aug. 9, 2004;
http://www.msnbc.msn.com/id/5539243/ns/news-the_mighty_miss/t/riverboat-casinos-
going-nowhere-fast/#.TonA_mUfeEw.
2. This chapter is based on the paper “Will Riverboat Proﬁts go up in Smoke? The Effect of
the Illinois State Smoking Ban on Casino Revenue,” presented at the Midwest Economics
Association Annual Meetings, Cleveland, March 2009.

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106
casinos
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Mandel, L. L., B. C. Alamar, and S. A. Glantz. 2005. Smoke-free law did not affect revenue
from gaming in Delaware. Tobacco Control 14(1):10–12.
McGowan, John R., and Muhammad Islam. 2003. Economic effects of proposed tax increases
and removal of loss limits on the Missouri gaming industry. White paper. St. Louis:
Taxpayers Research Institute of Missouri and Associated Industries of Missouri.
McGrath, D. S., and S. P. Barrett 2009. The comorbidity of tobacco smoking and gambling: A
review of the literature. Drug and Alcohol Review 28(6):676–681.
Minnesota Gambling Control Board. 2008. Charitable gambling impact study: A brief review
of the ﬁscal impact of a statewide smoking ban on lawful gambling. Roseville: Minnesota
Gambling Control Board, Department of Revenue.
Navin, John C., Timothy S. Sullivan, and Warren D. Richards. 2009. Will riverboat proﬁts go
up in smoke? The effect of the Illinois’ state smoking ban on casino revenue. Edwardsville:
Department of Economics and Finance, Southern Illinois University.
Pakko, Michael R. 2006a. Smoke-free law did affect revenue from gaming in Delaware. Tobacco
Control 15(1):68–69.
——. 2006b. No smoking at the slot machines: The effect of a smoke-free law on Delaware
gaming revenues. Working Paper No. 2005-054C. St. Louis, Mo.: Federal Reserve Bank of
St. Louis.
——. 2008. Clearing the haze? New evidence on the economic impact of smoking bans.
Regional Economist, Jan., 10–11.
Petry, N. M., and C. Oncken. 2002. Cigarette smoking is associated with increased sever-
ity of gambling problems in treatment seeking pathological gamblers. Addiction 97(6):
745–753.
Pettit, A. N. 1979. A non-parametric approach to the change-point problem. Applied Statistics
28(2):126–135.

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Pyles, M. K., and E. J. Hahn. 2009. Smoke-free legislation and charitable gaming in Kentucky.
Tobacco Control 18(1):60–62.
Rodda, Simone, Stephen L. Brown, and James G. Phillips. 2004. The relationship between
anxiety, smoking, and gambling in electronic gaming machine players. Journal of Gambling
Studies 20(1):71–81.
Thalheimer, Richard, and Mukhtar M. Ali. 2008. The demand for casino gaming with special
reference to a smoking ban. Economic Inquiry 46(2):273–282.

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chapter 6
........................................................................................................
OVERVIEW OF THE ECONOMIC AND
SOCIAL IMPACTS OF GAMBLING IN
THE UNITED STATES
........................................................................................................
douglas m. walker
Over the past two decades academic interest in gambling behavior and the economic
and social impacts of legal gambling has increased signiﬁcantly. Researchers in many
nations have devoted more attention to gambling issues as the industry has grown. The
majority of published research has focused on problematic gambling behaviors and
the diagnosis and treatment of them. The research on gambling behavior has grown
signiﬁcantly. However, a relatively small portion of gambling research has been per-
formed in the business and economics disciplines. This is curious, given that the major
reasons casinos and other forms of legal gambling exist are economic in nature. Indeed,
despite the negative impact that the 2007–2009 recession has had on the casino industry
worldwide, governments continue to look toward legal casinos as way to alleviate ﬁscal
stress. Nowhere is this more evident than in the United States, as numerous states are
in the process of or are currently considering legalizing casinos. A similar pattern can
also be seen in countries across the globe.
The purported economic beneﬁts from casino gambling include tax revenues,
increased employment, higher wages and payments to capital, and enhanced eco-
nomic growth. These beneﬁts, should they occur, are not necessarily without costs. For
example, the casino industry may partially or entirely cannibalize other industries. In
addition, a small percentage of gamblers may exhibit problem gambling behavior. Such
people are believed to cause signiﬁcant social costs. The analyses of these beneﬁts and
costs of gambling—the economics of gambling—is a young ﬁeld of research, with only
a handful of researchers actively researching the various issues.
This chapter describes some of the critical economic and social issues, mainly related
to casino gambling, and my research on them. Although the empirical analysis tends to
focus on the United States, the various issues are relevant to all countries that have, or
are considering adopting, commercial casino gambling. This chapter is organized into

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109
six sections, by topic. Section 1 examines the explanatory factors in the adoption of
commercial casinos. Section 2 is a discussion of the economic growth effects of casino
gambling, including how gambling can affect growth after a natural disaster. Section 3
discusses the relationships among different gambling industries and the implications
of these relationships on government tax revenues. Section 4 is an introduction to
the social costs of gambling, including the relationship between casinos and crime. In
Section 5, I describe some the hurdles in cost-beneﬁt analysis as it applies to gambling.
Section 6 concludes.
1 Determinants of Casino Adoption
.............................................................................................................................................................................
The legalization of casino gambling is typically a controversial issue. Disagreement over
casinos arises from moral and religious objections to gambling, concerns over poten-
tially negative social impacts, as well as uncertainty as to the economic beneﬁts from
legalization. Clearly, recent history has shown that casinos have been legalized in a vari-
ety of jurisdictions, for a number of different reasons. Perhaps the greatest motivation
for introducing casinos is to raise tax revenues. Casinos are generally taxed at a relatively
high rate and therefore offer politicians a relatively easy source of revenue. Yet, casinos
are not always welcome, as demonstrated by the ongoing debate over casino adoption
in the Penghu Islands, Taiwan. A recent newspaper article suggests that Kyrgyzstan may
banallcasinosandonlinecasinos(Pumper2011). U.S.statesthatalreadywelcomelegal-
ized gambling in the form of lotteries are sometimes unsympathetic to the prospects of
casino gambling. What factors help to explain why casinos are—or are not—legalized?
This issue has not been analyzed for casinos, until recently. Peter Calcagno, John Jack-
son, and I recently examined this issue for the United States (Calcagno, Walker, and
Jackson 2010). The economics literature has a number of papers that have examined
the adoption of lotteries. Our study followed this work and applied a similar model to
analyze what factors seem to explain the adoption of casinos in the United States.
Prior to 1989, commercial casinos were legal only in Las Vegas, Nevada, and Atlantic
City, New Jersey. After an important legal decision (California v. Cabazon Band of Mis-
sion Indians 1987) and subsequent legislation (Indian Gaming RegulatoryAct 1988) the
stage was set for commercial casino legalization. By 1995 commercial casinos had been
legalized in eight states; thirteen states had them by 2010. Tribal casinos now operate
in around 30 states. If casinos represent an easy source of tax revenues, and if a state’s
population can easily travel to out-of-state casinos, why not just legalize casinos in your
state? The interesting question may be why more U.S. states have not introduced com-
mercial casinos. Calcagno, Walker, and Jackson (2010) examined state governments’
adoption of commercial casinos; it did not examine tribal casino decisions.
Our analysis followed the earlier analysis by Jackson, David Saurman, and William
Shughart (1994) in explaining lottery adoption in the United States We posited a Tobit
model to explain the probability and timing of casino adoption using state-level annual

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data from 1985–2000, a period covering most of the casino expansion outside of Las
Vegas andAtlantic City. Among the variables included in the model are“ﬁscal”variables,
such as long- and short-term debt; whether the state has tax/expenditure limits, such
as balanced budget provisions; the level of state government revenue; and the amount
of federal government transfers to the state government. The model also includes
variables measuring the inﬂuence of the different political parties in the states as well
as the existing gambling opportunities within the state and in nearby states. Finally, a
variety of demographic variables were included.
Calcagno, Walker, and Jackson (2010) found mixed evidence to support the propo-
sition that “ﬁscal stress” explains casino adoption in U.S. states. They found more clear
evidence that interstate competition helps to explain casino adoption. States seem to
legalize casinos in order to attract tourism and to keep their own gamblers in the state
(“defensive legalization”). States are more likely to introduce casinos—and to do it
sooner—if neighboring states have casinos. But there is little evidence that intrastate
competition among gambling industries is relevant to the decision to adopt casinos.
Hence, the evidence is consistent with common sense, that legislators look to casinos
mainly as a way to increase tax revenues.
Although Calcagno, Walker, and Jackson (2010) examined data for the United States,
the same framework can be utilized at an international level to explain why some
countries have introduced casinos and others have not. The analysis could also be
applied to a more local level to explain why some communities welcome casinos and
others do not. Clearly the decision to adopt casinos depends, at least in part, on how
legislators and voters believe casinos will affect the local or state economy. Several
related issues are examined below.
2 Casino Gambling and Economic Growth
.............................................................................................................................................................................
Although the casino industry argues that it spurs local and regional economic growth
by providing high-paying jobs and paying taxes and fees to local and state governments,
there is little empirical research on the issue. Studies such as Arthur Andersen (1996),
commissioned by the casino industry, are biased and amount to little more than static
comparisons or listings of taxes paid and employees hired by the casino industry.
The lack of empirical studies on the U.S. casino industry is not surprising given
the relatively recent expansion of casinos. Even so, there have been few studies on
the economic effects of the casino industry. The studies that have been published
tend to focus on the relationships among casinos, other gambling industries, and tax
revenues. Other studies have examined the negative consequences of casino gambling
and pathological gambling behavior, such as crime and bankruptcy. Few studies have
examined whether casinos stimulate economic growth or supplement state government
revenues.

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Walker and Jackson (1998) were among the ﬁrst to study the effects of the new
casino industry in the United States. We analyzed the relationship between state-level
casino revenues and per capita income. To do this, we developed a process for adapting
Granger causality testing to panel data. The reason we utilized a panel was because at
the time of the analysis relatively few states had casino gambling. The states that did
have casinos, other than Nevada and New Jersey, had them for at most six years. Hence
it was impossible at the time to analyze the states individually. In a more recent paper
(Walker and Jackson 2007) we repeated the earlier study using annual data through
2005. The process we used to adapt Granger causality testing for use with panel data is
described below.
2.1 Granger Causality Applied to Panel Data
Granger causality is said to exist between two variables, say x and y, when past values
of one variable (x) signiﬁcantly enhance the ability to predict future values of the other
variable (y). The implication is that the ﬁrst variable is affecting or“causing”the second.
Admittedly, Granger causality does not prove the two variables are related, and it does
not imply that the one variable is the only, or even most important, factor affecting
the other variable. What it does do is allow us to assess the relative likelihood of the
following four possibilities: (1) x and y are not related, (2) x Granger causes y, (3) y
Granger causes x, or (4) x and y Granger cause each other.
In order to adapt Granger causality analysis to panel data, Walker and Jackson (1998,
52–55) proposed a three-step process: (1) detrending the data, (2) selecting the appro-
priate time series process that generates each variable, and (3) conducting the Granger
causality tests based on the results of the two previous steps. Our goal was to analyze
whether there was a Granger causal relationship between casino revenue and economic
growth (per capita income) at the state level.
The ﬁrst step involved detrending the casino revenue and per capita income data.
The basic goal was to extract from the data any systematic information associated with
state-speciﬁc factors (laws, institutions, etc.), time-trend factors, and any idiosyncrasies
of the data or data collection. The detrended variables, that is, the residuals from these
ﬁltering equations, should be stationary series. This is tested using a unit root test,
such as Phillips-Perron. Once the detrended series were conﬁrmed to be stationary we
moved to the next step.
Step (2) involved determining the time series (autoregressive or ARMA) process
that generated each variable. In other words, we tried to determine how many lagged
periods of each variable had a signiﬁcant predictive power for current observations of
the ﬁltered data. The goal was to use the shortest possible lag length for each series
such that no systematic relationship remained among the residuals of the estimated
process. Once the proper lag length has been determined the Granger causality test is
set up. This was step (3) in the testing procedure. It involved estimating a two-equation
vector autoregressive (VAR) system in which the current value of each ﬁltered variable

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was regressed on the appropriate number of past values for both variables. Then a set
of F-tests was performed to test whether the ﬁltered residuals have a Granger causal
relationship.
2.2 Results
The results of the two studies (Walker and Jackson 1998, 2007) suggest that there is
a short-term positive impact of casino gambling on economic growth but that the
effect dies out in the longer term. The 1998 study used quarterly data from the period
1978–1996. Our results showed that there was a Granger causal relationship for casino
revenue on per capita income. These results are perhaps not surprising. The effects of
capital expansion and increased demand on the labor market that would come with the
new casino industry in a state could be expected to have a positive impact on income.
Joseph Schumpeter (1934) indicated that one possible source of economic growth is
the introduction of a new good/service to an economy. Our results are suggestive of
such an effect.
When we repeated the analysis more recently (2007), we used annual data from
the period 1991–2005. Annual data are preferred to quarterly data, especially since
we had to interpolate the quarterly per capita income data from annual observations.
The more recent analysis indicated no Granger causality relationship between casino
revenues and per capita income. Hence we argued that the introduction of casino gam-
bling has a short-run stimulus effect but that it eventually dies out. Perhaps this can
be explained by competition for the gambling dollar with other legal gambling indus-
tries within the state itself or through direct competition with gambling opportunities
online or in neighboring states. Or perhaps casinos simply replace or cannibalize other
non-gambling industries within the state. These issues are discussed in more detail in
Section 3.
2.3 An Extension: Hurricane Katrina
As a further application of the theory that casinos cause economic growth, in two
recent studies Walker and Jackson (2008a, 2009) examined the effect the casino indus-
try had on the economic recoveries of Mississippi and Louisiana following Hurricane
Katrina in 2005. The hurricane completely devastated the casino industry in both
states, but shortly after the hurricane the industry began to rebuild. Using quarterly
personal income and casino revenue data, we tested the impact that the casinos had on
personal income in Katrina-affected states. Our model included variables to account
for the hurricane and casino activity after the hurricane. The results suggest that
the commercial casino industry has had a signiﬁcantly positive impact on state-level
personal income and that after the hurricane the effect was larger than the “normal”

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113
casino effect. Consistent with our earlier papers, the Katrina study suggests that casi-
nos can indeed have a positive impact on state-level economic growth, at least in the
short-term. Presumably these effects come about from an amalgamation of capital and
labor effects and the attraction of tourism.
The available empirical evidence suggests that casinos do indeed have a positive
economic growth effect, though it may be short-lived. Obviously the effect will vary
depending on speciﬁcs of the jurisdiction and market.
3 Relationships among Gambling
Industries
.............................................................................................................................................................................
Whether an economic growth impact exists may be of less concern to politicians than
the amount of tax revenues that casino or other gambling activities create for the
government. Of course the various gambling industries often point to the taxes they
pay as a measure of the tax relief provided by the industry to the state’s (or local) citizens.
For example, Missouri taxpayers and politicians may assume that the $742 million in
lottery sales or the $403 million in taxes paid by the casino industry represent net
increases in tax revenues (or reductions to the citizens’ tax burdens). This may be the
case, but it is more likely that government spending has increased or that the taxes
raised by gambling are offset by tax losses from other types of consumer expenditures.
The tax revenue effect is not as simple as it might at ﬁrst seem.
A number of studies have examined the impact of one gambling industry on other
gambling or non-gambling industries. Other papers have examined the impact of
gambling on state tax revenues.1 Overall, these studies ﬁnd that one industry either
harms another industry or does not affect it. No study has found that different gambling
industries help each other. In addition, the effect of gambling on state tax revenues is
mixed. Some of the published ﬁndings are summarized in table 6.1.
These studies have several limitations in terms of understanding general relationships
among U.S. gambling industries and their overall impact on state government revenues.
First, for the most part these studies examine a single industry’s effect on another
industry but not vice versa. Second, most of the studies examine a single state or
county. Third, there are some limitations to the types of models used. For example,
many of the studies account for the gambling industry only through a dummy variable.
Accounting for the mere existence of a casino, for example, is much less enlightening
than accounting for the size of the industry.
JacksonandIhaveprovidedageneralanalysisof therelationshipsamongthedifferent
gambling industries within the United States (Walker and Jackson 2008b). We also
have examined the overall impact of legalized gambling on state government revenues
(Walker and Jackson 2011). Our ﬁndings from these studies are described below.

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Table 6.1 Studies on the Relationships among Gambling Industries
Paper
Years
States/Counties
Findings
Anders, Siegel, and Yacoub (1998)
1990–1996
1 county (Ariz.)
Indian casinos cause a
reduction in tax revenue.
Borg, Mason, and Shapiro (1993)
1953–1987
10 states
Lotteries cause a decline in
some other tax revenues, but
total tax revenues increase.
Elliot and Navin (2002)
1989–1995
All states
Casinos and pari-mutuels
harm lotteries.
Fink, Marco, and Rork (2004)
1967–1999
All states
Net increase in lottery
revenue causes a decrease in
state aggregate tax revenues.
Kearney (2005)
1982–1998
All states
Lotteries do not harm other
forms of gambling.
Popp and Stehwien (2002)
1990–1997
33 counties (N.M.)
Indian casinos reduce county
tax revenues.
Siegel and Anders (1999)
1994–1996
1 state (Mo.)
A 10% increase in gambling
tax revenue leads to a 4%
decline in other tax revenues.
Siegel and Anders (2001)
1993–1998
1 state (Ariz.)
Slots harm lottery; horse and
dog racing do not affect
lottery.
Thalheimer and Ali (1995)
1960–1987
3 tracks (Ohio, Ky.)
Having both lottery and
horse racing increases tax
revenues.
Source: Walker and Jackson (2008b).
Since no paper had analyzed the general interindustry relationships for gambling
in the United States, we attempted to model the revenue for each type of gambling
industry in each state as a function of other in-state gambling industries, adjacent state
gambling industries, and a variety of demographic criteria. We collected annual data
on the volume of each type of gambling for the period 1985–2000: lottery, horse racing,
greyhound racing, commercial casino, and Indian casinos.2 Using the data that were
available, we have 816 observations.
We are attempting to explain gambling revenue. Of course, states elect whether to
offer particular types of gambling or not. Therefore, there is a self-selection issue that
must be dealt with. The dependent variables (industry volume) in our model are left-
censored, especially in the cases of casino gambling and horse racing, as fewer states
offer these forms of gambling. To deal with the left-censoring, we followed James
Heckman (1979) and obtained the inverse Mills ratio from a probit and included it in
the model of gambling revenue as an additional explanatory variable.

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Table 6.2 Summary of Intrastate Industry Relationships
Model Variable
Casino
Dog Racing
Horse Racing
Lottery
Casino
−
+
−
Dog racing
(−)
−
+
Horse racing
+
−
+
Lottery
−
+
+
Indian square foot
+
(+)
+
−
( ) indicates statistically insigniﬁcant at normal levels.
Source: Walker and Jackson (2008b).
We wanted to model state-level volume of casino gambling, lottery revenue, and dog
and horse racing handle. (We did not attempt to model Indian casino square footage.)
Because of the nature of the data, we elected to use a seemingly unrelated regression
(SUR) analysis. This procedure allowed us to estimate our four-equation model jointly
as a system of equations rather than apply OLS to each equation independently. A sum-
mary of the results for the interindustry relationships is provided in table 6.2. A positive
sign indicates a positive and statistically signiﬁcant coefﬁcient; a minus sign indicates
a negative and signiﬁcant coefﬁcient; and signs shown in parentheses are statistically
insigniﬁcant. As shown, the results are mixed. Some industries appear to help each
other (complements), such as casinos and horse racing, lotteries and dog racing, and
horse racing and lotteries. Others, such as lotteries and casinos, and dog and horse
racing, are apparently substitutes.
These results supplement the existing literature by providing a more general analysis
on the interindustry relationships. Obviously the relationships among industries may
vary by state, as each state has unique laws, demographics, and so on. But the evidence
provided by Walker and Jackson (2008b) may be helpful to policy makers and voters
currently considering the legalization of new types of gambling. One thing that our
analysis suggests quite clearly is that relationships among gambling industries are not
straightforward, obvious, or consistent.
3.1 Tax Revenues
The interindustry relationships among gambling industries will obviously have an
impact on the effect of legalized gambling on overall state tax revenues. For exam-
ple, if a state that currently has horse racing wishes to increase tax revenues and is
considering legalizing a new type of gambling, it may wish to consider a lottery but
not greyhound racing, as Walker and Jackson (2008b) found that lotteries and racing
tend to be complements whereas horse and greyhound racing act as substitutes. Just
knowing the relationships among the industries is not enough, however. Whether
a new type of gambling will increase or decrease overall state tax revenues depends

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on the interindustry gambling relationships, the relationships between gambling and
non-gambling industries, the taxes applied to gambling and non-gambling industry
expenditures by consumers, and possibly other factors.
If one considers the level of taxes typically levied on gambling industries, it would
seem obvious that legalized gambling will tend to increase state government revenues.
Consider, for example, that the average state sales tax rate is somewhere around 5 per-
cent. This tax applies to most consumer goods and often to services.3 The state lottery
typically represents about a 30 percent tax. That is, for each $1 ticket, approximately 50c/
is returned as prizes, 20c/ goes toward administrative costs, and roughly 30c/ are kept as
government revenue—effectively tax revenue. This breakdown for each lottery ticket is
moderately consistent across different states with lotteries. Casinos, on the other hand,
are taxed at rates that vary by state. Typically the gross casino revenues are taxed, and
then the casino also pays standard income taxes on any remaining proﬁt, as required in
most states. The gross gaming taxes range from a low of around 6 percent in Nevada
to a high of 55 percent in Pennsylvania.4 Whatever the state, it is safe to assume that
taxes applied to lotteries or casinos are higher than the regular sales tax. Then it would
seem that, even if 100 percent of casino and lottery revenues in a state come at the
expense of other non-gambling expenditures, casino and lotteries should increase net
state revenue.
We tested this proposition using the same 1985–2000 state-level data as in the
interindustry study (2008b) and performed an econometric analysis to determine
whether there are some general relationships between gambling industries and tax
receipts across states (Walker and Jackson 2011). After controlling for a variety of
gambling industry metrics and demographic variables, we found mixed results. In par-
ticular, we found that lotteries and horse racing have statistically signiﬁcant positive
effects on state government revenues, but casinos and greyhound racing seem to reduce
net government revenues. While the lottery ﬁnding was expected, the negative casino
result was surprising. Our gambling industry variables included a dummy variable for
the existence of each type of gambling in the state as well as a“marginal impact”variable
to measure the effect on state revenue from each additional dollar of handle in each
industry. The results are summarized in table 6.3.
Table 6.3 Summary of Gambling Industry Effects on Net State Government
Revenue
Industry Variable
Casino
Dog Racing
Horse Racing
Lottery
Presence of Industry
−$90m.
−$157m.
$671m.
$315m.
Marginal Impact of $1 Handle
−$0.07
−$7.61
−$1.46
−$0.30∗
∗indicates statistical insigniﬁcance. “m.” represents millions.
Source: Walker and Jackson (2011).

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As table 6.3 shows, the existence of the casino industry in a state corresponds to a
reduction in state government revenues, for the average casino state, of $90 million.
Each additional dollar of handle has a relatively small negative impact on state revenue
of only 7¢.5 The lottery results show a large positive “presence” effect, with a relatively
small decline in state revenue from the marginal dollar from ticket sales. Oddly, horse
and dog racing seem to have different effects—horse racing has, on net, a positive
impact on state revenue, while greyhound racing appears to have a signiﬁcantly negative
impact.6
Overall, our results suggest that lotteries and horse racing have a positive impact
on state government revenues but that casinos and greyhound racing actually have a
negative impact. The negative result on casinos may indicate that casino expenditures
come at the expense of non-casino expenditures to such a large extent that, despite the
high tax rates applied to casino revenues, the reductions in non-casino spending lead
to declines in sales tax revenues that are even larger. This result surprises us and should
be considered by states considering the expansion of existing casinos or the legalization
of new ones.
The Walker and Jackson (2011) paper provides a more general analysis than previous
studiesonthetaximpactsof legalizedgambling.7 Whilestate-speciﬁcstudiesoftenshow
a positive impact from casinos, our results suggest that, on average, casino gambling
probably does not have a positive effect on state revenues. Obviously there will be
exceptions. LasVegas is a prime example of a city in which the casino industry obviously
has a positive impact on state government revenues. But the casino industry in other
states may not attract as many tourists and may therefore not have a positive impact on
state revenues. More study on the tax issue at the market or state level is needed. But
our evidence suggests that states should at least be aware that the casino effect is not
always necessarily positive with respect to net tax revenues.
4 The Social Costs of Gambling
.............................................................................................................................................................................
Whatever economic beneﬁts casinos provide, whether in terms of economic growth,
additional tax revenues, or simply an additional choice of entertainment for consumers,
there is a potential downside of legalized gambling. In particular, about 1 percent of the
general population is believed to comprise pathological gamblers. These individuals
are believed to cause an enormous amount of social costs which at least partially offset
any economic beneﬁts from gambling.8
The gambling literature is fascinating in part because it is the product of researchers
from very different academic perspectives. For example, published papers on the
social costs of gambling have come from researchers with backgrounds in psychology,
sociology,law, political science, public administration, and even landscape architecture.
One consequence of having researchers with different areas of expertise discussing

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a particular issue, such as social costs, is that they often come to very different
conclusions—even more so than economists do.
When economists discuss social cost, they usually have something very particular
in mind. As a result, a traditional economic analysis of social cost leads to startlingly
different conclusions than are otherwise found in the gambling literature. For example,
one early social cost analysis performed by William Thompson, Ricardo Gazel, and Dan
Rickman (1997) estimated the annual social costs of gambling per pathological gambler
at $9,469. A more recent study by Thompson and Keith Schwer (2005) estimated the
social costs of pathological gambling in Las Vegas at $19,711. Earl Grinols (2004)
averaged a variety of (mostly unpublished and ﬂawed) studies to arrive at a cost estimate
of $10,330. Such diversity in cost estimates indicates that the different studies have not
measured social costs in the same way.
Questions about research quality/legitimacy have been raised in comprehensive
analyses (Australian Government Productivity Commission 1999; National Gambling
Impact Study Commission 1999; National Research Council 1999) as well as in more
narrow critiques. For example, the National Research Council (1999, 186) explained
that“most [cost studies] have appeared as reports, chapters in books, or proceedings at
conferences, and those few that have been subject to peer review have ... been descrip-
tive pieces.” The result has been questionable, if not counterproductive, research: “In
most impact analyses ... the methods used are so inadequate as to invalidate the con-
clusions. Researchers ... have struggled with the absence of systematic data that could
inform their analysis and consequently have substituted assumptions for their missing
data” (185).
To illustrate the problems with social cost estimates, consider the work by Thompson
and Schwer (2005), summarized in table 6.4. The cost estimate is based on a survey
of 99 Gamblers Anonymous members in Las Vegas. The fundamental problem with
this study, and others in the literature, is that the authors have failed to deﬁne “social
cost.”9 Instead, they attempt to estimate monetary values for any negative effects that
they can identify, measure, and somehow attribute to gambling. To be sure, there is
a lot of jargon in the gambling literature that may be confusing to researchers. All of
the following terms describing “costs” have been used in recent papers: private, social;
internal, external; direct, indirect; harms, costs; intangible, tangible; external costs,
externalities; and pecuniary externalities, technological externalities.
Walker and A. H. Barnett (1999) and Walker (2003) explained why the deﬁnition of
social cost is important and why researchers should be skeptical of cost estimates that
do not explicitly deﬁne what they are trying to measure. We give a detailed explanation
of the welfare economics (utilitarian) perspective on social costs. Essentially we argue
that a social cost requires that an action reduces the total “wealth” in society. This
implies that wealth transfers (gambling losses, bad debts, etc.) cannot be considered as
social costs.10 This follows from Gordon Tullock’s (1967) classic discussion of theft. In
addition, internalized costs would not qualify as social in nature. Many of the so-called
social costs estimated by Thompson, Gazel, and Rickman (1997), Thompson and
Schwer (2005), and Grinols (2004) turn out to be wealth transfers or internalized costs.

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Table 6.4 A Typical Estimate of the Social Costs of Gambling (in USD)
Employment
$ 5,125
missed work
2,364
productivity losses (quit jobs)
1,092
ﬁred from work (productivity lost)
1,582
unemployment compensation
87
Bad Debts and Civil Court
$10,271
bankruptcy debt loss
9,494
civil court costs (bankruptcy/debt/divorce)
777
Criminal Justice System
$ 3,809
theft
3,379
arrests
95
trials
85
incarceration
80
probation
170
Treatment and Social Services
$ 506
treatment costs
372
welfare
84
food stamps
50
Total estimated annual social cost per pathological gambler
$19,711
Source: Thompson and Schwer (2005, 83)
As a result, we argue that the social cost estimates in the literature seriously overstate
the actual social costs of gambling.
If the Thompson and Schwer (2005) estimate is reviewed from an economic perspec-
tive, many of the presumed costs drop out from the social cost estimate. For example,
all of the employment costs of $5,125 would either be internalized by the employer or
employee or they represent transfers of wealth. The bankruptcy debt losses, monetary
value of theft, and welfare/food stamps would be transfers. The actual social costs, as
deﬁned by Walker and Barnett (1999), would include civil court costs, criminal jus-
tice costs, and treatment of pathological gambling. These costs are estimated at about
$1,600 (Walker 2008a), signiﬁcantly different from the $19,711 estimate of Thompson
and Schwer.11 This“economic perspective”is upsetting to many social scientists because
it seems to ignore some potentially signiﬁcant harms. This exercise demonstrates that
the deﬁnition of social cost does matter, especially considering that social cost studies
have had a real impact on government policy toward gambling.
4.1 Casinos and Crime
One speciﬁc social cost issue that has received recent attention in the literature is the
potential relationship between casinos and crime. In probably each jurisdiction in
which casinos are being considered there is debate over whether casinos will create

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casinos
or attract crime. For example, the fact that casinos will attract tourists carrying cash
might be a catalyst for criminals to ﬂock to casinos—customers may represent easy
prey. Alternatively, people who develop into problem gamblers may turn to crime to
getmoneyforgambling. Anynumberof situationsmightsuggestarelationshipbetween
casinos and crime.
The study by Grinols and David Mustard (2006) purported to show through a
county-level analysis that casinos have, in fact, contributed to crime in the United
States. Grinols and Mustard used an exhaustive data set in an econometric analysis of
how casinos tend, with some time lag, to contribute to increases in crime rates. Yet, as
explained more recently (Walker 2008b), the empirical analysis by Grinols and Mustard
(2006), as well as that in other studies, is suspect because they often mismeasure the
crime rate.12
To explain, consider a community in which there is relatively little tourism, so that
crimes are committed by residents and the victims also are residents of the community.
Then the crime rate is represented as the number of crimes committed divided by the
population:
Crime rate = # of crimes committed
population at risk
This rate is often expressed per 100,000 people. Let’s use C to represent criminal acts
and P to represent population at risk of being victimized. Then the crime rate above is
C/P. Now in order to apply the crime rate to a case in which casinos are introduced, we
must recognize that likely there will be an inﬂow of tourists into the jurisdiction that
introduces casinos. Simply because the number of people in the area has increased, we
normally would expect an increase in the raw number of crimes committed. But the
actual risk of being a crime victim may rise or fall; it depends on whether the amount
of crime increases by a larger or smaller amount than the increase in the population
at risk.
More formally, if we now distinguish between criminal acts perpetrated by residents
(CR) and those perpetrated by visitors (CV ); and separate the population at risk into
the resident population (PR) and the visiting population (PV ), then we can see how
the crime rate would be represented in a case where there is a substantial amount of
tourism. Such is the case with many casino jurisdictions. The crime rate in this case
can be written as (CR +CV )/(PR +PV ). As I emphasized in my critique of Grinols and
Mustard’s paper (Walker 2008b), it is important that the crime rate accurately reﬂect
the risk of being victimized. When a jurisdiction experiences a large number of tourists,
both residents and visitors may commit and/or be victimized by crime.
In the analysis by Grinols and Mustard (2006), the authors counted the crimes com-
mitted by visitors (CV ) in the numerator but omitted the visitors from their measure
of the population at risk, in the denominator. So the crime rate measure they use is
(CR + CV )/(PR). This rate will necessarily be larger than (CR + CV )/(PR + PV ). For
this reason, I argued that the Grinols and Mustard study may signiﬁcantly overstate the

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casino effect on crime. There are several other problems with the Grinols and Mus-
tard analysis. For example, their empirical work does not enable them to differentiate
between tourism-related crime, in general, and casino tourism-related crime, in par-
ticular. Furthermore, their variable accounting for casinos is a simple dummy variable;
they do not distinguish among different sizes of casino industries or casino volume.
So in their model Clark County, Nevada (Las Vegas), would be treated the same as a
county in Colorado with a single small casino. Taken together, these issues raise serious
questions as to whether the crime effect Grinols and Mustard attribute to casinos can
be believed.
A recent study by William Reece (2010) helps to alleviate some of the concerns with
the Grinols and Mustard study. Although Reece studied only one state (Indiana), he
posited a more careful model. First, he attempted to control for casino volume by
including casino turnstile count as an explanatory variable. Reece also included the
number of hotel rooms as a variable; this helped to control for tourism in general.
Reece’s results indicate that increased casino activity reduces crime rates, except for
burglary. He speciﬁcally indicates that leaving out a measure of casino activity creates
a “serious speciﬁcation error.” Finally, the results indicate that the building of hotel
rooms subsequent to casinos opening tends to reduce crime. Overall, Reece’s study
provides important evidence that counters the claims by Grinols and Mustard (2006)
that casinos attract crime.
Thereisclearlygoodreasontoexpectsomerelationshipbetweencasinosandcriminal
activity. However, based on an overview of the literature, there is no conclusive evidence
on the relationship between casinos and crime. More careful econometric analyses are
needed.
5 Measurement Problems in Cost-Benefit
Analysis
.............................................................................................................................................................................
It is doubtful that researchers will adopt a pure economic conception of social cost
such as that described by Walker and Barnett (1999).13 Even if the proper deﬁnition
of social cost were clear, there are other obstacles to actually measuring the social costs
of gambling. Of course, the inability to measure costs does not mean that the costs do
not exist. Rather, it simply means that researchers and policy makers must be careful in
interpreting social cost studies.
Perhaps the most serious obstacle in performing valid social cost estimates is the
issue of comorbidity. That is, pathological gamblers may have other problems that
contribute to their socially costly behavior, meaning that the costly behavior results
from multiple disorders rather than one. One study found that almost 75 percent of
pathological gamblers also have alcohol use disorders, and almost 40 percent have drug
problems (Petry, Stinson, and Grant 2005). Consider a problem gambler who is also

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casinos
an alcoholic. Suppose his behavior results in social costs of $1,000. Most gambling
researchers, including Thompson, Gazel, and Rickman (1997), Thompson and Schwer
(2005), and Grinols (2004) would simply attribute the entire $1,000 cost to gambling,
even though the drinking may be responsible for some (or even most) of the total
cost. How should comorbidity be handled, in terms of estimating the costs due to
a particular afﬂiction? This question has not been addressed by researchers, but it is
critical to creating valid social cost estimates.
A second issue is the counterfactual scenario. What if casinos were not legal? Would
pathological gambling and the associated social costs disappear? Probably not. A valid
estimate of the costs of pathological gambling, as it relates to government policy, is not
the total cost of pathological gambling behaviors. Rather, the relevant cost is the dif-
ference between the costs when casinos are legal and when they are not. Unfortunately,
it is very difﬁcult to know with accuracy the counterfactual scenario. Since most social
cost estimates do not consider this, they must be viewed with skepticism.
A third problem with estimating the social costs of gambling is that many of the
published estimates have been based on unreliable survey data. In some studies authors
have based their cost estimates on diagnostic tools like the DSM-IV or SOGS.14 Some
papers use original surveys in which problem gamblers are asked about the extent of
their gambling losses or the sources of their money used for gambling. The study byAlex
Blaszczynski et al. (2006) found that many survey respondents are unable to estimate
their gambling losses, even if given instructions on how to do so. This evidence suggests
that it would be difﬁcult for the same individuals to reliably report the source of their
gambling losses. This is because budgets are fungible (Walker 2007a, 121). Yes, a person
may gamble too much. But he or she also may have a very high car payment. How
conﬁdent are we that this person (or the researcher for that matter) could accurately
identify what source of income—paycheck, bank loan, cash gifts, theft, and so on—was
used to ﬁnance a speciﬁc expenditure? Those taking a survey on problem gambling
may be predisposed to blame all of their problems on gambling even though they have
other problems as well. This suggests that estimated costs for bad debts, theft, and the
like are likely invalid.
The fourth and ﬁnal problem discussed here relates to how government expenditures
are handled. A large portion of the social costs of gambling may be related to govern-
ment expenditures. For example, suppose government-provided treatment is available
and many pathological gamblers commit crimes that create legal costs. Most social cost
estimates simply take the value of these government expenditures and call them social
costs. It seems obvious to some analysts that, since government spending requires taxes,
these expenditures should be considered social costs. Indeed, most people would agree
that lower spending on these sorts of things would be preferred to higher spending. But
the same is not necessarily true of, say, education. People often vote for more public
education spending. The point is that government expenditures are not equivalent to
social costs. If they were, then we could reduce the social costs of gambling by simply
reducing spending on gambling-related problems! Unfortunately, this does not leave us
with a clear and appropriate way to classify gambling-related government expenditures.

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Yes, such expenditures may be a reﬂection of social costs, but they may also represent
the social costs of policy decisions. This issue has been addressed by Edgar Browning
(1999). As with the previous issues discussed here, there is no ideal way to deal with
this one.
Finally, since the above problems (among others) make it very difﬁcult to obtain
credible data on the social costs of gambling, many researchers rely on a variety of
wildly arbitrary assumptions in performing their analyses. The result is sometimes
nothing but meaningless cost estimates.
There are other problems in the gambling literature that make cost-beneﬁt analyses
unreliable. This section has focused only on cost-side issues, but there are beneﬁt-side
problems as well. Until researchers can adequately deal with some of these problems,
policy makers and voters must be cautious in how they interpret and use the cost-
beneﬁt analyses of gambling studies. In many ways the problem gambling literature
parallels the substance abuse literature, both reﬂecting a “cost-of-illness” approach.
That work provides a possible path for gambling researchers to follow. But even
the better established substance abuse literature has its critics (e.g., Reuter 1999 and
Kleiman 1999).
6 Conclusion
.............................................................................................................................................................................
This chapter summarizes my previous research on the economic and social impacts
of casino gambling in the United States. Empirical studies have demonstrated a short-
term positive economic growth effect from casinos, at least those using state-level
data. Subsequent studies have conﬁrmed that, in the case of recovery from Hurricane
Katrina, casinos seem to have made signiﬁcant positive contributions to state-level
personal income. This is likely due to straightforward economic development effects
resulting from capital investment and the employment provided by casinos.
What is less clear is whether casinos make a net positive contribution to state-level
revenues. Our empirical analysis indicates that casinos actually detract from state
government revenues, perhaps due to a large substitution away from other types of
spending. Evidence on lotteries appears to be consistent with the common sense notion
that lotteries enhance state revenue. These contradictory results suggest that legalized
gambling is not always a positive contributor to state government coffers. It likely
depends on what types of gambling the jurisdiction has as well as the speciﬁcs of the tax
policies.
One of the primary arguments used to oppose the introduction of casinos is that they
may be the catalyst for signiﬁcant social costs. Most of these costs are attributable to
such pathological gambling behaviors as criminal activities and to requiring treatment.
There has been much debate over the magnitude of such costs, and I have argued that
most of the empirical estimates of the social costs are largely arbitrary. When we focus

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casinos
on the speciﬁc issue of crime, we ﬁnd that many of the studies from the literature may
have overstated the crime effect from casinos. This is because studies often use a ﬂawed
measure of the crime rate in their analyses. The best evidence suggests an unclear crime
effect from casinos. Although there certainly are social costs attributable to pathological
gambling,mostpublishedestimatesarewildlyinaccurate. Finally,Ihaveidentiﬁedsome
fundamental problems with the nature of social costs and data availability that make it
unlikely that signiﬁcant improvement in such estimates will happen anytime soon.
The economics of gambling is a fascinating area of research. It is a young ﬁeld
with countless potential research topics. More developed casino markets, such as Aus-
tralia, Canada, Macau (China), the United Kingdom and the United States, have been
the recipients of most of the research attention. But all casino jurisdictions deserve
more attention from economists. It is my hope that economic research on casino gam-
bling will continue to expand as data availability improves, covering more markets
around the world. Only with more attention from researchers can we develop a better
understanding of the actual economic and social effects of casino gambling.
Notes
This chapter is based on a paper presented at the Macao Polytechnic Institute Global
Gaming Management Seminar Series, Oct. 23, 2009. The author gratefully acknowledges
ﬁnancial support from the Macao Polytechnic Institute; the U.S. Department of Educa-
tion, Title VI-A, International Studies and Foreign Language Program; and the Global
Trade Resource Center at the College of Charleston.
1. These studies include Anderson (2005), Anders, Siegel, and Yacoub (1998), Elliott and
Navin (2002), Fink, Marco, and Rork (2004), Kearney (2005), Mobilia (1992), Popp and
Stehwien (2002), Ray (2001), Siegel and Anders (1999, 2001), and Thalheimer and Ali
(1995).
2. Unfortunately, volume is not measured or reported the same in each industry. Volume
for lotteries is total ticket sales; for commercial casinos it is net revenue; for horse and
greyhound racing it is handle (the total dollar amount of bets placed). Because Indian
casinos are not required to publicly disclose casino data, there is no obvious or easy way
to measure their volume. Instead, we collected data on the total square footage of Indian
casino ﬂoor space for each state. The casino industry uses a basic formula for casino
layout, and revenues would be expected to vary directly with square footage. Obviously
this is not a perfect measure, but it perhaps the best proxy for Indian casino volume that
has been developed in the literature.
3. State sales taxes are obviously more complicated than this statement implies. The com-
plexities of state sales taxes are not important for the argument being made here, so they
are ignored.
4. Casino taxes are complex in some states, with graduated marginal tax rates, various fees,
and so on.
5. See (Walker and Jackson 2011) for an explanation of how we estimated handle from the
revenue data, in light of the problem discussed above in note 2.

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6. It should be noted that we are not conﬁdent in the validity of the large negative marginal
impact from greyhound racing. Nor can we explain it. Yet we get similarly large and
negative results whatever model speciﬁcation is used.
7. For examples of studies that examine particular states’ or localities’ tax impacts from
legalized gambling, see Anders, Siegel, and Yacoub (1998), Borg, Mason, and Shapiro
(1993), Fink, Marco, and Rork (2004), Siegel and Anders (1999), and Thalheimer and Ali
(1995).
8. There are different degrees of pathological gambling and corresponding different terms.
We ignore these details here. It is not clear the extent to which legalizing gambling causes
an increase in the prevalence of pathological gambling. However, it seems reasonable
that we would see an increased prevalence closer to casinos, for example. This does not
necessarily imply, however, that eliminating casinos or other forms of gambling would
decrease the prevalence rate markedly, since individuals could still gamble illegally or
travel to nearby legal establishments.
9. For this discussion we will ignore the potentially serious problems of using survey data
from Gamblers Anonymous members to generate an estimate of social costs for the
representative pathological gambler.
10. This is not a generally a controversial statement for economists. For example, the Federal
Reserve Bank of Minneapolis’s gambling issue of Fedgazette (2003) cited the Walker and
Barnett paper in discussing transfers.
11. This estimate excludes other legitimate social costs that have been ignored in the literature.
For example, lobbying on the part of the casino industry and casino opponents could be
classiﬁed as social costs related to gambling.
12. Relatively good crime-related studies include Albanese (1985), Curran and Scarpitti
(1991), and Stitt, Nichols, and Giacopassi (2003). For a review of the casinos and crime
literature, see Walker (2010).
13. This section is adapted from Walker (2007b, 2007c).
14. The DSM-IV is American Psychiatric Association’s Diagnostic and Statistical Manual
of Mental Disorders 4e. The SOGS is the South Oaks Gambling Screen developed by
H. R. Lesieur and S. B. Blume (1987). Both instruments indicate likely pathological
gamblers based on their responses to a variety of questions about their gambling-related
behavior.
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s e c t i o n ii
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SPORTS BETTING
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chapter 7
........................................................................................................
THE ECONOMICS OF ONLINE
SPORTS BETTING
........................................................................................................
george diemer and ryan m. rodenberg
i Introduction
.............................................................................................................................................................................
The technological shock ushered in by the Internet has brought about signiﬁcant
structural changes in many industries. The sportsbook industry is one such example.
Michael Smith and Leighton Vaughan Williams (2008, 404) have concluded that it is
“now widely accepted that the technologies associated with the internet have spawned
radical new business models and formats [and a]spects of the gambling industry are
being transformed by these pervasive technologies.” More pointedly, Mark Davies et
al. (2005) have explained how ﬁve distinct technological forces have revolutionized
sports wagering—(1) Moore’s Law pertaining to computing power, (2) Metcalfe’s Law
regarding networks, (3) decreased transaction costs as explained by the Coase Theo-
rem, (4 increased potential for customer clustering (also known as the “ﬂock of birds
phenomenon”), and (5) diminished barriers to entry via the so-called “ﬁsh tank phe-
nomenon.” The technology-induced boom in Internet sports gambling has, in turn,
rendered the somewhat antiquated laws “virtually unenforceable” (Cabot and Faiss
2002, 2).
The pre-Internet economic and legal environment of sports wagering was relatively
clear, as the industry was heavily concentrated. In this previous era, with full-scale
wagering on sports illegal in 49 out of 50 states in the United States,1 American gamblers
had only two options: (1) they could travel to Nevada and gamble on sports legally (at
what are known as “terrestrial” gambling sites) or (2) they could place illegal wagers
with their local bookie. In the post-Internet age, however, the legal and economic
issues involved in sports gambling are much more complex and uncertain. The sports
gambling sector has changed dramatically from an oligopolistic to a monopolistically
competitive industry unhampered by geography. The geographical sportsbook market

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sports betting
was local in nature. The Internet changed that market to a global one. Although there
have been sporadic legislative attempts to regulate and/or prosecute the industry in
the United States, the legality of the sports gambling industry is currently in a state
of ﬂux.
The purpose of this chapter is to provide an overview of the online sports betting
industry from an economic and a legal perspective. Our dual focus is one of necessity,
as the overlapping, and sometimes conﬂicting, regulatory environment lends itself to a
decidedly “law and economics” inquiry. After an overview of the pre-Internet environ-
ment, we proceed to a multifaceted treatment of the online sportsbook, explaining the
decided shift in its economic characteristics and the ambiguous legal status in which
the industry resides. For the avoidance of doubt, our economic-based coverage is appli-
cable globally. In contrast, the accompanying legal discussion will focus primarily on
jurisprudence in the United States, a nation that holds the somewhat ironic distinction
of being the world’s largest single-nation sports gambling market and the only major
industrial jurisdiction whose laws leave bettors and gambling-related businesses in a
legal grey area regarding the permissibility of sports wagering activities.
ii Pre-Internet Legal and Economic
Environment
.............................................................................................................................................................................
The pre-Internet legal and economic environment for sports gambling was highly
regulated and heavily concentrated among a few key businesses and locations. It was
dominated by terrestrial gambling sites and illegal sportsbooks, both of which operated
within relatively stable geographical and legal constraints. While the operations of
the illegal sportsbooks are largely clandestine with a few exceptions (Strumpf 2003),
the licensed terrestrial gambling sites “present signiﬁcant opportunities for economic
analysis” (Sauer 1998, 2021).
A Terrestrial Sports Gambling Sites
Terrestrial gambling sites, such as the legal sportsbook casinos in Las Vegas and other
locations in Nevada, operate in an oligopolistic industry shaped by large barriers to
entry. Signiﬁcant start-up costs, regulatory licenses, and a heavy tax rate serve as bar-
riers to entry into the industry and result in a limited number of competitors in the
highly regulated jurisdiction. This may be changing, however. First, Cantor Fitzgerald, a
well-knownWallStreetﬁrm,hasrecentlymadeinroadsintotheVegas-basedsportsbook
industry through its subsidiary afﬁliate Cantor Gaming, operating the upscale M Resort
and licensing its real-time “Inside Wagers” technology to a handful of other sports-
books around Las Vegas. Second, William Hill, a prominent British bookmaking ﬁrm,

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133
announced the 2011 acquisitions of Nevada-based sportsbooks American Wagering,
Club Cal Neva Satellite Race and Sportsbook Division, and Brandywine Bookmaking
LLC.
As is the case with most oligopolistic industries, these ﬁrms can earn an exces-
sive economic proﬁt. Terrestrial sports gambling sites use a traditional fee, known as
vigorish, of 10 percent on all losses. This fee is often thought of as a commission. Tra-
ditional literature assumes that the objective of a sportsbook is to balance the action
or amount wagered on each side of the game or event. If this objective is attained, the
sportsbook takes no risk on the game, as sportsbooks are neutral regarding the actual
outcome of the game or event, collect all losing bets (plus the 10 percent vigorish),
and pay out the winning bets. This leaves the sportsbook with commission revenue
of 5 percent of all action.2 Terrestrial sportsbooks are often content with this com-
mission, especially when it brings in additional action to the table games on-site. In
addition to traditional wagers, most sportsbooks offer a limited number of so-called
exotic wagers similar in form to the pari-mutuel system used by a racetrack to handle
its gambling. These systems take in 14 to 20 percent before distributing the winnings
(Davies et al. 2005).
B Local Bookies
Prior to the 1840s, most gambling in the United States was heavily rigged and con-
sisted of poker games that took place on steamboats. Gambling was disorganized
and decentralized, but this all changed with the construction of major horseracing
tracks, such as Saratoga in 1864 and Churchill Downs in 1875. In the 1870s race-
tracks began introducing Paris Mutual (or pari-mutuel) betting. Pari-mutuel wagering
is a type of bet in which the payout odds are tabulated after the race has completed.
These odds are a function of where the money was wagered and in what amounts.
Updated odds give the gamblers an idea of the expected payout. This type of wager
took time to gain popularity but remains the dominant type of racetrack wager
today.
Peter Reuter (1983) estimated that the illegal sportsbook industry in New York City’s
four-ﬁrm concentration ratio was no more than 35 percent. He concluded that book-
maker operations were relatively small, with frequent entry barriers but almost no
exit barriers. Reuter also found that efforts toward collusion often failed and that the
market seemed to operate competitively. However, one signal of monopoly power in
the industry still existed—third-degree price discrimination. Koleman Strumpf (2003)
found evidence of such third-degree price discrimination within the illegal sportsbook
industry. Using a unique data set provided by a county district attorney following sev-
eral high-proﬁle arrests, Strumpf reached this conclusion by examining six bookmakers
who operated in and around the New York City area in the 1990s. Strumpf described
the client differentiation that is required in such activity as being relatively easy. Simply
by moving the point spread of the local team to make it more expensive to bet on them,

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sports betting
the local sportsbooks discriminate against the local geographical bias of the fan base in
that area.
C Sportsbook Corruption Pre-Internet
The industry of the racetrack bookmaker relied on an information network just at a
time when communication technology was evolving. Bettors with results of prior races
that were allowed to wager on off-track locations opened the door for “past-posts.”
Exploiting information gaps became a lucrative business for professional gamblers.
Filling any existing information gaps became a great concern for bookmakers as they
used the services of Western Union for up-to-date information. Federal authorities
opted against cracking down on legal or illegal gamblers at these early racetracks,
largely so that they could go after afﬁliated services provided by legally operating
businesses like Western Union. By pressuring companies that contributed to illegal
gambling, the government sought to indirectly curb the bookmaking business, a trend
that continues today.3 Finally, in 1904 Western Union announced it would end the col-
lection and dissemination of race results. This move resulted in large proﬁts for illegal
wire transfers companies that practiced price discrimination in connection with the
information.4
From 1950 to 1951, the U.S. Senate, the nation’s most powerful legislative body,
conducted what was ofﬁcially called the Senate Special Committee to Investigate Crime
in Interstate Commerce and commonly referred to as the Kefauver Committee (U.S.
Congress 1951). The primary objective of this committee was to investigate organized
crime. The investigation led to the conclusion that illicit bookmaking resulted in illegal
monopolization of racing information and, in turn, police corruption. This ﬁnding
put a spotlight on the link between organized crime and bookmaking and served as
the impetus for the Wire Act of 1961 (Wire Act), one of the most prominent federal
anti-gambling statutes.
The National Gambling Impact Study Commission (NGISC) was authorized by
Congress in 1996 and completed its work in 1999 (NGISC 1999). Except for tribal
and Internet gambling, the NGISC recommended that gambling be given statewide
autonomy. Furthermore, the NGISC advised curtailing statewide lotteries, espe-
cially to the extent that they target lower income neighborhoods. The NGISC
recommended that collegiate and other amateur sports gambling be reduced or
eliminated, a recommendation that was not enacted as legislation at the federal
level.5
The illegal bookmaking industry changed in many ways between the Kefauver Com-
mittee and the time the NGISC was commissioned. What was once dominated by
horse races slowly began moving toward what is now known as traditional sports bet-
ting. Information gaps were no longer problematic for bookmakers, as transmitting
information about the games by broadcasters was acceptable. In addition, with the
popularity of the point spread system, taking bets became simpler with fewer events

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the economics of online sports betting
135
and only two possible outcomes to wager on. Finally, terminology began to change with
legitimate bookmaking rings being known as sports books.
iii Post-Internet Legal and Economic
Environment
.............................................................................................................................................................................
Deﬁning the geographical and legal markets for Internet sportsbooks is a complex task.
Since its enactment, the Wire Act has prohibited gamblers and bookies from making
transactions across state lines over telephone wires.6 As such, to steer clear of the statute,
bettors and bookies had to be in the same place at the same time. Today, however, there
are up to three locations for gambling activity: (1) a domain name registered location,
(2) a place of business operation, and (3) a target market where individual gamblers
reside. One marketplace often covers multiple geographical locations. As Mark Wilson
(2003, 1246) explained: “An example of online gambling is Casino Australia, which
has a name suggesting Australia, a domain name registered in New Hampshire in the
United States, and a website based in the Netherlands Antilles.”
The example of Casino Australia is illustrative of how uncertain the legal environ-
ment has become, notwithstanding the fact that a number of Internet sports books are
publicly traded in well-respected stock exchanges, such as the London Stock Exchange.
In these cases, it is hard to initially identify which nation is responsible for enforcing
which nation’s gambling laws. Given the reactive nature of lawmaking, statutes and
code are just now being codiﬁed with Internet-based transactions in mind. For exam-
ple, on August 7, 2007, after several court rulings had chipped away at the law, the
U.S. Congress amended the Foreign Intelligence Surveillance Act of 1978 (FISA) to
better ﬁght terrorism. This update allows American investigative bodies to use modern
technology in a more expansive way.7 It is conceivable that a similar update to the Wire
Act could be forthcoming in the not too distant future.8 Subsequent interpretations
of FISA, the Wire Act, and similarly situated laws enacted before the emergence of the
Internet will shape the industry moving forward.
In their examination of international legal regulations in the Internet age, Stephan
Wilske and Teresa Schiller (1997) set forth several legal principles for regulating Internet
activity within and across national borders. The ﬁrst and most relevant to Inter-
net gambling is the territoriality principle, which states that a nation has authority
over locally produced Web content. This effectively grants a nation the power to
have laws restricting Internet businesses from offering services to its citizens, even
if the business operates within the nation’s borders and provides the services of for-
eigners legally. A business can comply with such laws by identifying the geographic
location of potential customers through their Internet addresses. This practice is
common in the Internet sports industry. For example, Australia allows local online
gambling sites to operate provided no Australian citizens are allowed to gamble

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sports betting
on their sites. In the United States, the territoriality principle is unevenly applied.
As a result, many Internet sportsbooks have decided to restrict access to American
customers.9
A considerable portion of the aforementioned NGISC centered on the then-
novel type of gambling that appeared on the landscape—Internet gambling. In its
recommendations, the NGISC report concluded:
The Commission recommends to the President, Congress, and the Department of
Justice (DOJ) that the federal government should prohibit, without allowing new
exemptions or the expansion of existing federal exemptions to other jurisdictions,
internet gambling not already authorized within the United States or among parties
in the United States and any foreign jurisdiction. Further, the Commission rec-
ommends that the President and Congress direct the DOJ to develop enforcement
strategies that include, but are not limited to, internet service providers, credit card
providers,10 money transfer agencies, makers of wireless communications systems,
and others who intentionally or unintentionally facilitate internet gambling trans-
actions. Because it crosses state lines, it is difﬁcult for states to adequately monitor
and regulate such gambling.11
Related NGISC ﬁndings included a call for passage of legislation that would curb
or prohibit wire transfers involving gambling websites and a recommendation to the
president and Congress to facilitate cooperation with foreign governments.
As for the economic environment, the industry appears to be in transition. The post-
Internet era of sportsbooks is one that is not oligopolistic or localized. Instead, it is
highly monopolistically competitive with a global marketplace. Complicating matters
are two non-American judicial proceedings with far-reaching free trade and consumer
protection implications—the European Court of Justice’s Liga Portuguesa decision in
2009 and the 2003 World Trade Organization’s Antigua and Barbuda v. United States
case.12 The multi-jurisdictional nature of these disputes, coupled with the now monop-
olistically competitive nature of the industry, suggest an uncertain and likely litigious
future.
A Entry Barriers
In the post-Internet era, there are few signiﬁcant entry barriers in this industry. Start-
ing up a no-frills Internet sportsbook costs approximately ten thousand U.S. dollars,
which is used to handle such tasks as acquiring domain names, obtaining the use of
servers and phone lines, purchasing or licensing gambling software, and advertising. By
operating in Internet-friendly nations (such as Antigua or Costa Rica), these new Inter-
net sportsbooks conduct business with less regulation, lower tax rates, fewer licensing
requirements, and little to no threat of legal prosecution vis-à-vis online sportsbooks
in jurisdictions with stricter laws and policies.

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the economics of online sports betting
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B Market Shares
The Internet sportsbook industry is currently in a state of ﬂux for a number of reasons.
As the market for online sportsbooks matured, the number of virtual sports gambling
portals increased rapidly and subsequently stabilized. Whether this trend will continue
is unclear because of the increasing threat of prosecution and the uncertainty with
which it is associated. For example, on May 23, 2011, an American federal grand jury
returned indictments charging various online sports betting businesses and individuals
with illegal gambling and money laundering (Millman 2011). The domain names for 10
online sportsbooks were seized, including the popular website Bookmaker.com. Several
prominent online sports betting portals responded to the crackdown by rerouting
trafﬁc to domain names with different website sufﬁxes, such as .ag or .eu instead of the
ubiquitous .com.
Wilson (2003) cites 1,122 gambling websites in June 2001, though his number likely
includes non-sports-related gaming sites as well. In the summer of 2007, Sports-
bookReview.com (SBR) graded 755 sportsbooks as acceptable and 886 sportsbooks
as blacklisted, which in this context refers to a sportsbook that has liquidity problems
and/or may be fraudulent. In June 2011, according to SBR, the number of blacklisted
sites increased to 1,052 (many presumably have since closed down) and 579 other sites
were currently in operation. Accurate revenue ﬁgures are impossible to establish in
this industry due to existing regulations (or lack thereof) and an absence of incen-
tive to disclose ﬁnancial ﬁgures. Estimates by Christiansen Capital Advisors (CCA)
indicate enormous growth in the industry.13 Revenues increased from USD3 billion
in 2001 to an estimated USD18 billion in 2007. These ﬁgures include non-sports-
related gambling but nonetheless provide some insight into the growth of the industry.
Time will tell how new legislation affects the industry’s expansion. In the post-Internet
era, sportsbooks operate in complete autonomy compared to U.S. corporations. If
nothing else, local land-based bookmakers now face increased competition, though
there is some evidence that terrestrial gambling companies support online betting
(Richtel 2001).
C Product Differentiation
In the pre-Internet sportsbook market, a bookie would only collect money after the
sporting event was over. Thus the burden of establishing credibility lay solely on the
bookie, who had to decide if a gambler was worthy of credit. Information gath-
ered by the gamblers about the bookies was obtained by word of mouth and only
really concerned the bookies’ reputations of paying out any winning wagers. In con-
trast, Internet sportsbooks require fully funded accounts to be set up by gamblers
before they place wagers. The burden of establishing credibility has shifted to the
gambler, who must establish that the sportsbook site will pay out on wins. In addi-
tion to ﬁnancial credibility, gamblers must be concerned also with the stability of the

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sports betting
Internet sportsbook as legislative bodies attempt to regulate the industry. Informa-
tion gathered by the gamblers can take many forms, including rating websites, such
as SBR, that the credit worthiness and customer service track record of each Internet
sportsbook.
Classic signs of competition in the marketplace have appeared online, for example,
the introduction of new forums for gambling. The traditional system of a bookmaker
setting odds that a gambler wagers on has been challenged by online exchanges that
act more like stock exchanges than traditional sportsbooks. Instead of the traditional
gambling methods, online gambling can now take the form of playing the bookie or
investing in a predictive market. Also, one would expect the product’s price to decrease
as competition is introduced. This reduction in the price of gambling has taken place
as online sportsbooks have begun to decrease the vigorish they take in. Aside from the
new predictive market forums, traditional sportsbooks also offer more types of wagers.
In-game style sports betting (wagering on a game while the event is taking place) has
increased in popularity. Research has found that such real-time markets operate just as
efﬁciently as traditional wagers (Debnath et al. 2003).
D Demand Elasticity
Due to the elimination of geographical restrictions, demand is more elastic to price
in the post-Internet sports gambling era. Currently, small point-spread ﬂuctuations
change bettor tendencies, as bettors can have multiple accounts and move quickly from
sportsbook to sportsbook. In addition, if the point spread differential is too great, there
exists the opportunity for what is known as arbitrage, in which a bettor wagers on both
sides of a game with different point spreads (Grifﬁn 2011). If the game in question
results in a score between the two spreads, the bettor wins both wagers. This kind of
activity creates an incentive for sportsbooks’ point spreads to converge. The end result
is multiple ﬁrms with prices (or point spreads) very close to each other and the end of
third-degree price discrimination, as we would expect in a more competitive economic
environment.
E Economies of Scope
Some economies of scope do exist between the Internet sportsbook industry and other
Internet gaming industries. An Internet sportsbook will often offer more traditional
Internet games, such as blackjack, slots, or poker. Calls to regulate the industry could
not be more understandable in this case, as the recreational gambler likely has no idea
of the true expected payouts, which in regulated terrestrial gambling casinos are closely
monitored (and transparently displayed). Overall the impact of the economies of scope
compared to the terrestrial games has greatly decreased.

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F Sportsbook Efﬁciency
In the classic framework of the sportsbook, the objective was simple. By balancing
the action on each side of the game the sportsbook is guaranteed no risk and a
safe (5% on all action) return. Recent literature has challenged this assumption, a
change likely attributable to greater competition in the online sportsbook industry.
Steve Levitt (2004) has suggested that oddsmakers adjust the lines to take advantage
of their superior forecasting ability, a suggestion supported by Wayne Winston (2009).
George Diemer (2009) followed up this research and identiﬁed two types of sports-
books, a proﬁt-maximizing type and an exposure-minimizing type. Rodney Paul and
Andrew Weinbach (2011) also found imbalance but attributed it to bettor’s bias toward
the favorite teams. Deniz Igan, Marcelo Pinheiro, and John Smith (2011) highlighted
bookies’ recognition of bettor racial biases as inﬂuencing unbalanced books and the
initial setting of point spreads. No matter the cause, the assumption of the traditional
terrestrial sportsbook’s balanced action is being reevaluated.
G Online Sports Betting Exchanges as
an Anti-Corruption Tool
Stephen Easton and Katherine Uylangco (2010) found a high level of efﬁciency in the
online tennis betting market, making it a useful predictor of match outcomes. Given
the betting market’s forecasting ability, it could be used as a statistical screening device
for nefarious conduct in the market. Similarly, Karen Croxson and J. James Reade
(2011) pinpointed prompt and accurate price updates in the online soccer wager-
ing market following any change in scoring, indicating considerable market efﬁciency.
Unexpected deviations from the documented efﬁciency could trigger a follow-up inves-
tigation regarding whether such deviation was benign or indicative of chicanery. Using
Betfair-derived data, Alasdair Brown (2012) found trace amounts of inside informa-
tion in trading during the epic 2008 Wimbledon men’s ﬁnal between Roger Federer and
Rafael Nadal. Betting exchanges such as Betfair have also contributed to the detection
of corruption in sport (Drape 2008). As quoted by Davies et al. (2005, 539), a Betfair
spokesperson said, “We are putting a searchlight on the sport and helping it clean up
its act. There is a clear paper trail on our site that doesn’t exist in high street [betting]
shops. We are entirely transparent. We have no vested interest in the outcome of a horse
race” or other sporting event.
In2007,Betfairdetectedsuspiciousbettingpatternsinvolvingatennismatchbetween
Russian Nikolay Davydenko and Italian Martin Vassallo Argüello and took the then
unprecedented step of halting further trading on the match and turning over transac-
tion records to the appropriate tennis authorities. The subsequent investigation cleared
both players of wrongdoing but resulted in Ben Gunn and Jeff Rees’s (2008) “Envi-
ronmental Review of Integrity in Professional Tennis,” which (1) identiﬁed 45 matches

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sports betting
with prima facie
evidence of fraud that merited further inquiry and (2) led to the
establishment in 2009 of the Tennis Integrity Unit (TIU), a joint venture of the Inter-
national Tennis Federation, the four Grand Slam tournaments, the ATP World Tour,
and the Women’s Tennis Association, each of the governing bodies in global elite-level
tennis.14 The TIU rendered its ﬁrst signiﬁcant enforcement action on May 31, 2011,
when the organization placed a lifetime ban on Austrian player Daniel Kolleher for
gambling-related match-ﬁxing.
iv The Future of the Internet
Sportsbook Industry
.............................................................................................................................................................................
Sports gambling is now in its third incarnation. The ﬁrst generation of sports gam-
bling has existed for centuries. Whether the wagers take place directly between bettors
without an intermediary, at a government-regulated brick-and-mortar establishment,
or through a neighborhood bookie operating illegally, this ﬁrst-generation sports bet-
ting continues to be popular. The second generation of sports-based gambling was
described by Steven Crist (1998) in a Sports Illustrated cover story that reported on
bettors placing wagers based on ﬁxed odds remotely through the Internet. By offering
odds, point spreads, totals, and other wagering opportunities, online (and often off-
shore) sportsbooks mimicked terrestrial sites in Las Vegas and were more convenient
because they do not require the bettor to be on-site to place a wager.15 During this time,
only one American sportsbook operator conducting business offshore was convicted
by a jury of violating the Wire Act,16 and only one individual bettor was charged with
placing a sports wager over the Internet.17 The third generation, sports gambling 3.0,
characterized by real-time online betting exchanges with attributes analogous to any
modern stock exchange, has been described by Smith and Vaughan Williams (2008,
404–405) as“an interactive web-based platform for placing and laying bets on sporting
events” that offers in-running markets and lower commission rates. Betfair in London
is the most recognizable (and popular) example of a sports betting exchange (Davies
et al. 2005). Recognizing this as a potential growth area, at least one land-based, in-
person sportsbook, Cantor Gaming’s upscale M Resort in Las Vegas, has begun offering
similar options for patrons (Benston 2010). Given this backdrop, a number of notewor-
thy developments over the course of the past decade have illustrated the uncertainty
currently associated with Internet gambling and the online sportsbook industry.
A BetOnSports.com
No case study explains the uncertainly in the industry as well as what transpired in
connection with BetOnSports.com. Between 2002 and 2004, the Costa Rica–based

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141
company listed on the London Stock Exchange took in almost USD4 billion in
wagers, 98 percent of which came from Americans. On July 17, 2006, company
CEO David Carruthers was arrested at the airport in Dallas, Texas, en route to
Costa Rica. He was charged with racketeering, conspiracy, and fraud connected to
an illegal gambling enterprise. In addition, the government charged BetOnSports.com
founder Stephen Kaplan with multiple counts of promoting illegal gambling. These
charges illustrate how current laws are being enforced in connection with Inter-
net sports gambling businesses and are suggestive of how future cases may be
prosecuted.
B Unlawful Internet Gambling Enforcement Act of 2006
The latest attempt by Congress to curtail sports gambling was made in October 2006,
when it passed the Unlawful Internet Gambling Enforcement Act (UIGEA) as part
of an otherwise unrelated anti-terrorism bill.18 UIGEA was signed into law in 2006
but did not go into effect until June 1, 2010. The statute’s preamble acknowledges:
“New mechanisms for enforcing gambling laws on the Internet are necessary because
traditional law enforcement mechanisms are often inadequate for enforcing gambling
prohibitions or regulations on the Internet, especially where such gambling crosses
State or national borders.”
UIGEA prohibits payment processing entities, such as banks and credit card compa-
nies, from accepting or distributing monies derived from gambling (Ramasastry 2006).
Prior to UIGEA, a gambler could fund his or her account by using a credit card. The
intent of Congress was to eliminate the ease of ﬁnancing overseas sports gambling
and to cut sportsbooks’ liquidity. A number of Internet gambling sites responded by
withdrawing from U.S. markets. Certain private websites continue to access the Amer-
ican market, but they face the threat of prosecution. Similarly, bettors with money on
deposit risk being unable to redeem their winnings and account funds if the website is
shut down and assets are seized.
UIGEA contains a number of important exemptions. Such carve-outs include wildly
popular online fantasy sports, government-run lotteries (some of which have intel-
lectual property licensing deals with professional sports teams and leagues), entirely
intrastategambling,certaininterstatehorseracing,andgamblingtakingplaceonIndian
reservations. The indirect anti-gambling enforcement mechanism inherent in UIGEA
and the numerous exceptions to what is deﬁned as “gambling” therein have resulted in
a situation described as “the absence of a comprehensive federal policy toward internet
and sports wagering”(Cabot 2010, 271),“the troubled legal status of internet gambling
casinos in the United States in the wake of [UIGEA]” (Nelson 2007, 39), and “an exer-
cise in futility” (Kelly 2011, 257). In addition, Jennifer Chiang (2007) highlighted how
compliance with federal laws such as UIGEA may still result in violations of state law.
Finally, the passage of UIGEA has re-ignited calls for Internet gambling to be regulated
at the state, not federal, level (Wajda 2007).

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sports betting
C Galileo Fund
The proliferation of online sportsbooks and the accompanying decreased concentra-
tion of market power have resulted in a considerable increase in the number of “outs”
available to both casual bettors and professionals who make a living wagering on sport-
ing events. Such professional bettors gamble systematically in a way resembling stock
market investors and include individuals with large bankrolls as well as syndicates using
sophisticated computer-driven algorithms. Accordingly, it was only mildly surprising
when Gibraltar-based Quay Financials and London-headquartered Centaur introduced
the Galileo Managed Sports Fund (Galileo), a hedge fund intending to focus on the
sports exchange market (Millman 2010; Popper 2010; Wachter 2010). Darren Rovell
(2010) reported that Galileo would bet on outcomes in “soccer, tennis, cricket, horse
racing and golf, with plans to expand to [American football] and baseball over the
next year.” The minimum initial investment in Galileo is e100,000. As of June 1, 2011,
Galileo did not accept investors from the United States, although fund managers were
reportedly seeking the government’s stamp of approval.19 If the Galileo fund is suc-
cessful (in terms of investment volume and returns), online sportsbooks and exchanges
almost certainly will respond.
v Conclusion
.............................................................................................................................................................................
The Internet sportsbook industry is in transition. As some American-based sports
leagues shift to tepidly supporting legalized gambling (McKelvey 2004a, 2004b; Thom-
sen 2009), the sometimes polarizing discussion continues regarding the (beneﬁcial and
detrimental) impact gambling has on economies and ﬁnancial systems (Kindt 2010).
Future legal developments, in both the United States and elsewhere, will continue to
shape the industry (Cabot 2010; Chan 2010). AbsentAmerican intervention in the form
of legislation and prosecution, the Internet sportsbook industry will probably converge
toward a competitive industry with normal economic proﬁts and wagering options
available to the consumer. That likelihood notwithstanding, government regulation for
U.S.-based bettors and sportsbooks would almost certainly be welcomed by those in
the Web-based sports gambling industry, as such oversight would likely increase the
legitimacy, transparency, and long-run certainty for the industry globally.
Notes
1. Three other U.S. states (Delaware, Oregon, and Montana) are permitted to offer limited-
scope sports wagering under the Professional and Amateur Sports Protection Act of 1992
(PASPA) (Galasso 2010). Although largely outside the scope of this book chapter, it is
noteworthy that a lawsuit brought by a New Jersey senator and an Internet gaming trade

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the economics of online sports betting
143
association challenging the legality of PASPA was dismissed in March 2011 (Rodenberg
and Young 2011).
2. If the sportsbook is successful in balancing the action, 50 percent of the money will be
winners and 50 percent will be losers. The 10 percent vigorish on the losses comes to
5 percent of aggregate money wagered on each event.
3. As discussed in detail below, government pressure on legal businesses indirectly afﬁliated
with sports gambling continues today as evidenced by the Unlawful Internet Gambling
Enforcement Act of 2006 (UIGEA), which makes it illegal for companies to process
payments for gambling companies.
4. For more information, see Peter Reuter’s (1983) discussion of John Payne and Mont
Tennes.
5. The scope of the NGISC’s coverage regarding gambling was extensive, and Internet
gambling was but one section.
6. In relevant part, Section 1084(a) of the Wire Act states: “Whoever being engaged in the
business of betting or wagering knowingly uses a wire communication facility for the
transmission in interstate or foreign commerce of bets or wagers on any sporting event
or contest, or for the transmission of a wire communication which entitles the recipient
to receive money or credit as a result of bets or wagers, or for information assisting in
the placing of bets or wagers, shall be ﬁned under this title or imprisoned not more than
two years, or both.” David Schwartz (2005) has provided a comprehensive analysis of the
Wire Act.
7. For example, prior to being amended, FISA was interpreted to prohibit examination of
an e-mail exchange between two foreign individuals even if both were outside American
territory. The amendments closed such apparent loopholes.
8. Although none has passed into law, several bills to amend the Wire Act have been
considered by Congress over the past 15 years.
9. As Chad Millman (2011) summarizes: “The decision of whether to take a bet from the
United States seems to be based as much on a founder’s tolerance for risk as it is on
existing law. If the boss is willing to taunt the authorities, the billion-dollar American
betting market is something they’ll openly tap.”
10. This recommendation may have led, at least partially, to passage of UIGEA in 2006.
11. The complete NGISC report can be found online at http://govinfo.library.unt.edu/ngisc/
reports/ngisc-frr.pdf.
12. Edward Morse (2010) and Luca Rebeggaini (2010) discuss both cases in detail.
13. Full details of CCA’s estimates can be found online at http://www.cca-i.com.
14. Shortly after the report by Gunn and Rees (2008), gambling-related suspensions were
levied against several professional tennis players from Italy. The Italian players subse-
quently sued the ATP World Tour challenging their suspensions (Bass and Rodenberg
2011).
15. Steve Budin and Bob Schaller (2007), Sean Patrick Grifﬁn (2011), and Michael Konik
(2006) have provided intricate accounts of how online sportsbooks operate.
16. Antigua-based World Sports Exchange founder and president Jay Cohen was convicted by
a trial court jury of violating the Wire Act when his company took bets from Americans
in New York and elsewhere (United States v. Cohen, 260 F.3d 68 (2nd Cir. 2001); Schwartz
2010). An in-depth discussion of the case is presented by David McGinty (2003).
17. Dave Forster (2003) has explained how Jeffrey Trauman is believed to be the ﬁrstAmerican
individual bettor to be charged with a crime for placing a sports wager over the Internet.

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18. I. Nelson Rose and Martin D. Owens (2009) provide comprehensive coverage of UIGEA
and related federal anti-gambling statutes.
19. On a related note, Michael Macchiarola (2010) has suggested that federal securities laws
could be used to regulate sports betting.
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chapter 8
........................................................................................................
THE FOOTBALL POOLS
........................................................................................................
david forrest and levi p´erez
Introduction
.............................................................................................................................................................................
In principle, the term football pools could be applied to any pari-mutuel wager-
ing concerning the outcomes, or any other aspects, of football (soccer) matches.
However, it has long been used more speciﬁcally to refer to long-odds, high-prize
gambling games where entitlement to a share of the jackpot is linked to football
results. Long odds are inherent in the product and are achieved by requiring players
to match their guesses or forecasts with the results of a long list of ﬁxtures. This form
of gambling therefore closely resembles lotto, the principal difference being depen-
dence of winning on football results rather than the drawing of numbers by random
process.
The similarity of football pools to lotto games has shaped both the history of the
pools and academic research on this form of gambling. The history is one of rise and
fall, with the decline of the pools from its status as a mass participation activity evidently
triggered by the introduction of lotto to the gambling market. Academic research on
football pools has been inﬂuenced by the literature on lottery demand. e.g., the way
in the price variable has been speciﬁed, and calculated, to facilitate estimation of own-
and cross-price elasticities of demand. In turn, academic research on the pools has
turned up ﬁndings potentially relevant to modeling lotto sales and to public policy
issues relating to lotto games.
Academic work on football pools has focused on two markets, the United Kingdom
and Spain. So too does this chapter, reﬂecting not only that these are the countries where
research has taken place but also that they present two particularly interesting cases.
The British pools industry is interesting for its history. As recently as the early 1990s it
was by far the dominant mode of gambling in the country, attracting a clear majority
of the male population and a large proportion of the female as well. By 2010 it had
all but faded away, with barely 3 percent of adults participating and turnover likewise

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reduced (Gambling Commission 2010). The Spanish case is interesting because it is the
largest pools market in Europe, accounting for about one-half of sales on the continent
as a whole. A point for investigation is why Britain’s industry almost disappeared in
the age of lotto games whereas that in Spain was able to establish a signiﬁcant niche
in the gambling market despite substantial initial cannibalization when lotto was ﬁrst
introduced.
The Games Explained
.............................................................................................................................................................................
Football pools are offered in a variety of jurisdictions outside Europe, for example, in
Argentina, China, Singapore, and (with other sports substituted) in parts of the United
States and Canada. However, it is a form of gambling most closely associated with
Western Europe, where pools usually are marketed by the operator of the state lottery.
In Britain, however, it is run by a private sector enterprise (which is also a monopoly
but, in this case, a non-statutory one).
The football pools emerged as a popular gambling medium in the years immediately
after World War II, when the British ﬁrm Littlewoods invented the game known as
the treble chance. This was the ﬁrst (very) long-odds gambling game on football and
remains the core product in Britain today. Rules have varied only in detail over the
years. From the mid-1990s the number of football matches included on the weekly
coupon was 49. A single entry consists of eight selections, though customers are
expected to make multiple entries by choosing 10 or 11 matches (with every com-
bination of 8 matches within the set then comprising one play). If a player enters a
combination of eight matches where all eight subsequently result in score-draws (any
tie except for 0–0, for example, 1–1 or 2–2), he wins a share of the jackpot prize.
Those close to having picked eight score-draws are rewarded with a share of a lower
tier prize. In the event that there are no winners of the jackpot, there is a rollover,
with the prize available on the jackpot added to that for the next edition of the pools.
In the event that any of the football matches included in the game do not in fact
take place, due to adverse weather for example, the competition still goes ahead with
the outcome then related to football results invented by a panel of experts appointed
by the operator (Forrest and Simmons 2000, modeled how the panel reaches its
forecasts).
The football pools also arrived in Continental Europe in the 1940s, but the core
game offered then and now differs from that in Britain. Here, the core toto game
has a 1X2 formula whereby a player is required to guess or forecast whether each
match in a named set of 12–15 (the number differs by country and has also varied
over time) will end in a home win (1), a draw (X), or an away win (2). In countries
with relatively low status football leagues, the set of matches may include ﬁxtures
from higher proﬁle foreign competitions, such as the premier leagues of England or

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149
Spain, or even from alternative, locally popular sports. The number of matches to
be guessed tends to be lower in small market countries, such as Austria and Finland,
where otherwise the jackpot would be won too infrequently because the game would be
too hard.
Everywhere, a share of the jackpot is claimed on the basis of the player matching all
of his or her forecasts with the football results, and there are lower tier prizes for those
coming close. Commonly, if a jackpot is not won, it rolls over to the next time. As in
Britain, this is an adaptation of the original rules, which had provided for funds from
the jackpot pool to cascade down to lower tier prizes when there was no jackpot winner.
The change to rollovers postdates the introduction of lotto and made game structure
resemble lotto even more closely.
Football Pools in Britain
.............................................................................................................................................................................
Pools were offered from the 1920s but in a different form from the current version
of this gambling product. During that period, players were asked to forecast results
in small groups of matches for small stakes and small prizes. The industry struc-
ture was competitive, with the number of ﬁrms in the market in the hundreds. In
1946 one of those ﬁrms introduced the long-odds treble chance game, and it quickly
became popular. The shift of demand to the new long-odds game then both grew
the total market and led to substantial market concentration. Roger Munting (1996)
noted that there were still 231 companies in 1948 but that the number fell to 42 by
1950 and rapidly thereafter, so that two companies, Littlewoods and Vernons, soon
claimed virtually the entire market (Competition Commission of Great Britain 2007).
The shift away from competition may be understood as a consequence of the product
transforming from essentially a betting product to one akin to a lottery, where the
appeal of the size of the prize offset an extremely low probability of winning. Philip
Cook and Charles Clotfelter (1993) noted the importance of economies of scale in
consumption in lotto markets. Their research showed that the utility derived by a pur-
chaser depends on the number of other entries because it is that which determines
the size of the jackpot pool. Consequently, in long-odds competitions, like lotto but
also like the pools, there is a tendency to natural monopoly, since whichever ﬁrm
has the largest, and therefore most exciting, prize will attract more customers from
smaller companies, making the games of the latter even less appealing by the next
period, and so on, until all competitors collapse. This is consistent with what hap-
pened in the pools sector. It is somewhat surprising that only two ﬁrms, rather than
one, eventually dominated the market. They ﬁnally merged in 2007, under the owner-
ship of Sportech plc, their coexistence until then explained by one ﬁrm compensating
for lower jackpots with a much lower entry fee (Competition Commission of Great
Britain 2007).

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sports betting
The Heyday of the Pools in Britain
.............................................................................................................................................................................
Such was the rapidity of development of the pools market once it was based on the new
long-odds game that it soon became (at least for men) a majority pastime, “more so
than elsewhere deeply rooted in the nation’s recreational and social fabric”(Miers 1996,
360). Even by the late 1980s, more than one-third of adults were still playing (Sharpe
1997, 360). They were playing for payouts exceeding £2m when there was an outright
winner, comparable in real terms to U.K. lotto payouts today. Such life-changing wins
attracted considerable popular interest, and a celebrated stage show and subsequent
ﬁlm tracked the “spend, spend, spend” lifestyle of one (female) winner.
David Forrest (1999) has noted that, in this period, the pools served the role of a
National Lottery from the perspective of both the government and the public. The gov-
ernment exploited the willingness of players to tolerate high takeout rates in gambling
games where a large top prize is available by extracting signiﬁcant tax revenue. Within
two years of the emergence of the treble chance game in the 1940s, it had introduced a
new pools tax, set at 10 percent of stakes. This was increased successively to 20, 25, 33,
40 and (in 1982) 42.5 percent. It was still 42.5 percent at the time of the launch of the
National Lottery, though with the variation that 5 percent was by then hypothecated to
(mainly sports-related) good causes nominated by the pools industry foundation. The
proportion of the stake accruing to tax was therefore very close to that applied subse-
quently to the National Lottery (40–41%). The relative lateness of the United Kingdom
in introducing a state lottery was no doubt related to the fact that the country already
effectively had a proxy lottery with similar ﬁscal function.
Certainly the public tended to treat the pools as an alternative form of lottery product
rather than as sports betting. Nearly half of all players purchased in advance, for a block
of weeks, with the same numbers entered for each of those weeks, such that their entries
weremadewithoutevenknowledgeof whichfootballgameswouldcorrespondtowhich
numbered lines on the entry form. Even those who purchased their entries week by
week appear to have chosen numbers rather than matches: the operators themselves
suggested that 80–95 percent of all customers chose numbers on the coupon without
regard to which teams were covered (Forrest 1999). Thus there may have been conscious
selection rather than random play, but it was largely based on selecting numbers of
personal signiﬁcance rather than by assessing teams’prospects as a sports bettor would.
It was by no means unreasonable for pools customers to treat the pools product
as if it were a numbers game. The rules require players to guess which matches will
be drawn. Perhaps the most detailed statistical forecasting model in all of sport, the
football forecasting model outlined in its ﬁrst version by Stephen Dobson and John
Goddard (2001), proves to be effective in picking which team in a match is more
likely to win but very ineffective in calling draws, which the authors regarded as near
random events. Similarly, ﬁxed-odds bookmakers offer odds for draws that display
very low variance across matches. This implies that there is almost no scope for the

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151
application of skill in selecting eight matches as draws, let alone score-draws. That
there was no advantage to being knowledgeable about football will have been helpful in
developing the pools product as a mass market activity, but this feature may have been a
hindrance later when the pools needed to ﬁnd a niche in the face of migration of players
to lotto.
The Impact of the Lottery on the
Football Pools in Britain
.............................................................................................................................................................................
The Royal Commission on Gambling (1978) had foreseen such migration and had
forecast that any future introduction of a national lottery would damage the pools. But
the pace with which they declined was nevertheless striking. The 6/49 lotto game was
launched in the course of the 1994–1995 football season, and pools turnover for the
whole season was 12 percent lower than in the season before. In 1995–1996 there was
a further decline of 28 percent. By 1996–1997, turnover was about £400m, compared
with well over £900m in the last full season without lotto, for a cumulative decline of
close to 60 percent.
Analysis below will show an immediate effect of similar magnitude in the case of
the Spanish pools when that country launched its ﬁrst lotto game. But, whereas in
Spain the pools market then stabilized, in Britain relentless decline continued. By the
time of the Competition Commission (1997) inquiry into the pools industry, annual
sales were down to £77m. Statistics from regulatory returns (Gambling Commission
2010) indicated turnover of only £52m in 2009–2010, two years after the merger of
Littlewoods and Vernons. Thus, even without adjustment for inﬂation, 95 percent of
the market had been lost over the period since the introduction of a national lottery.
The pools had become marginal to the gambling industry. For example, the regulatory
statistics indicated annual turnover in football bookmaker betting of over £1b and in
total non-remote betting of more than £9b. The adult four-week participation rate for
the pools had fallen to 3.1 percent (Gambling Commission 2010).
Substantial cannibalization of the pools by the lottery was, with hindsight, inevitable
since demand for the pools product likely largely represented suppressed demand for
a lottery. Promoters of an actual lottery have advantages over the pools. First, their
product is more consistent in that it can be offered year-round and more than once a
week if they deem that likely to be proﬁtable. Second, both lotto and pools games can
produce large variations in the number of winners from week to week, with disappoint-
ing individual payouts if popular numbers are drawn in the case of lotto or if draws
occur in a large number of matches in the case of the pools; but the problem is easier
to control in the case of a pure numbers game, and the risk of multiple winners each
receiving very little may be reduced by choice of an appropriate game matrix. Third,
the lottery can attract additional players, particularly among women, whose aversion

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to football may deter them from playing the pools. These inherent advantages made
it likely that the new lottery would gain a larger market than the pools, threatening
the latter’s survival if initially loyal customers subsequently switched their expenditures
because the lottery had emerged, as it did immediately and by a substantial margin,
as the medium with the larger jackpot. However, the pools industry also displayed
weaknesses of its own making that made it still more vulnerable to this possibility of
continuing decline. A fundamental problem to retaining customers was that it offered
poor value for money, with a takeout rate of 70 percent compared with 50 percent for
the lottery. This gap was so wide, despite similarity in tax rates, because operating costs
in the pools accounted for 30 percent (rather than 10%, as in the lottery) of sales rev-
enue, reﬂecting a failure to modernize distribution and processing systems. Most pools
customers still purchased from an army of 96,000 door-to-door collectors (Munting
1996), which was not only costly for the companies but also inconvenient for customers
relative to the possibility offered by lotto to buy tickets at computer terminals operated
in supermarkets, convenience stores and petrol stations.
It is therefore completely understandable why the introduction of lotto initiated a
rapid decline in the pools sector. Of more interest is why demand continued to decline
precipitously in a continuous fashion. It might have been thought that the pools sector
would respond to the new environment by improving its product and that market size
would eventually stabilize when it found a core of customers for whom a link with
football was an appealing feature of a long-odds product.
The pools companies did respond over time to the lottery. From government, they
won such concessions as a lower tax rate, the freedom to advertise on television, and the
lowering of the minimum age for playing, from 18 to 16. To boost headline prizes, they
offered players a “free” chance to win £2m prizes (unlikely to be paid out, as they were
related to freakish sets of football results) and initiated rollovers of the jackpot. They
modernized their distribution systems to embrace, for example, entering through the
Internet or at a bookmaker’s shop. All these measures were no doubt positive. However,
the companies also raised the takeout rate, despite a fall in the rate of tax charged to
pools. The Competition Commission of Great Britain (2007) inquiry noted that value
for money had worsened in the period since the introduction of lotto, with a takeout of
75–80 percent in the immediately preceding years to its Report. Post-merger, takeout
remained highly uncompetitive with any other gaming product. In 2009–10, Gross
Gaming Yield was £41.0m on stakes of £52.4m (Gambling Commission 2010). This
represents a takeout rate of 78.2 percent.
It is instructive to ask who plays the pools given the poor value it offers compared
with other modes of gambling. The Competition Commission of Great Britain (2007)
commissioned research that provides a snapshot proﬁle of customers at that time, based
on a sample of 1,100 participants (nearly all of whom proved to play weekly, consistent
with the commission’s observation that weekly sales appeared to be invariant to the
size of lotto jackpots). The customer base was strongly skewed toward older males (in
fact, only 6% of players were below age 45). Most customers had played for a very long
time, 70 percent for over 20 years and more than half for over 30 years. This appears

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the football pools
153
to be illustrative of a striking failure to refresh the customer base to replace those lost
through mortality or defection.
The remaining players of the pools seemed largely ignorant of the effective price
of entering the game. Effective price, rather than entry fee, is commonly used by
economists to model demand for lottery-style products and is the expected player loss
per unit stake. But only 1 percent of this sample was able correctly to identify the
proportion of the stake paid out in prizes as in the band 21–30 percent. Those who
have stayed with the pools seem to have done so out of both inertia and a lack of
awareness of the high effective price.
The failure of the industry to recruit new customers is not surprising, given that for
those seeking gambling opportunities with high potential winnings, the portfolio of
games available from the National Lottery offers far superior value. For those with a
taste for football, the pools offer a main game that does not challenge them to employ
their football knowledge because it cannot realistically be claimed to be based on skill.
Moreover, long-odds wagers can be constructed by wagering on football with ﬁxed
odds bookmakers who, in a vigorously competitive sector, have been offering much
fairer bets than in the past (Forrest 2012). It is hard not to speculate that the pools
industry strategy was not to pursue the market captured by football bookmakers but
to be content to extract maximum revenue from existing players attached to the pools
by habit and poor awareness of price.
The Football Pools in Spain
.............................................................................................................................................................................
Based on information for 2007, provided by the World Lottery Association, Spain is
clearly the leading football pools market in Europe, with annual sales of e547m, which
we calculate to represent e12.24 of stakes per inhabitant. France, the second-ranked
country by absolute turnover, reported a market only about one quarter as large.
Some smaller countries, particularly the Nordic group, recorded high expenditures
in per capita terms: Norway (e18.87), Sweden (e9.27), Finland (e6.73), Denmark
(e4.45), Greece (e4.11), and Morocco (e2.30) (included in the data as a member
of European Lotteries) exhibited greatest enthusiasm. For comparison, the sales of
the shrunken British industry were equivalent to only about one euro per person
per year.
Our focus is on Spain, where the relative importance of the pools has stimulated
the only formal econometric modeling of pools games. The core product, known as
La Quiniela, was launched in the 1946–1947 season into a market that already had
passive national lottery games (but no legal bookmaking). The ﬁrst coupon invited
players to forecast results (1, X, or 2) for just 7 matches, but the list was soon increased
to 14 (Pujol 2009), possibly in light of the success of the new long-odds treble chance
game in Britain. The format remained at 14 matches until season 1987–1988, but a 15th

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matchwasaddedin1988–1989(itrevertedto14in2003–2004butonlyfortwoseasons).
Rule changes have included provision for the top prize to roll over to the next game
(from 1988–1989) and adding a new lower-prize tier for those with 11 (1991–1992) or
10 (2003–2004) correct selections. The entry fee was increased regularly, from 2 pesetas
at the beginning to e0.50 from 2003–2004. The takeout rate is 45 percent, of which
11 percent accrues to provincial governments to provide sports facilities, 1 percent to
the National Council of Sports, and 10 percent to the Football League. The pools are
operated by the same state-sanctioned agency that runs national lotto games. Lotto was
ﬁrst introduced in October 1985 in the form of the weekly La Primitiva. Subsequently,
similar to the evolution of lotto in other countries, a second weekly draw was added,
and over time a variety of alternative lotto games augmented the portfolio. Legal sports
betting appeared in some regions from 2008.
With this background in mind, ﬁgure 8.1 shows real sales revenue (at 2007 prices),
on a game-by-game basis, from 1970. Econometric analysis reviewed below attempts to
account for the considerable variation from coupon to coupon. But the most striking
features are the sharp fall in sales following the introduction of lotto and the subsequent
recovery and stabilization. Stabilization was achieved at a level at which the pools
remained a signiﬁcant part of the operator’s portfolio, in-season attracting similar
weekly sales as one of the two weekly drawings of the core lotto product, La Primitiva
(Forrest and Pérez 2011).
Who is entering the game? Brad Humphreys and Levi Pérez (2010) analyzed the
ﬁndings from two random sample telephone surveys conducted in Spain in 2005 and
2006, with over 2,600 observations. Of the respondents, 49.7 percent reported having
played La Quiniela at some time in their lives, with one-ﬁfth of these playing weekly.
A probit model showed that the likelihood of participation was positively related to
income and negatively related to age. Compared with the British pools, the Spanish
game attracted a much higher participation rate and disproportionately appealed to the
40
35
30
25
Real sales revenues (€ millions)
(CPI = 100 in 2007)
20
15
10
5
0
0
100
200
300
400
500
600
700
800
Coupon number
900 1000 1100 1200 1300 1400 1500
figure 8.1 Real sales revenues of Spanish football pools

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## Page 176

the football pools
155
young and afﬂuent. This makes the customer proﬁle more like that for British sports
betting. The Spanish pools no doubt beneﬁted from the absence of a legal bookmaking
sector but also had a product that was more skill-based than the British treble chance
and one with a takeout rate approximately 30 percentage points lower. These seem
likely reasons for the Spanish operator’s success in maintaining a niche for the pools
in a lotto world. Its principal challenge for the future may be to maintain this position
as the emerging legal bookmaker betting market in Spain matures. Legalization of
sports betting in some provinces appears to have coincided already with some fall off
in demand.
Modeling Sales of La Quiniela
.............................................................................................................................................................................
A number of papers (García and Rodríguez 2007; García, Pérez, and Rodríguez 2008
and 2011; Forrest and Pérez 2011) have analyzed pools sales using the same framework
as followed in the lotto demand literature since the model developed by David Gulley
and Frank Scott (1993). The Gulley-Scott model regresses the number of entries in a
draw on the effective price of entries to that edition of the game (and controls). Effective
price is the expected loss per unit stake from a single entry, assuming that all players
select their entries randomly, and shows considerable variation according to the pattern
of rollovers. The problem of endogeneity (sales themselves inﬂuence expected loss) is
addressed by instrumenting effective price on the size of rollover. Variations include
substituting the size of jackpot for effective price (Forrest, Simmons, and Chesters 2002)
and adding variance and skewness of returns to the speciﬁcation (Walker and Young
2001).
Applying the basic model for lotto to the pools game is problematic in terms of
the calculation of effective price. It is straightforward to calculate the expected value
of entering a randomly selected combination of numbers into a lotto game but not
self-evident what would be meant by random choice of a set of football results. The
studies reviewed here calculate expected loss on the basis that any entry will have the
same probability of success of winning at each prize tier as is observed across entries
in the long run (for example, the whole data period). It therefore treats players as if
each perceives his or her chance of success as equal to that of anyone else. It could be
argued that this is less plausible in a game which purports to require skill than in a pure
numbers game, but it is a necessary simpliﬁcation and one that, on the whole, appears
not to prevent the models from achieving satisfactory ﬁt.
On the other hand, modeling pools sales in the context of Spain offers some advan-
tages over much of the literature on lotto, which may allow the exercise to yield stronger
evidence than hitherto concerning the behavior of players of lotto-style games. First,
most modeling of lotto sales has been conducted in jurisdictions where the entry fee
has never varied from one unit of local currency, preventing results from informing

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## Page 177

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sports betting
policy debate on whether there should now be an updating of the price of a ticket, given
high cumulative inﬂation since the inception of lotto. Second, the Gulley-Scott model
abstracts from prize structure, and though this varies from draw to draw everywhere,
effective price, size of jackpot, and variance and skewness of returns always move in
sympathy with each other as size of rollover varies, given constancy in game rules.
This makes it hard to distinguish the effects of each of these variables and therefore
frustrates attempts to evaluate the merits of alternative game designs. But the history
of La Quiniela
incorporates multiple changes of entry fee, game design, and prize
structure, which induce additional variation in the data and make it potentially easier
to test hypotheses compared with lotto markets in America and Britain. Econometric
modeling of pools demand in Spain may therefore serve more than a local purpose.
The Relationship between the Pools
and Lotto Markets
.............................................................................................................................................................................
Controlling for features of the coupon (which teams are represented), within-season
trend, real entry fee and effective price, Forrest and Pérez (2011) focused on how
pools sales have been and are inﬂuenced by the parallel existence of the core lotto
product in Spain, La Primitiva. They investigated two issues. First, to what extent did
the introduction of the lotto game displace pools demand? Second, do consumers
switch between pools and lotto on a week-by-week basis, depending on the incidence
of rollovers, making them substitutes? The two issues are frequently conﬂated in the
literature on gambling but are in fact quite distinct. For example, a new product
may cause structural change in the market for an existing product because a group
of consumers changes permanently to buying the new product. But that does not
imply that the two products will be substitutes for each other in the economic sense of
cross-price elasticity henceforth being positive.
The analysis was based on observations from 1,514 editions of the pools game
between April 1970 and December 2007. The lotto game was present in the market
from observation 618, and the introduction of a second weekly draw coincided with
observation 857. It should be noted that the new competing game was sold at exactly
the same outlets as the pools and that consumers could therefore readily choose for
which product to purchase tickets. It should further be noted that the second weekly
lotto draw was timed for the weekend, when, in season, there is always a pools coupon.
Cannibalization was measured employing two dummy variables, respectively indi-
cating whether it was a period with a Thursday-only lotto game or a period with
Thursday and Saturday lotto. The results indicate a 52 percent fall in the number of
pools entries as a result of the introduction of the lotto game, broadly similar to what
was observed in Britain in the aftermath of the launch of its national lottery. With two
lotto draws per week available, pools entries were estimated to be 87 percent lower than

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## Page 178

the football pools
157
in the no-lotto case. The consistency of the order of magnitude of impacts in Britain
and Spain suggests that, pre-lotto, more than half of the pools market was expressing
purely a demand for long-odds gambling rather than for a speciﬁcally football-related
game. Perhaps indeed this applied more strongly in Spain to the extent that, in contrast
to Britain, there was no inducement to switch because lotto had a lower takeout rate
(in Spain, both the pools and lotto offered a 45% takeout).
After cannibalization, whether consumers subsequently switch expenditure between
pools and lotto on a week-to-week basis, as rollovers modify the relative value of the two
products, is of practical importance to operators in Europe because, typically, the two
types of game are provided by the same agency. Game formats are designed to produce
periodic rollovers to boost sales above the normal level, but if extra sales were achieved
just because players switched from an alternative product for that week, the rollover
money would be wasted in terms of boosting the agency’s global revenue. Forrest and
Pérez (2011) estimated the elasticity of pools sales with respect to the effective price of
Thursday lotto and the effective price of Saturday lotto. It was possible of course that
the pools and lotto could be either substitutes or complements (the latter could apply,
for example, if extra customers drawn to the lottery shop by a lotto rollover also bought
a pools entry given that there would be no additional transaction costs). In the event,
cross-price elasticity was zero for Thursday lotto. For Saturday lotto, it was positive and
statistically (p = .02), but not economically, signiﬁcant (i.e., numerically the estimate
was close to zero). For practical purposes, it appears that the two gaming opportunities
are not regarded as substitutes by consumers, consistent with the observation by the
Competition Commission of Great Britain (2007) that in the United Kingdom national
lottery rollovers do not deﬂate pools sales.
Sensitivity of Demand to Own-Price
and to Game Design
.............................................................................................................................................................................
The structure of lotto-style games lends itself to modeling demand, given that the
exogenous pattern of rollovers induces strong variation in the value for money offered
from draw to draw. Typically, value for money is captured by effective price and esti-
mates of the elasticity of sales with respect to effective price are used to evaluate whether
the takeout has been selected at a level where net revenue for the state is maximized
(this is the approach, for example, in Farrell, Morgenroth, and Walker 1999 and For-
rest, Gulley, and Simmons 2000). But the approach has problems to the extent that it is
implausible that consumption decisions are driven only by effective price. It abstracts
altogether from entry fee, which in most jurisdictions has been constant in nominal
terms and declining in real terms for the whole period of any data set. It also ignores
the potential importance of prize structure. Whenever there is a large rollover, lotto
tickets become better value for money, but this happens only because of augmentation

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sports betting
of the top tier prize; what is perceived by the model as a response to value for money
may in fact just be a response to the size of a jackpot.
The papers here have the opportunity to address these two problems directly given
the variability in the data on the pools and the length of the data set (records of sales
are available from 1970). Regarding entry fees, multiple changes have been made over
time, the overall trend being upward (García and Rodríguez 2007) such that periodic
adjustments have more than compensated for inﬂation. Between adjustments of course
real entry fee depreciates given that inﬂation in Spain has been consistently positive.
With effective price included as one of their controls,Forrest and Pérez (2011) estimated
the elasticity of the number of entries with respect to the real entry fee as −0.66 over the
entire data period. This implies that, over the period, pushing up real entry fees lowered
sales less than proportionately, allowing real revenue to rise. Successive, sometimes
substantial, entry fee increases after lotto was introduced (with takeout held) therefore
compensated the pools to some extent for the loss from cannibalization. The converse
of the result is that allowing inﬂation to erode real entry fees indeﬁnitely would have
lowered real revenue (and the erosion of the real jackpot would then play a role in
deterring consumers). This ﬁnding may be relevant to jurisdictions where the real price
of a lotto ticket has fallen substantially since the game ﬁrst appeared.
Forrest and Pérez (2011) also evaluated elasticity with respect to own-effective price
as inelastic (-0.74), indicating that the pools game may, over the period, have been too
generous from the perspective of raising money for the state and other claimants on
the proﬁts. But, in their case, there were no proxies in the speciﬁcation for features of
the game, such as prize structure or how hard it is to win. Jauma García and Plácido
Rodríguez (2007) included in their speciﬁcation proxies for the prize structure (real
jackpot) and the probability of winning (a dummy representing when the game was
based on 15 rather than 14 matches). Sales were shown to respond positively to the size
of the jackpot and positively to the hardness of the game, but they found little role for
effective price. This illustrates the danger of modelers misinterpreting the signiﬁcance
of effective price in a basic model. If effective price merely proxies other variables which
inﬂuence sales, coefﬁcient estimates cannot reliably be employed to predict the effect
of any variations in takeout that would alter the size of all the prize pools and not
just the jackpot. Success in game design requires careful attention to prize structure
and game matrix, and simulations based on a model with only effective price will be
inadequate for this purpose. In terms of pools policy, the importance of game design
was underlined when sales were observed to fall after the pools reverted temporarily to
14 rather than ﬁfteen 15 in 2003–2004 (the season after the end of the period employed
in the econometric analysis).
The ﬁndings have implications here for lotto analysts outside Spain. Forrest, Robert
Simmons and Neil Chesters (2002) also drew attention to the inadequacy of models
based only on effective price by showing, tentatively, that U.K. Lotto sales were tracked
more closely when the size of the jackpot pool replaced effective price in the spec-
iﬁcation. However, they were unable to include both in the same model because of
collinearity. In the Spanish pools case, adequate variation in the data permitted García

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the football pools
159
and Rodríguez (2007) to distinguish between the effects of the two variables, and they
found that the size of the jackpot pool mattered to consumers. Omission of this vari-
able or alternative variables related to prize structure is therefore likely to bias results
in modeling lotto demand, and it is important to attempt to capture prize structure
as well as effective price if ﬁndings are to offer useful guidance to operators and gov-
ernments. In this spirit, Ian Walker and Juliet Young (2001) attempted to represent the
various dimensions of a lottery ticket by including the mean, variance, and skewness of
returns but were hampered by the problem of insufﬁcient instruments for the number
of endogenous variables.
Does the Football Matter?
.............................................................................................................................................................................
The modeling reported so far treats the football pools as if they were a lottery game,
and indeed it appears that players respond similarly as lotto players to stimuli linked to
the costs and returns of playing. However, the ability of the pools in Spain to sustain a
market, even with lotto readily available, suggests that basing a game on football results
is an attraction to a segment of the market. Therefore, how football features in the game
is liable to inﬂuence demand.
In their models, García and Rodríguez (2007) and Forrest and Pérez (2011) included
as controls variables related to which matches feature on the coupon. In a full program
of ﬁxtures, the 15 matches chosen for La Quiniela constitute all Spanish First Division
matches and some from the Second Division. However, a full program of matches is
not always scheduled, for example, because the national team is playing. In this case
there might be no First Division games and even no First or Second Division games on
the coupon. Were the game regarded universally as just another lottery, this would not
impact sales, but, in fact, faced with less familiar clubs making up the coupon, both
papers ﬁnd that players collectively purchased far fewer entries. For example, Forrest
and Pérez (2011) predicted a 38 percent decrease in sales if there were no First Division
matches, with the impact rising to 60 percent if the Second Division also was not
featured. These estimates are for the entire period from 1970. García and Rodríguez
(2007) reported slightly lower and slightly higher estimates, respectively, for subperiods
when lotto was not and was available, consistent with a higher proportion of players in
the later period treating the pools as a football-related product rather than a surrogate
lotto game. In any case, it is clear that the link of the pools to football is important to
those who buy. It is less clear why fewer purchase when the grade of football covered by
the coupon is lower. One explanation is that a signiﬁcant proportion of entries is made
by customers who actively attempt to apply skill to the process of selecting their sets of
results. They may feel less conﬁdent about having a chance of winning a prize when the
teams featured are unfamiliar to them, or they may ﬁnd it less fun if they cannot draw
on their knowledge of the top teams in the top competitions. Alternatively the reason

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sports betting
may be less tangible, as no doubt there are also many (non-gambling) products where
brand association with the glamorous end of football increases sales.
A different but related issue is investigated in García, Pérez, and Rodríguez (2008).
They employed panel data to model annual per capita sales of La Quiniela by province
over the period 1985–2005. They found considerable variation from province to
province, which is explained in their model by variables including per capita income
(which has a positive effect) but also the number of teams in the province playing in the
First Division and the number playing in the Second Division. The system of promotion
and relegation provides that these variable show variation across time as well as across
space. Both variables are signed positive, that for the First Division proving strongly
signiﬁcant (p < .01) but that for the Second Division only marginally so (p = .06).
The long-run impact from a province having a team playing in the First Division was
estimated as raising per capita sales by 11 percent. Again the reason for the ﬁnding
is unclear. Players may simply be attracted more to products with local relevance, or
they may think they can win with higher probability when they have been following
the league closely, acquiring relevant knowledge on the way. Alternatively the proba-
bility of a First Division club being present in a province may be correlated with other
characteristics of the province which, independently, predispose it to high pools sales.
Despite uncertainty over causation, the evidence points to a complementarity between
the sport and gambling on the sport. This may justify the payment of a signiﬁcant part
of pools gross revenue to the football league.
If association with football is part of the appeal of the pools game, which does indeed
appear now not to be just another lottery, does this imply that signiﬁcant numbers of
players in Spain actively seek to forecast rather than merely guess the results? And,
if they do, are they any good at it? These are less researched questions. García and
Rodríguez (2007, 336) claimed that “the number of players getting all forecasts right
is usually much higher than the number we would expect if the ﬁnal results were
completely random.” This remark implies that the game is skills-based and that many
players possess and apply the requisite skills. However, no detail is provided to justify
that claim. It is not obvious what the benchmark proportion of winners is or how this
would be calculated. How would a random set of results or forecasts be deﬁned? Would
it be with equal probabilities of the three results (1, X, 2), or would it be with matches
allocated results randomly within the constraint that speciﬁed proportions would be
allocated as home win/ draw/ away win?
There could be many routes to players scoring a higher success rate than would
be expected from some deﬁnition of random play. For example, Barcelona and Real
Madrid attract nationwide support, and their large numbers of fans may always select
their team to win out of loyalty rather than because they are actively forecasting the
result. But most of the time, these teams do win, therefore raising the aggregate success
rate of pools winners. Consequently it is very hard to test whether skill is being suc-
cessfully employed in the game. A further complication is that some players may seek
out unlikely combinations of results because they take into account that they may win

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the football pools
161
more money if no one else has matched all the results. Such behavior, though based on
well-informed play, would tend to lower overall measured success rates in the game.
Francesc Pujol (2009) modeled the proportion of bettors who win over the course
of more than 1,000 editions of the game. Controlling for the number of home wins
on the coupon and the number of entries in the game, he identiﬁed a weak negative
long-run trend, which he attributes to the decline in home advantage making matches
harder to forecast and a strong positive within-season trend. The latter he interprets as
reﬂecting pools players learning as the season goes on. At the beginning of a season,
many clubs will essentially have a new squad, and some will have a new coach or be
playing in a new division. Results will then be relatively hard to forecast, but as the
season’s events unfold, information is revealed about team strengths, and Pujol argues
that this information is absorbed and processed efﬁciently by enough pools players
that their collective win rate increases with time. The ﬁndings are certainly consistent
with this explanation, though others might be investigated (for example, there may be
less randomness in results as the season progresses if players on the top teams become
more incentivized as the shape of the league table hardens or if players in new squads
gradually gel to produce results commensurate with their total valuation on the transfer
market).
How pools players make their selections is an area that requires additional research.
As noted earlier, there have been few empirical studies of pools. Any future research will
continue to focus on Spain because it is perhaps the one pools market where the size of
the sector is large enough for investment of academic resources to be worthwhile.
References
Competition Commission of Great Britain. 2007. Anticipated acquisition by Sportech plc of
the Vernons Football pools business from Ladbrokes plc: Final report. London: Competition
Commission.
Cook, Philip J., and Charles T. Clotfelter. 1993. The peculiar scale economies of lotto. American
Economic Review 83:634–643.
Dobson, Stephen, and John Goddard. 2001. The economics of football. Cambridge: Cambridge
University Press.
Farrell, Lisa, Edgar L. W. Morgenroth, and Ian Walker. 1999. A time-series analysis of U.K.
lottery sales: Long run and short run elasticities. Oxford Bulletin of Economics and Statistics
61(4):513–526.
Forrest, David. 1999. The past and future of the British football pools. Journal of Gambling
Studies 15(2):161–176.
——. 2012. Online gambling: An economics perspective. In Routledge International Hand-
book of Internet Gambling, edited by Robert Williams, Robert Wood, and Jonathan Parke.
London: Routledge 29–45.
Forrest, David, and Levi Pérez. 2011. Football pools and lotteries: Substitute roads to riches?
Applied Economics Letters 18(3):1253–1257.
Forrest, David, and Robert Simmons. 2000. Making up the results: The work of the Football
Pools Panel, 1963–1997. The Statistician 49(2):253–260.

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Forrest, David, O. David Gulley, and Robert Simmons. 2000. Elasticity of demand for UK
National Lottery tickets. National Tax Journal 53(4, pt. 1):853–863.
Forrest, David, Robert Simmons, and Neil Chesters. 2002. Buying a dream: Alternative models
of demand for lotto. Economic Inquiry 40(3):485–496.
Gambling Commission (2010). Industry Statistics 2009/10. Birmingham, U.K.: Gambling
Commission.
García, Jaume, and Plácido Rodríguez. 2007. The demand for football pools in Spain: The
role of prices, prizes, and the composition of the coupon. Journal of Sports Economics
10(8):335–354
García, Jaume, Levi Pérez, and Plácido Rodríguez. 2008. Football pool sales: How important
is a football club in the top divisions? International Journal of Sport Finance 3(3):119–126.
——. 2011. Guessing who wins or predicting the exact score: Does it make any difference
in terms of the demand for football pools? In Contemporary issues in sports economics:
Participation and professional team sports, edited by Wladimir Andreff. Cheltham, U.K.:
Edward Elgar, 114–130.
Gulley, O. David, and Frank A. Scott Jr. 1993. The demand for wagering on state-operated
lotto games. National Tax Journal 46(1):13–22
Humphreys, Brad R., and Levi Pérez. 2010. A microeconometric analysis of participation in
sports betting markets. Economic Discussion Paper 02/2010. Oviedo, Spain: Department of
Economics, University of Oviedo.
Miers, David. 1996. The implementation and effects of Great Britain’s National Lottery.
Journal of Gambling Studies 12(4):343–373.
Munting, Roger. 1996. An economic and social history of gambling in Britain and the USA.
Manchester, U.K.: Manchester University Press.
Pujol, Francesc. 2009. Football betting as a cyclical learning process Faculty Working Paper
05/09. Pamplona, Spain: Department of Economics, University of Navarra.
Royal Commission on Gambling. 1978. Report of the Royal Commission on Gambling. London:
H.M. Stationery Ofﬁce.
Sharpe, Graham. 1997. Gambling on Goals: A Century of Football Betting. Edinburgh:
Mainstream Publishing.
Walker, Ian, and Juliet Young. 2001. An economist’s guide to lottery design. Economic Journal
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chapter 9
........................................................................................................
THE EFFICIENCY OF SOCCER
BETTING MARKETS
........................................................................................................
john goddard
1 Introduction
.............................................................................................................................................................................
Academic interest in the informational efﬁciency of ﬁxed-odds betting markets for
the results of professional soccer (football) matches dates back to the 1980s. In the
ﬁrst study of this topic, Peter Pope and David Peel (1989) analyzed the prices set
by four national High Street bookmakers for English Football League matches played
during the 1981/1982 season. As a basis for tests of the weak-form efﬁciency hypothesis,
regressions of match outcomes against implicit bookmaker’s probabilities are reported.
Let Hi,j = 1 if the match between team i and team j results in a home win and 0
otherwise, and let ϕH
i,j denote the bookmaker’s implied probability for a home win. In
the linear probability model Hi,j = ρ1 + ρ2ϕH
i,j + vi,j, a necessary condition for weak-
form efﬁciency is {ρ1 = 0, ρ2 = 1}. Equivalent conditions apply in the corresponding
regressions for the draw and away-win dummy variables. In general, Pope and Peel
failed to reject the condition {ρ1 = 0, ρ2 = 1} for the odds on home-win and away-win
match outcomes. The odds for draws have no signiﬁcant predictive content for draw
outcomes, however, suggesting a departure from weak-form informational efﬁciency
conditions.
In a later study using similar methods, Michael Cain, David Law, and Peel (2000)
reported evidence of favorite-longshot bias in the ﬁxed-odds betting market for match
results and scores in English soccer. The odds available for bets on speciﬁc scores
are dependent only on the odds posted for the three possible match results (home
win/draw/away win). Estimates of the“fair”odds for speciﬁc scores are computed, con-
ditional on the bookmaker’s posted home-win odds. In comparisons of the estimated
“fair” odds with the bookmaker’s actual odds for speciﬁc scores, the former are gener-
ally found to be signiﬁcantly longer than the latter for long-shot bets. The “fair” odds

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sports betting
are sometimes shorter than the bookmaker’s odds for bets on strong favorites. Bets on
strong favorites may offer limited proﬁtable betting opportunities.
A second generation of soccer betting market efﬁciency studies, published in the late
1990sandearly2000s,investigatedsimilarquestionsusingforecastingmodelsestimated
from past match-results data to test the proﬁtability of betting strategies informed by a
comparison of bookmaker odds with the expected returns implied by probabilities for
match results obtained from the estimated forecasting model. For example, Mark Dixon
and Stuart Coles (1997) and Dixon and Peter Pope (2004) reported that bets for which
the ratio of their forecasting model’s probability to the bookmaker’s implicit probability
exceeded a threshold of 20 percent would have produced a positive return to the bettor.
John Goddard and Ioannis Asimakopoulos (2004) compared probabilistic forecasts
obtained from their model with a High Street bookmaker’s ﬁxed odds. A strategy of
selecting bets ranked in the top 15 percent by expected return according to the model’s
probabilities would have generated a positive return. (For further discussion of soccer
match–results forecasting models and betting market applications see Crowder et al.
2002 and Graham and Stott 2008.)
During the 2000s, the growth of the Internet and the migration of a signiﬁcant share
of sports betting business from High Street bookmakers’ shops to websites operated
by established bookmakers and new online betting ﬁrms likely have had profound
implications for the informational efﬁciency of all sports betting markets, including
those for soccer. The odds offered by competing bookmakers are easily compared,
by visiting either the bookmakers’ own websites or price comparison websites, such as
oddschecker.com. The spectacular growth of the online betting exchange Betfair, which
charges a commission of between 2 and 5 percent on the winnings of its successful
clients, has placed downward pressure on the much larger margins that, tradition-
ally, were built into the betting industry’s ﬁxed-odds betting pricing structure. Rapid
enhancements in computing power have greatly facilitated the capability of industry
members and sophisticated bettors to process large volumes of sports data in an effort
to identify both inefﬁciencies in the market and opportunities for proﬁtable trading
that will, in time, tend to eliminate the inefﬁciencies. More generally, the Internet
has increased the ﬂow and quality of information on all aspects of sporting compe-
tition that is available to industry members and to sophisticated and leisure bettors
alike.
In the light of these developments, this chapter evaluates the performance of fore-
casting models of the kind used in several of the academic studies reviewed brieﬂy
above when confronted with recent ﬁxed-odds betting market prices data. Section 2
provides a brief, nontechnical description of a forecasting model for soccer match
results that is based on a large-scale number-crunching exercise using historical match
results and other relevant data. Section 3 examines whether the claims made in sev-
eral earlier academic studies, that forecasting models of this kind can provide the
basis for the development of proﬁtable ﬁxed-odds betting strategies, are sustainable
when the model is confronted with recent ﬁxed-odds betting prices. A prior hypothesis
is that opportunities for proﬁtable betting that were available during earlier periods

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the efficiency of soccer betting markets
165
might have been largely eliminated by the increased sophistication of contemporary
sports betting markets, which have been greatly enhanced by advances in computing
technology. Finally, Section 4 provides a brief summary and conclusion.
2 Statistical Analysis of Patterns in
English Soccer Match Results
.............................................................................................................................................................................
This section provides a brief, nontechnical description of the match-results forecasting
model whose capability to inform the development of a proﬁtable ﬁxed-odds betting
strategy is examined later in the chapter. A full technical description of the speciﬁcation
and estimation of this model is presented by Stephen Dobson and Goddard (2011).
Early prototypes of the model, constructed along similar lines but with some variations
in the choice of covariates, are described by Goddard and Asimakopoulos (2004) and
Goddard (2005).
The variant of the forecasting model evaluated in this chapter is derived from an
ordered probit regression in which match results in the home win/draw/away win
format are the dependent variable. It is assumed that the result of the match between
home team i and away team j, denoted here as Ri,j = 1 for a home team win, 0.5 for a
draw, and 0 for an away team win, depends on an unobserved or latent variable denoted
y∗
i,j and an independent and identically distributed disturbance term, εi,j, which follows
the standard normal distribution:
Homewin : Ri,j = 1 if μ2 < y∗
i,j + εi,j
Draw : Ri,j = 0.5 if μ1 < y∗
i,j + εi,j < μ2
Awaywin : Ri,j = 0 if y∗
i,j + εi,j < μ1
The two cut-off parameters μ1 and μ2 are to be estimated. The latent variable y∗
i,j is a
linear function of a set of covariates, which are deﬁned using match results and other
data that are easily observable before the match between teams i and j is played. The
coefﬁcients of the linear equation determining y∗
i,j are to be estimated. The covariates
of this equation include the following:
• All previous league match results of teams i and j over the 24 months prior to the
current match, which are used to calculate win ratios (the ratio of wins to matches
played, with draws treated as half wins) indexed according to their timing within
the 24-month period. More recent win ratio data have stronger predictive content
for the current match than do earlier data. The indexing is also by division in which
the team was playing at the time each win ratio was recorded. A discount is applied
to win ratio data from a lower division, and a premium to data from a higher

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sports betting
division, in evaluating the contribution of past performance to the probability of
winning the current match.
• The few most recent league match results of teams i and j appear separately and
individually among the covariates to allow for any patterns in sequences of results
deriving from winning or losing streaks. Dobson and Goddard (2003, 2011) found
that the durations of both good and poor sequences tended to be shorter than
would be expected if streaks were irrelevant. In other words, a team currently
enjoying a run of good results has a higher probability (relative to the probability
conditioned only on that team’s underlying quality) of a poor result in its next
match and vice versa.
• The geographical distance between the stadiums of home team i and away team j.
The phenomenon of home ﬁeld advantage is pervasive throughout many pro-
fessional team sports. Despite some erosion of the importance of home ﬁeld
advantage for English soccer match results over recent decades, a large gap still
remains between average performance at home and away from home. The magni-
tude of home ﬁeld advantage is, to a modest extent, dependent on the geographical
distance the away team has to travel in order to complete the ﬁxture: the greater
the geographical distance, the stronger the home ﬁeld advantage effect.
• Dummy variables are used to identify matches that are relevant or irrelevant for
end-of-season championship, promotion, or relegation issues for either team.
Teams that have end-of-season issues at stake are more likely to win matches
played late in the season against teams with no issues at stake.
• Dummy variables are used to distinguish between teams that are currently involved
in the FA Cup and European club competitions, and teams whose involvement has
ended at the time the current league match is played.
• Recent average home league match attendance data for teams i and j, which (after
adjustment for league position) are used as a proxy for any big club/small club
effect on match results.
3 Evaluation of the Forecasting Model’s
Information Content Relative to
Bookmakers’ Fixed-Odds Betting Prices
.............................................................................................................................................................................
Thissectionexaminestheextenttowhichthematch-resultsforecastingmodeldescribed
in the previous section could have informed the development of a proﬁtable ﬁxed-odds
betting strategy had it been employed for this purpose in real time over the course of
the three English soccer seasons 2008/2009 to 2010/2011 (inclusive).
After the estimation of the forecasting model, the ﬁtted home win/draw/away win
probabilities for any out-of-sample match for which a probabilistic forecast is required

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the efficiency of soccer betting markets
167
are obtained by substituting the evaluated ˆy∗
i,j for the match in question, and the
estimated cut-off parameters ˆμ1 and ˆμ2, into the following expressions:
home win probability = pH
i,j = P(εi,j > ˆμ2 −ˆy∗
i,j) = 1 −( ˆμ2 −ˆy∗
i,j)
draw probability = pD
i,j = P( ˆμ1 −ˆy∗
i,j < εi,j < ˆμ2 −ˆy∗
i,j)
= ( ˆμ2 −ˆy∗
i,j) −( ˆμ1 −ˆy∗
i,j)
away win probability = pA
i,j = P(εi,j < ˆμ1 −ˆy∗
i,j) = ( ˆμ1 −ˆy∗
i,j)
( ) denotes the standard normal distribution function. Let OH
i,j denote the book-
maker’s decimal odds for a bet on a home team win in the match between home team i
and away team j. If the home team wins, the bettor’s net proﬁt on a unit bet is OH
i,j −1;
if the home team fails to win, the bettor’s net proﬁt is −1. The bettor’s expected proﬁt
from a bet on a home team win, according to the probabilities obtained from the
model, is
EH
i,j = pH
i,j(OH
i,j −1) −(1 −pH
i,j) = pH
i,jOH
i,j −1
OD
i,j, ED
i,j, OA
i,j and EA
i,j are deﬁned similarly for the bets on a draw and on an away win.
The empirical investigation reported in this section examines ﬁxed-odds betting on
match results in all four divisions of the English Premier League and Football League,
expressed in home win/draw/away win format, during the 2008/2009, 2009/2010 and
2010/2011 soccer seasons. The ﬁxed odds are those published by 10 High Street and
online bookmakers: Bet365, Bet&Win, Gamebookers, Interwetten, Ladbrokes, Sport-
ingbet, William Hill, Stan James,VC bet, and Blue Square. The data source is the soccer
website www.soccer-data.co.uk.
Table 9.1 reports the mean overround (bookmaker’s margin) of each bookmaker
per season, where the overround 1/OH
i,j + 1/OD
i,j + 1/OA
i,j −1 is the difference between
the sum of the bookmaker’s implied “probabilities” (deﬁned as the reciprocals of the
decimal odds) and the sum of “fair”probabilities (which must add up to one). The ﬁnal
row of table 9.1 reports the mean overround based on a set of “best odds,” constructed
by taking the longest of the decimal odds for each outcome quoted by any of the
10 bookmakers. Naturally the overround calculated from “best odds” is smaller than
the overrounds calculated from the odds of each of bookmaker individually. It is
interesting to note, however, that the “best odds” overround was positive for every
match and was never zero or negative. This means that there were no “pure” arbitrage
opportunities such that a bettor could have guaranteed a positive return by placing
suitably calibrated bets on all three possible outcomes at “best odds.” Table 9.1 also
illustrates the general trend, identiﬁed previously, toward the erosion of the overround
or the bookmakers’ margins, with some (but not all) of the 10 bookmakers recording
signiﬁcant reductions in their mean overrounds during the three-season observation
period.

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sports betting
Table 9.1 Mean Overrounds, 10 High Street and Online Bookmakers, 2008/2009
to 2010/2011 Seasons (Inclusive)
Bookmakers
2008/2009
2009/2010
2010/2011
All
Bet365
0.063
0.063
0.063
0.063
Bet & Win
0.109
0.107
0.106
0.107
Gamebookers
0.091
0.093
0.093
0.092
Interwetten
0.130
0.127
0.130
0.129
Ladbrokes
0.095
0.082
0.065
0.081
Sportingbet
0.101
0.101
0.101
0.101
William Hill
0.103
0.107
0.067
0.092
Stan James
0.091
0.089
0.078
0.086
VC bet
0.096
0.083
0.041
0.073
Blue Square
0.078
0.075
0.074
0.076
“best odds”
0.040
0.039
0.025
0.035
For the development of a proﬁtable betting strategy, the information content of
{pk
i,j} for k = H,D,A must be sufﬁciently strong for the bettor to generate a positive
realized return by selecting those bets for which Ek
i,j exceeds a certain threshold value,
overcoming the in-built bias against the bettor caused by the bookmaker’s overround.
Tables 9.2 and 9.3 report the outcomes that would have been achieved through the
implementation of such a strategy using the “best odds” for various threshold values
for Ek
i,j. The threshold values are selected by ranking all available bets at “best odds”
(three for each match) in descending order of Ek
i,j and setting the threshold at each
of the following quantiles of the ranked distribution of Ek
i,j: 0.5, 1, 1.5, 2, 3, 4, 5,
10 and 20 percent. Table 9.2 reports the total realized returns, numbers of bets, and
average returns per bet for bets that fall within each quantile band. Table 9.3 reports
the corresponding cumulative realized returns, the cumulative number of bets, and
the cumulative average returns per bet, assuming the bettor had selected all bets with
expected returns larger than the threshold value. For completeness, the ﬁnal two rows of
tables 9.2 and 9.3 report the corresponding ﬁgures at the 50 and 100 percent quantiles,
even though bets falling into these bands normally would not be selected in view of
their large, negative expected returns.
The results reported in tables 9.2 and 9.3 suggest that the forecasting model does
contain relevant information not captured by the bookmakers’odds but that the model
does not always produce forecasts that can be relied upon to deliver positive returns,
especially over relatively small numbers of bets. According to table 9.3, setting the
threshold parameter at the 2 percent quantile of the ranked distribution of Ek
i,j over all
three soccer seasons would have delivered a positive return of just over 1 percent on 366
bets. The same strategy applied season by season would have delivered positive returns

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the efficiency of soccer betting markets
169
Table 9.2 Total Return and Average Return for Bets in Various Quantiles of the
Distribution of Bets Ranked by Expected Returns Obtained from the Forecasting
Model
Bets Ranked
by Expected
Return
Total Return and Number of Bets
Average Return per Bet
2008/2009 2009/2010 2010/2011
All
2008/2009 2009/2010 2010/2011
All
top 0.5%
16.2
−3.4
−11.5
1.3
0.675
−0.071
−0.575
0.014
24
48
20
92
0.5%–1%
−2.5
−12.8
12.0
−3.3
−0.105
−0.283
0.545
−0.036
24
45
22
91
1%–1.5%
8.7
−19.3
7.5
−3.1
0.433
−0.410
0.301
−0.033
20
47
25
92
1.5%–2%
−6.8
16.4
−0.8
8.8
−0.261
0.443
−0.027
0.097
26
37
28
91
2%–3%
12.5
−46.4
−18.9
−52.7
0.228
−0.760
−0.278
−0.287
55
61
68
184
3%–4%
−3.2
19.1
−10.4
5.5
−0.067
0.258
−0.170
0.030
48
74
61
183
4%–5%
3.0
−22.7
2.8
−16.8
0.055
−0.343
0.046
−0.092
55
66
62
183
5%–10%
11.6
−29.0
40.3
22.9
0.046
−0.093
0.114
0.025
251
313
352
916
10%–20%
−43.7
−33.8
−58.5
−136.0
−0.077
−0.060
−0.083
−0.074
564
560
709
1833
20%–50%
−12.2
−176.9
−22.7
−211.8
−0.008
−0.099
−0.011
−0.039
1628
1792
2077
5497
50%–100%
−237.2
−28.8
−30.6
−296.6
−0.069
−0.009
−0.011
−0.032
3413
3065
2684
9162
of 16.5 percent over 94 bets in 2008/2009 and 7.7 percent over 95 bets in 2010/2011,
partially offset by a negative return of −10.8 percent over 177 bets in 2009/2010. Clearly
the returns realized in each year are highly variable, and the bettor would need to adhere
to the prescribed betting strategy for a period of several years’ duration, in order to see
the emergence of a more stable long-run average return.
These results suggest that using a forecasting model based on extrapolation from
large volumes of historical match results and other data to identify ﬁxed-odds bets
offering relatively good value for money, which will either reduce or eliminate the losses
that would otherwise be expected owing to the bookmaker’s overround, is a feasible
proposition. Developing a betting strategy that will reliably deliver a positive return in
the long run is a more difﬁcult task, however, though perhaps not an impossible one. In
pursuit of a positive return, the statistician-bettor must be willing to adhere patiently
to his or her chosen strategy for a long period and must be prepared to tolerate the
possibility of realizing signiﬁcant short-run losses from time to time.

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sports betting
Table 9.3 Total Cumulative Return and Average Cumulative Return for Bets in
Various Quantiles of the Distribution of Bets Ranked by Expected Returns Obtained
from the Forecasting Model
Bets Ranked
by Expected
Return
Total Cumulative Return and Cumulative
Number of Bets
Average Cumulative Return per Bet
2008/2009 2009/2010 2010/2011
All
2008/2009 2009/2010 2010/2011
All
top 0.5%
16.2
−3.4
−11.5
1.3
0.675
−0.071
−0.575
0.014
24
48
20
92
top 1%
13.7
−16.2
0.5
−2.0
0.285
−0.174
0.012
−0.011
48
93
42
183
top 1.5%
22.3
−35.4
8.0
−5.1
0.328
−0.253
0.120
−0.018
68
140
67
275
top 2%
15.5
−19.0
7.3
3.8
0.165
−0.108
0.077
0.010
94
177
95
366
top 3%
28.1
−65.4
−11.6
−49.0
0.188
−0.275
−0.071
−0.089
149
238
163
550
top 4%
24.9
−46.3
−22.0
−43.5
0.126
−0.148
−0.098
−0.059
197
312
224
733
top 5%
27.9
−69.0
−19.2
−60.3
0.111
−0.182
−0.067
−0.066
252
378
286
916
top 10%
39.4
−97.9
21.1
−37.4
0.078
−0.142
0.033
−0.020
503
691
638
1832
top 20%
−4.2
−131.8
−37.4
−173.4
−0.004
−0.105
−0.028
−0.047
1067
1251
1347
3665
top 50%
−16.5
−308.7
−60.1
−385.2
−0.006
−0.101
−0.018
−0.042
2695
3043
3424
9162
all bets
−253.7
−337.5
−90.7
−681.8
−0.042
−0.055
−0.015
−0.037
6108
6108
6108
18324
Finally, to illustrate the degree of patience that might be required, consider the
relationship between the number of bets placed (denoted N), the expected return from
N bets, and the 95 percent conﬁdence interval for the actual proceeds from N bets,
assuming that the bettor employs a betting strategy that offers a small expected return
of μ on each bet. For simplicity, assume all bets are placed at the same “fair” odds. The
variance of the proceeds from any bet is σ 2 = (Ok
i,j −1−μ)2pk
i,j +(−1−μ)2(1−pk
i,j),
where pk
i,j is the probability that the bet wins. A 95 percent conﬁdence interval for the
actual proceeds from N bets is Nμ ± 1.96σ
√
N. Suppose μ = 0.05 and bets are placed
at “fair” decimal odds of Ok
i,j = 3 so that pk
i,j = 0.35. With N = 300 bets (for example),
the expected proceeds are +15, but the 95 percent conﬁdence interval extends from
−33.6 to +63.6. In this case, no fewer than N = 3,146 bets would be required in order
to make the lower limit of this conﬁdence interval zero, implying a 0.95 probability of
achieving a positive return.

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the efficiency of soccer betting markets
171
4 Conclusion
.............................................................................................................................................................................
This chapter evaluates the performance of a statistical match-results forecasting model
that relies on a large-scale number-crunching exercise using historical match results
and other relevant data when confronted with recent ﬁxed-odds betting prices. Our
prior hypothesis, that opportunities for proﬁtable betting that were available during
earlier periods might have been reduced or eliminated by the increased sophistication of
contemporary sports betting markets, appears to be substantiated to some extent. While
it appears that the forecasting model contains some relevant information that is not
captured by the bookmakers’ published ﬁxed odds, the model does not always produce
forecasts that will reliably deliver a positive return, especially if the number of bets is
relatively small. And while there is some evidence for the existence of proﬁtable betting
opportunities, the statistician-bettor would need to adhere patiently to the chosen
strategy for a long period in order to be conﬁdent of achieving a positive average or
total return. The evidence for the existence of proﬁtable betting opportunities appears
somewhat weaker than claims that were made concerning informational inefﬁciency
in ﬁxed-odds betting markets by the authors of several papers of late-1990s and early-
2000s vintage that adopted a similar modeling approach. This observation is consistent
with the hypothesis that there has been an improvement over time in the informational
efﬁciency of ﬁxed-odds soccer betting markets.
References
Cain, Michael, David Law, and David Peel. 2000. The favourite-longshot bias and market
efﬁciency in UK football betting. Scottish Journal of Political Economy 47(1):25–36.
Crowder, Martin, Mark Dixon, Anthony Ledford, and Mike Robinson. 2002. Dynamic mod-
elling and prediction of English Football League matches for betting. The Statistician
51(2):157–168.
Dixon, Mark J., and Stuart G. Coles. 1997. Modelling association football scores and
inefﬁciencies in the football betting market. Applied Statistics 46(2):265–280.
Dixon, Mark J., and Peter F. Pope. 2004. The value of statistical forecasts in the UK association
football betting market. International Journal of Forecasting 20(4):697–711.
Dobson, Stephen, and John Goddard. 2003. Persistence in sequences of football match results:
A Monte Carlo analysis. European Journal of Operational Research 148(2):247–256.
——. 2011. The economics of football. 2nd ed. Cambridge: Cambridge University Press.
Goddard, John. 2005. Regression models for forecasting goals and match results in association
football. International Journal of Forecasting 21(2):331–340.
Goddard, John, and Ioannis Asimakopoulos. 2004. Forecasting football results and the
efﬁciency of ﬁxed-odds betting. Journal of Forecasting 23(1):51–66.
Graham, I., and H. Stott. 2008. Predicting bookmaker odds and efﬁciency for UK football.
Applied Economics 40(1):99–109.
Pope, Peter F., and David A. Peel. 1989. Information, prices and efﬁciency in a ﬁxed-odds
betting market. Economica 56(223):323–341.

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chapter 10
........................................................................................................
the efficiency of pelota
betting markets
........................................................................................................
loreto llorente, josemari aizpurua,
and javier pu´ertolas
Introduction
.............................................................................................................................................................................
We study the very attractive betting system used in pelota games in the Navarra, Basque
Country, and La Rioja regions of Spain. In what follows we call this the pelota betting
system. This betting system may also be of interest due to its similarities to person-to-
person betting, that is, betting on the exchanges. Before presenting the main work, we
provide a brief introduction regarding pelota games and the betting system.
Most authors who have studied the origins of the Basque sport of pelota believe it
is linked to the medieval hand-ball game of jeu de paume or “real tennis.” The history
of this game was passed down orally, so the ﬁrst written references to it do not appear
until 1331. In the eighteenth century the game began to die out in France, Italy, and
England, but it grew more popular in the Basque Country, where increased economic
prosperity led to the building of more courts.1
Although there is evidence of betting on ball games in ancient times, there is no
evidence of what type of wagers were made. We do not know when the betting system
currently used on the pelota courts of the Basque Country ﬁrst came into being, but we
can say that no evidence has been found of this system operating outside this region.
Traditionally the rules of the system were not written down but were passed on orally,
which makes it harder to study. We have found a similar betting system that has been
implemented on the Internet. The betting system followed on betting exchanges, for
example Betfair, is similar to the pelota betting system in that bettors can make as
many bets as they want provided there is another bettor on the other side and that
the market maker takes a percentage of the money as a commission. As shown by
Edelman and Llorente (2010), the primary difference between the two systems is the
pelota betting system’s odds scale. Michael Smith, David Paton, and Leighton Vaughan

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the efficiency of pelota betting markets
173
Williams (2006) have studied market efﬁciency in person-to-person betting, and David
Marginson (2010) has studied efﬁciency in the exchanges, pointing out the impact of
betting on a“known loser.” The latter takes on importance when a sport can have more
than two mutually exclusive and exhaustive outcomes, as in horse races.
In America a different kind of game known as jai alai or cesta punta also is played.
Jai alai originated from the version of pelota called cesta punta, but the sport is now
different. Bets are also made in jai alai, but the betting system in America is totally
different from the system described here. A more related topic, betting on team jai alai,
the game played in Mexico City, Connecticut, Florida, Nevada, Rhode Island, and other
locales, has been studied by Daniel Lane and William Ziemba (2008). But the betting
system they analyzed also differs from the pelota betting system in terms of the study
of efﬁciency.
In this chapter, we examine efﬁciency in the pelota betting system under different
scenarios. We make use of the three concepts of efﬁciency widely utilized in various
empirical settings; Constant Returns, Absence of a Proﬁt Opportunity, Equilibrium
Pricing Functions (Sauer 1998, 2024), and give some suggestions for further research.
In the ﬁrst section, we describe the game and the betting system (a complete descrip-
tion can be found in Llorente and Aizpurua 2008). In section 2, we position the pelota
betting system within the framework of the economic literature. In section 3, following
Llorente 2007, we exploit peculiarities of the betting system to make some assump-
tions that allow us to analyze what we will call the general odds rule. Analyzing the way
odds are determined in this market, we ﬁnd inefﬁciencies both assuming equal return
of bets and when no proﬁtable betting strategies are allowed. A third notion of efﬁ-
ciency, reporting ﬁndings from an analysis of ﬁeld data in these markets, is presented
in section 4, and section 5 considers hedging strategies. The ﬁnal section contains a
summary discussion and conclusions.
1 A Description of the Pelota
Betting System
.............................................................................................................................................................................
All pelota (pelota vasca) matches are played by two teams: reds (R) and blues (B) play
against each other by hitting a ball in turn against a wall on a court called a frontón.
The team that serves ﬁrst is chosen by tossing a coin. When a team makes an error the
opponent scores one point and serves to start the next point. The team that reaches a
pre-set number of points wins the match.
A bet on these matches is made based on two quantities that inform the odds: the
amount of money the bettor loses for failing to predict the winning team and the
amount the bettor wins for guessing right. Bets can be made during the entire match,
so as points are scored, odds change. A bettor can place as many bets as he or she wants,
provided someone can be found to accept those bets.

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sports betting
This betting system is popular in the Basque Country, Navarra, and La Rioja, where
several types of pelota games are played. There are slight differences between the
different types. In what follows we will describe the betting system in particular to
the type called remonte. The rules of the betting system are not written, thus all our
explanations are based on information obtained at the frontón. More speciﬁcally, our
study is based on information collected at the Euskal Jai Berri, a frontón where the
pelota game played is remonte. This frontón was chosen because it has screens that
display the odds as they change during the game, a peculiarity that is very helpful for
obtaining ﬁeld data.
1.1 A Brief Description of Remonte
Remonte is a type of pelota game that looks like a jai alai game. The frontón on which
it is played consists of a playing court limited by three walls at the front, the left, and
the back. It measures about 54 meters long, 12 meters wide, and 11 meters high.
In this game, reds and blues hit a ball with a wicker scoop called the cesta that
is attached to the players’ hands. The teams usually have two players each but may
occasionally have one or three. Each team has to hit the ball in turn, starting with the
team chosen by the ﬁeld judge by tossing a coin. When one player fails to hit correctly
the opponents score one point and serve the ball in order to start the next point. The
ﬁrst team to reach 40 points wins the match.
To play a point, each team has two possibilities. The ﬁrst and most common one
is to hit the ball against the front wall so that the ball bounces on the ﬂoor inside the
limits marked. The second one is to hit the ball against the left wall so that it rebounds
against the front wall and then bounces on the ﬂoor inside the court. Once the ball hits
the front wall the other team is allowed to hit the ball either before or after it touches
the ﬂoor (only once) or even after it bounces off the back wall. Each game usually lasts
around one hour.
1.2 A Brief Description of the Betting Market in Remonte
Throughout the game spectators are allowed to place as many bets as they want. On
each bet the bettor chooses either the red team or the blue team and wagers an amount
of money against another spectator who chooses the other team and wagers a different
amount of money (these amounts become the odds). The bettor who guesses correctly
wins the money that the other bettor loses. For example, if you bet 100 euros on the
reds against an opponent who bets 100 on the blues and the blues win the match, you
pay your opponent 100 euros. But all bets are placed through a middleman who works
for the organizers and takes 16 percent of the winnings of the successful bettor (in
what follows this is called the commission); so in the previous example, you would pay

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the efficiency of pelota betting markets
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Table 10.1 The Screen at Euskal Jai Berri frontón
Odds
Score
OR is the amount a bettor risks by betting on reds.
(reds)
OR
sr
OB is the amount a bettor risks by betting on blues.
(blues)
OB
sb
sr (sb) is the red (blue) team’s score.
Table 10.2 An Example of the
Presentation of Odds and Score
Odds
Score
(reds)
100
5
(blues)
80
2
your opponent 100 euros, but he or she would only receive 84 because the middleman
takes 16.
Throughout the remonte match a screen (see table 10.1) shows the effective odds in
the market and the current score.
The odds consist of two numbers, with the bigger one always being 100 euros and
the smaller one varying between 2 and 100 as points are played. Generally the smaller
odd is one of the set {2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 25, 30, 40, 50, 60, 70, 80, 90, 100}.
In the example in table 10.2 the red team has scored 5 and the blue team 2. The odds
are 100 to 80, denoted by (100, 80). The bettor who bets on reds risks 100 euro to win
80, and the one who bets on blues risks 80 euro to win 100. From here on the chapter
will follow this convention in describing the various bets, and we will denote these odds
(OR, OB). Bets are always between spectators, so if one spectator places a bet on red
there must be another who bets on blue. What happens when the game is over?
Bet on reds: A bettor on reds will lose 100 euros if blues win the match. Otherwise, if
redswinthematchthebettorwillwin80eurosminusthe16percentcommission,
that is, 67.2 euros.
Bet on blues: A bettor on blues will lose 80 euros if reds win the match. Otherwise,
if blue wins the match the bettor will win 100 euros minus 16 percent, that is, 84
euros.
This describes a single bet. A bettor can make as many bets as he or she wants to,
provided there is someone on the other side who will take the bets. For example, with
the same screen as represented in table 10.2, if a bettor places 10 bets on the reds he or
she will lose 100 × 10 = 1,000 euros if blues win the match. Otherwise, if reds win the
match the bettor will win 67.2 × 10 = 672 euros.

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sports betting
Moreover, a bettor can bet at different times during the game, choosing one team in
one period and the other team in another. Therefore the result above concerns only the
particular bet analyzed here.
1.3 The Way the Odds Are Fixed in the Market
In remonte there is an auctioneer, who posts the odds that appear on the screen. We call
him the coordinator. He is usually someone who has been a player and a middleman for
many years. This coordinator is an expert on remonte, usually the person at the frontón
who is most knowledgeable about the game. The coordinator chooses the handmade
balls used by players to play the match, and he posts the odds at which people bet.
The coordinator sits in front of a computer, in a privileged place behind the spectators,
where he can follow the match and see the spectators and all the middlemen. He posts
the odds that appear on the screens. After a team scores a point it is closer to winning
and thus more likely to win the match than before the score was made. Therefore the
money a bettor risks betting on that team should be higher in order to maintain the
expected value of the bet.
There are some general rules that the coordinator follows to set and change the odds:
If there is no reason to think of either team as the favorite just before the match starts,
the score is zero-zero and the odds (OR, OB) are (100, 100). If there is a favorite team,
the odds may be different. For example, if red is favorite, with the same score as above,
we would have odds (OR, OB) of (100, 80).
Once it is clear what the initial odds are, the match goes on and points are scored.
The general rule is that the difference between the amounts of the odds increases by 10
euros on the team that has just scored a point, keeping in mind that the larger amount
in the odds is always 100.
If the odds differ by more than 70 (100, 30), they change by only 5 euros for each
point. If they differ by more than 90, the odds change by only 2 euros for each point.
When one team has accumulated approximately 30 points, the change in the odds
doubles for each point then scored and trebles or quadruples when the end of the
match is very near. For example, if the score is (38, 39) the odds would be (40, 100).
Of course, sometimes these rules are modiﬁed because of changes in supply and
demand among spectators. When a middleman ﬁnds two people who want to bet at
odds different from those on the screen, the middleman has to ask the coordinator to
change the odds on the screen so that he can print the receipts for the bettors. There
are no bets on the frontón at odds different from those on the screens. In general the
odds vary mainly as the above rules indicate.
It is important to realize that the coordinator works for the ﬁrm that organizes pelota
matches, so his goal could be described as making people bet as much as possible. We
can conﬁdently assume therefore that the odds he posts are those at which people are
most willing to bet, that is, equilibrium odds where there is no excess of demand of
bets.

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2 The Pelota Betting System: Similarities
and Differences with Other Studies
.............................................................................................................................................................................
Studies of different sports and differing betting systems can require different analyses
and/or hypotheses, and this affects how efﬁciency in the market is analyzed. Raymond
Sauer (1998) mentions different deﬁnitions of market efﬁciency that are widely utilized
in empirical settings.
Before presenting different ways of analyzing efﬁciency in the pelota betting market,
this section presents an overview of the betting systems that were prominent in the
economic literature before betting exchanges were established on the Internet. It also
will be useful to show the framework of our study within the economic literature,
pointing out, according to our point of view, which are the relevant characteristics of
other studies related to the pelota betting system.
2.1 Summary of Betting Systems Prominent in the
Economic Literature
According to Sauer (1998) and Richard E. Quandt (1986), three forms of wagering
are prominent in the relevant economic literature: pari-mutuel odds, odds offered by
bookmakers, and point spread, also offered by bookmakers. The pari-mutuel system
is used exclusively by racetracks in North America, France, Hong Kong, and Japan
and coexists with the bookmaking market in Australia and Great Britain. Nevada
bookmakers take bets on races at major tracks and offer odds on point spreads on
team sports such as baseball, basketball, and football. The legal bookmaking market is
less restricted, more extensive, and more liquid in Great Britain and Australia.
In pari-mutuel betting individuals invest in shares of the various horses. The prices
of the shares are standardized, but the payoffs depend on the amount bet on a par-
ticular horse relative to the amount bet on all horses. Particularly in a pari-mutuel
market people place wagers on which of two or more mutually exclusive and exhaus-
tive outcomes will occur at some time in the future. A predetermined percentage is
taken out of the betting pool to cover the market maker’s costs, and after the true
outcome becomes known, the remainder is returned to winning bettors in proportion
to their individual stakes. Therefore the possible payoffs are not known until the last
bet is placed. Pari-mutuel markets are common at horse races, dog races, and jai alai
games.
Bookmakers offer their customers a set of payoffs conditioned on the outcome of a
given event. The payoffs offered may change during the betting period—in general the
more likely an outcome, the lower the payoff—but the payoff for each bet is determined
at the time the bet is placed. The return conditioned on winning is thus known at the
time of the wager; this is in contrast to the pari-mutuel system, where heavy betting late

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sports betting
in the period can reduce returns below acceptable levels. Individuals who make bets
large enough to affect the odds may prefer to bet with a bookmaker.
Point spread betting on football games is the staple of the Las Vegas sports bet-
ting market. In a point spread wager the payoff depends on the difference in points
scored by the two opposing teams. Point spreads (PS) are typically reported as the
number of points by which one team is favored to beat another. The actual differ-
ence in points (DP) is deﬁned as the points scored by the favored team less those
scored by the underdog. Bets on the favorite pay off when DP−PS >0, bets on the
underdog pay off when DP−PS <0, and all bets are refunded when DP = PS. The
eleven for ten rule characterizes standard terms in the Las Vegas market. Where com-
mission ts = 0.1 and successful bets return net winnings of $1 to every $(1 + ts)
wagered. The point spread represents a price in this market. Let p represent the prob-
ability that wagers on the favorite will pay off, that is, that p = prob (DP−PS) >0.
The expected cost of an attempt to gain $1 by betting on the favorite is the amount
wagered times the probability of losing or $(1+ts)(1−p). Since p falls as PS increases,
the expected cost of a wager on the favored team, that is, its price, increases as PS
increases.
The pelota betting system ﬁlls an unrealized gap in the relevant literature before the
advent of online betting exchanges. Although its territorial scope is limited, its cultural
importance is high. Many fans follow pelota matches not only at the frontón but also
on television. We emphasize that although the Pelota betting system has operated for
centuries in the regions of Navarra, the Basque Country, and La Rioja, its rules are not
written down but passed on verbally. This has hindered its spread to other regions, and
thus it has not been studied, even though its importance in the area is remarkable. Both
its peculiarities and its theoretical simplicity make analyzing the pelota betting market
an interesting exercise. Nowadays the relevance of this system is more obvious due to
its similarity with the betting exchanges (see Edelman and Llorente 2010).
2.2 The Pelota Betting System in the Economic Literature
Stephen Skiena (1988) studied a jai alai game where both the game and the betting
system are completely different from those described here. Conversely, the team jai
alai game studied by Lane and Ziemba (2008) is similar to the sport of pelota, but the
betting system they studied is bookmaking.
The pelota betting system is similar to that on betting exchanges. Edelman and
Llorente (2010) compared both and showed that normalizing the odds in the pelota
betting system (dividing them by OR) makes a bet on the reds similar to a Back on the
reds at odds x and betting on the blues similar to Laying a bet on the reds at odds x
whenever OB
OR = x −1. Smith, Paton, and Vaughan Williams (2006) and Marginson
(2010) studied efﬁciency in person-to-person betting or betting exchanges. The latter
study focused on the case of the “known loser” in sports, where there are more than
two possible results, as in horse races. In pelota there are only two states of nature,

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the efficiency of pelota betting markets
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either the reds win or the blues win. Another point of view is to model pelota bets
as a game between two bettors, as done by Werner Güth, Anthony Ziegelmeyer, and
Llorente (2009), who used pelota bets to study experimentally inconsistent beliefs in a
betting game.
3 The General Odds Rule
.............................................................................................................................................................................
In this section, following Llorente (2007), we take advantage of the peculiarities of the
betting system to make some assumptions that allow us to analyze what we call the
general odds rule.
We were told by the coordinator in the market that games are arranged in such a
way that the chances of winning for each team are as similar as possible. From this
peculiarity we assume that, in general, the probability of the following point being
scored by each team is 50:50. As we will see, this assumption allows us to obtain each
team’s theoretical probability of winning (see subsection 3.1).
The coordinator also told us that he follows a general rule to set odds in the market so
long as nothing atypical happens (where atypical means that there is an excess of people
willing to bet on one color). Odds differ from those of the general rule if, for example,
it can be seen that a player has lost his ability to play or something happens that causes
more bettors to bet on one team more than the other. From that we can infer that odds
in the general rule are equilibrium odds (i.e., there is no excess of willingness to bet on
one of the two teams), when players have the same probability of scoring the following
point. Therefore we posit the general odds rule as the equilibrium price in the market
when the probability of scoring the following point by each team is 50:50. From these
market odds, and under some assumptions that will be explained in subsection 3.2, we
can obtain the probabilities inferred from market odds.
We will compare the theoretical probability with the probability inferred from market
odds to check whether the market is efﬁcient or not.
3.1 Teams’ Theoretical Probabilities of Winning the Match
Assuming that the likelihood of a team scoring the following point is the same through-
outthematch,thetheoreticalprobabilityof theteam’swinningthematchcanbederived
at any time. With no loss of generality we perform such a calculation for the reds. Given
the reds’ score, sr, the blues’ score, sb, and the reds’ probability of scoring a point at
any moment during the match, p, the reds’ probability of winning the match, pr, is
given by
pr(sr,sb,p) =
40−sb−1

i=0
 i + 40 −sr −1
i

p40−sr (1 −p)i.
(10.1)

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This equation is obtained by the addition of as many amounts as there are different
possible ﬁnal scores where the reds are the winners (i is the number of points the blues
could score, from 0 to 39−sb). For each of these possible ﬁnal scores, the amount added
is obtained by multiplying the probability of this ﬁnal score by the number of different
ways in which it can be reached.
In pelota games the probability of each team scoring the following point and the
probability of winning the match are unknown, but we know that matches are arranged
so that the chances of each team winning are as similar as possible according to the
subjective perception of the organizer of the match: when one team is superior the
odds are shortened by using match-balls that favor the worse team and so on. When
one team is superior the other may even be allowed to use one more player. Thus for
the sake of simplicity we set the reds’ probability of scoring the following point at p =
0.5. This in conjunction with equation 10.1, above, allows us to calculate, for a given
score, the reds’ probability of wining the match, pr, as
pr(sr,sb) =
39−sb

i=0
 i + 39 −sr
i

0.540−sr 0.5i.
We call this the reds’ theoretical probability of winning the match.
These theoretical probabilities for some possible scores are shown in table 10.3.
Table 10.3 Reds’
Theoretical
Probabilities of Winning Given
the Current Score
(sr,sb)
Theoretical pr
(1,0)
0,545
(2,0)
0,5901
(3,0)
0,6345
(4,0)
0,6778
(5,0)
0,7193
(6,0)
0,7586
(7,0)
0,7952
(8,0)
0,8288
(9,0)
0,859
(10,0)
0,8858
(11,0)
0,9091
(12,0)
0,929
(13,0)
0,9456
(14,0)
0,9592
(15,0)
0,97
(16,0)
0,9785
(17,0)
0,985

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the efficiency of pelota betting markets
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Actually, the particular problem of betting analyzed here is closely connected with
the so-called problem of points that initiated the study of probability. That problem,
also known as the division problem, was proposed by Antoine Gombaud, chevalier
de Méré, to Blaise Pascal and led to correspondence between the latter and Pierre de
Fermat in the summer of 1654 (see Edwards 1982). Based on this correspondence
Pascal and Fermat are said to be among the joint discoverers of probability calculus
(see David [1962] 1998, 75). According to their discussion it can be concluded that
the probability of winning for a player who needs j points to win (each obtained with
probability p) against another who needs k points to win (each point obtained with
probability q = 1 −p) is given formally2 by Pj,k =
j+k−1

l=j
 l
−1
j
−1

pjql−j. As can be
easily checked, the equation that we propose, (10.1), is very similar. Indeed, it is the
same formula after a change of variables. We use equation (10.1) for ﬂuency to obtain
the theoretical probability given the score in our particular betting market.
3.2 Teams’ Probabilities of Winning the Match Inferred
from Market Odds
In this subsection we try to analyze the market with orthodox methods; particularly
we analyze the general odds rule followed in the pelota betting system under certain
assumptions that may be somewhat strong but are also usually made in studies of
other wagering markets. Thus we start by assuming that bettors are expected value
maximizers. A condition for equilibrium is that the expected value of a bet on the reds
should be equal to the expected value of a bet on the blues; if not, all bettors prefer to
bet on the color with the higher return. In subsection 3.2.2 we discuss the probability
inferred from the market assuming equal returns on each bet and determine that there
is a difference between the probability inferred from market odds and the theoretical
probability of a team winning the match. Low probabilities are overestimated while
high probabilities are underestimated.
In these markets there are commissions, so the equilibrium condition of equal return
of bets implies that each bet has a negative expected return. Therefore it seems more
convenient to introduce the less restrictive restriction of not allowing proﬁtable bets in
the market. This is done in subsection 3.2.3, where we calculate what the probabilities
inferred from the market odds must be to satisfy this less restrictive restriction of no
proﬁtable bets, that is, to satisfy the condition of the expected value of each bet being
lower than or at most equal to zero. Comparing this probability inferred from market
odds with the actual probabilities we ﬁnd that in these markets there are proﬁtable
betting strategies.

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Table 10.4 General Odds Rule
Score
Odds
(sr,sb)
(OR,OB)
(1,0)
(100,90)
(2,0)
(100,80)
(3,0)
(100,70)
(4,0)
(100,60)
(5,0)
(100,50)
(6,0)
(100,40)
(7,0)
(100,30)
(8,0)
(100,25)
(9,0)
(100,20)
(10,0)
(100,15)
(11,0)
(100,10)
(12,0)
(100,8)
(13,0)
(100,6)
(14,0)
(100,4)
(15,0)
(100,2)
(16,0)
(100,2)
(17,0)
(100,2)
3.2.1 The General Odds Rule
As already mentioned, for each score we can derive the odds in the market by applying
the general odds rule. Table 10.4 shows some scores and their corresponding market
odds.
3.2.2 Efﬁciency of the General Odds Rule Assuming Equal Return on Bets
Now that we know the odds in the market for each score, we can derive the probabilities
inferred from these odds as follows. If a pelota betting market is efﬁcient, where “efﬁ-
ciency” means that the expected returns are equal on the various bets (see the different
meanings of “efﬁciency” in Sauer 1998, 2024), then equation (10.2) should apply.
pr
1 −pr
= OR
OB
,
(10.2)
where pr is the likelihood of the reds winning the match, OR is the money risked in a
bet on the reds and OB is the money risked in a bet on the blues.
Proof.
Denote by EVR the expected value of a bet on the reds and EVB the expected
value of a bet on the blues. We know that EVR = pr OB(1 −t) −(1 −pr)OR and that

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the efficiency of pelota betting markets
183
EVB = (1−pr)OR(1−t)−prOB,where t is the middleman’s commission. If the market
is efﬁcient the two expected values should be equal, thus prOB(1 −t) −(1 −pr)OR =
(1 −pr)OR(1 −t) −prOB, and by operating we obtain
pr
1−pr = (2−t)OR
(2−t)OB , which proves
that equation (10.2) is true no matter what the commission is.
Rearranging equation (10.2), pr = OR
OB (1 −pr); pr

1 + OR
OB

= OR
OB ; pr =
OR/OB
 OB+OR
OB
;
therefore
pr =
OR
OB + OR
.
(10.3)
The probability inferred from the odds is obtained by equation (10.3). These
probabilities are shown in table 10.5.
In table 10.6 we put together four columns: ﬁrst, of all the scores; second, the market
odds for each score applying the general odds rule; third,the reds’theoretical probability
of winning the match obtained for each score; and fourth, the reds’ probability of
winning the match obtained from the market odds by applying equation (10.3).
In ﬁgure 10.1 a scatterplot is shown of the probabilities inferred from markets odds,
πr, against the corresponding theoretical probability, pr.
Table 10.5 Probability of Reds Winning
Inferred from Market odds Assuming
Equal Return of Bets
Note: Obtained by equation (10.3).
Odds
pr Derived from
(OR,OB)
Market Odds = πr
(100,90)
0,5263
(100,80)
0,5556
(100,70)
0,5882
(100,60)
0,625
(100,50)
0,6667
(100,40)
0,7143
(100,30)
0,7692
(100,25)
0,8
(100,20)
0,8333
(100,15)
0,8696
(100,10)
0,9091
(100,8)
0,9259
(100,6)
0,9434
(100,4)
0,9615
(100,2)
0,9804
(100,2)
0,9804
(100,2)
0,9804

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sports betting
Table 10.6 Probability of Reds Winning; Theoretical and Derived
from Market Odds
Score
Odds
Theoretical
pr Derived from
(sr,sb)
(OR,OB)
pr
Market Odds
(1,0)
(100,90)
0,545
0,5263
(2,0)
(100,80)
0,5901
0,5556
(3,0)
(100,70)
0,6345
0,5882
(4,0)
(100,60)
0,6778
0,625
(5,0)
(100,50)
0,7193
0,6667
(6,0)
(100,40)
0,7586
0,7143
(7,0)
(100,30)
0,7952
0,7692
(8,0)
(100,25)
0,8288
0,8
(9,0)
(100,20)
0,859
0,8333
(10,0)
(100,15)
0,8858
0,8696
(11,0)
(100,10)
0,9091
0,9091
(12,0)
(100,8)
0,929
0,9259
(13,0)
(100,6)
0,9456
0,9434
(14,0)
(100,4)
0,9592
0,9615
(15,0)
(100,2)
0,97
0,9804
(16,0)
(100,2)
0,9785
0,9804
(17,0)
(100,2)
0,985
0,9804
(0,1)
(90,100)
0,455
0,4737
(0,2)
(80,100)
0,4099
0,4444
(0,3)
(70,100)
0,3655
0,4118
(0,4)
(60,100)
0,3222
0,375
(0,5)
(50,100)
0,2807
0,3333
(0,6)
(40,100)
0,2414
0,2857
(0,7)
(30,100)
0,2048
0,2308
(0,8)
(25,100)
0,1712
0,2
(0,9)
(20,100)
0,141
0,1667
(0,10)
(15,100)
0,1142
0,1304
(0,11)
(10,100)
0,0909
0,0909
(0,12)
(8,100)
0,071
0,0741
(0,13)
(6,100)
0,0544
0,0566
(0,14)
(4,100)
0,0408
0,0385
(0,15)
(2,100)
0,03
0,0196
(0,16)
(2,100)
0,0215
0,0196
(0,17)
(2,100)
0,015
0,0196
The graph shows that for low theoretical probabilities the probability inferred from
market odds is higher, and for high probabilities the probability inferred from market
odds is lower than is actually the case. Thus this analysis, as well as that in other studies,
supports the long-shot bias. Empirical evidence on horseracing is found in Dowie
(1976), Henery (1985), Thaler and Ziemba (1988), and Vaughan Williams and Paton
(1997). And empirical evidence of the long-shot bias in greyhound racing is found in
Cain, Law, and Peel (1992).

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the efficiency of pelota betting markets
185
Probability inferred from market odds 
assuming EVr = EVb
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Theoretical probability
Probability inferred from market odds
pr derived from market odds
Identity line
figure 10.1 A scatterplot of the theoretical probability against probability inferred from market
odds (table 10.6) together with the identity line.
3.2.3 Efﬁciency of the General Odds Rule Assuming
No Proﬁtable Bets
Nevertheless, as there are commissions, t = 0.16, when a bet takes place both bettors’
expected values add up to a negative amount. Thus when analysing efﬁciency it is more
convenient to ask for no possible proﬁtable bets in the market. This implies that the
expected value of a bet, both on the reds and on the blues, has to be lower than or equal
to zero, and as shown in the following proposition, this implies that both equations
(10.4) and (10.5) have to be fulﬁlled.
In a pelota betting market there are no proﬁtable bets if and only if
pr ≤
OR
OB(1 −t) + OR
(10.4)
and
OR(1 −t)
OB + OR(1 −t) ≤pr.
(10.5)
Proof.
The expected value of a bet on the reds lower than zero and the expected value
of a bet on the blues lower than zero implies
prOB(1 −t) −(1 −p)OR ≤0.
(10.6)
and
(1 −pr)OR(1 −t) −prOB ≤0,
(10.7)

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pr s.t. EVb  ≤ 0 (t = 0,16)
0,0
0,2
0,4
0,6
0,8
1,0
0
0,1 0,2
0,3 0,4 0,5 0,6 0,7
0,8 0,9
1
theoretical probability
pr inferred from market odds
(no profitable bets) 
 pr s.t. EVr ≤ 0 (t = 0,16)
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0
0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9
1
theoretical probability
pr inferred from market odds 
(no profitable bets)
figure 10.2 On the left, pr assuming that the expected value of a bet on the reds is at most zero:
equation (10.4). On the right, pr assuming expected value of a bet on the blues is at most zero:
equation (10.5).
respectively. Rearranging equations (10.6) and (10.7) we obtain equations (10.4) and
(10.5).
We represent equations (10.4) and (10.5) ﬁrst in two separate graphs, Figure 10.2,
and then together, Figure 10.3.
Given a score, we know both the theoretical probability of winning for the reds
(applying equation (10.1)) and the market odds (applying the general odds rule).
Therefore in ﬁgure 10.2 (left), the horizontal axis shows the theoretical probability
and the vertical axis shows the upper bound probability inferred from market odds
(applying equation (10.4)). The marked area corresponds to the probabilities inferred
from markets odds assuming that the expected value of a bet on the reds is lower than
zero.
Given a score, we know both the theoretical probability of winning for the reds
(applying equation (10.1)) and the market odds (applying the general odds rule).
Therefore in ﬁgure 10.2 (right) the horizontal axis shows the theoretical probabil-
ity of winning for the reds. The vertical axis shows the lower bound probability
inferred from market odds (applying equation (10.5)). The marked area corresponds
to the probabilities inferred from market odds assuming that the expected value of
a bet on the blues is lower than zero. Because the conditions in both equations
(10.4) and (10.5) are necessary for the market to have no possible proﬁtable bets,
the probability inferred from market odds should be at the intersection of both
areas.
From ﬁgure 10.3 it can be seen that there are odds in the market at which proﬁtable
bets could be made. It can be seen that when the theoretical probability of the reds
winning is {.68, .72, .75} it is proﬁtable to bet on the reds: the odds are respectively
{(100, 60), (100, 50), (100, 40)}. Symmetrically, when the theoretical probability of
the reds winning is {.24, .28, .32}the odds are respectively {(40, 100), (50, 100), (60,
100)}, and it is proﬁtable to bet on the blues, whose probabilities of winning are
complementary. Overall, when the odds differ by 40, 50 or 60 euros, it is proﬁtable to
bet on the favorite.

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187
pr inferred from market odds
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Theoretical pr
pr s.t. no profitable bets  
a
figure 10.3 The probability inferred from market odds, such that no proﬁtable bets are pos-
sible, has to be in the area between both curves. In this area, equations (10.4) and (10.5) are
fulﬁlled.
Linda Woodland and Bill Woodland (1994) found deviation from efﬁciency in the
baseball betting market, but their analysis failed to allow for proﬁtable betting strategies
when commissions are considered. Here we ﬁnd proﬁtable betting strategies taking
commissions into account.
If the expected value of a bet on the reds must be equal to the expected value of a bet
on the blues, equation (10.2), the probability inferred from market odds is just in the
middle of the area between the two lines, a probability for which the expected value of
a bet is negative. This is shown in ﬁgure 10.4.
4 Field Data Analysis
.............................................................................................................................................................................
Llorente and Aizpurua (2008) found a theoretical explanation for the existence of
this market in a world where both sides of the market are not different in beliefs
and preferences. They found that for a bet to exist when bettors are rank-dependent
expected utility maximizers, they have to be optimistic; that is to say, they underestimate
the probability of the worst result occurring when they bet. Based on this theoretical
explanation, the authors conducted a preliminary analysis of ﬁeld data. Although the
samplewassmall,theiranalysiswasbasedonactual,observedbets. Theyfoundevidence
of underestimation of the favorite’s chances of winning, supporting the well-known
long-shot bias.

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sports betting
pr
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Theoretical pr
pr inferred from market odds  as the a
           pr s.t. EV on the reds = 0
           pr s.t. EV on the blues = 0
           pr s.t. EVr = EVb
figure 10.4 The solid line represents the probability inferred from market odds when bets have
the same return, i.e. equation (10.2) is fulﬁlled. In this case the expected value of each bet is
negative.
Here we explain the methodology they used. They collected data at the frontón, for
each score, the odds and the approximate volume of bets. The odds are presented as
pairs (Of ,Ol) where f denotes the favorite team and to which the higher number of
the odds is associated, and l corresponds to the non-favorite or long-shot team.
For each set of odds, the total number of bets made at those odds was tabulated. Then
it was counted for each given odds, the number of times the favorite team turned out
to be the winner, and the number of times the favorite was defeated. Then frequencies
were obtained (favorite wins and favorite loses).
For each given odds betting on l means accepting that Ol will be lost with some
probability denoted by πl
f and that Of (1 −t) will be gained with probability 1−πf
l . A
bettor who bets on l indicates that his subjective probability of the worse event (the
favorite team wins) is πl
f ≤
Of (1−t)
Of (1−t)+Ol . This is the upper bound on the worse event for
a bettor on l, with commission t = 0.16.
Similarly, for a given odds betting on f means accepting that Of will be lost with
some probability denoted by πf
l and that Ol(1 −t) will be gained with probability
1−πf
l . A bettor who bets on f indicates that his subjective probability of the worse
event (the non-favorite team wins) is πf
l ≤
Ol(1−t)
Ol(1−t)+Of . This is the upper bound on the
worse event for a bettor on f , with commission t = 0.16.
For any given odds the worse event for a bet on l is the favorite wins. And πf
l is
interpreted as the weight a bettor on l attaches to this frequency.
Similarly, for any given odds the worse event for a bettor on f is the favorite loses.
And πf
l is interpreted as the weight a bettor on f attaches to this frequency.

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189
0,00
0,10
0,20
0,30
0,40
0,50
0,60
0,70
0,80
0,90
1,00
0,00
0,20
0,40
0,60
0,80
1,00
real probability of the worst outcome
probability of the worst outcome inferred from
market's odds s.t. EV= 0
data
identity
nonlinear regression
figure 10.5
Source: Llorente and Aizpurua (2008)
The frequency with which an event occurs and the weights that different bettors place
on that probability are represented in ﬁgure 10.5. High probabilities that the favorite
will win are associated with weights that are lower than those probabilities; that is, the
market odds underestimate the real chances that the favorite will win the match, and
low probabilities that the favorite will lose are associated with weights that are higher
than those probabilities, evidence of the well-known long-shot bias studied in Sauer
(1998) and Woodland and Woodland (1994).
The following function is estimated
π =
δ(“real p”)γ
δ(“real p”)γ + (1 −“real p”)γ
R2 = .839,
with δ = .84 and γ = .55, both signiﬁcantly lower than 1 at the 95 percent conﬁdence
level (ﬁgure 10.5). For this parameter value π(“real p”) + π(1 −“real p”) < 1 for all
“real p.”
The result is a weighting function of optimistic bettors who overestimate low
probabilities and underestimate high ones. In addition p∗(cross point with the iden-
tity line) is 0.38, very close to that obtained by Richard Gonzalez and George Wu
(1999). These parameter values are similar to those obtained in the parameter-free
elicitation of the probability weighting function studied by Mohammed Abdellaoui
(2000). Their ﬁndings then are similar to those obtained in studies of weighting
functions.

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sports betting
5 Hedging
.............................................................................................................................................................................
Many bettors follow a strategy of hedging their bets. In this context, hedging refers to
betting at two different moments during the game in such a way that the second bet
intends to offset potential losses that may be incurred by the ﬁrst. The bettor could
then receive a payout independently of which team wins the match.
In subsection 2.2 we mentioned the Lane and Ziemba (2008) study on team jai alai,
where the game is similar to pelota but the betting system is bookmaking. Differences
between the betting system they analyzed and ours affect the meaning of what a consis-
tent bet is. Therefore the arbitrage strategy they employ when the bookies’ odds make a
positive expected value possible due to the minimum payout on a bet makes no sense in
pelota betting systems. On the other hand, when they use what they call risk arbitrage
strategies, even though the betting game is different, the sport is similar and their idea
of studying all feasible paths could help in the study of efﬁciency in the pelota betting
system. Calling G the set of scenario game paths from (0,0) to the ﬁnal outcome, they
show the cardinality of G (262), which can be of interest in our study. Lane and Ziemba
also discuss the applicability of jai alai study in traded options and warrants markets
(270). Although we do not have details to present here, we actually are researching
hedging strategies.
6 Summary and Concluding Remarks
.............................................................................................................................................................................
There are two peculiarities that differentiate the pelota betting system from other well-
known betting systems. Unlike pari-mutuel betting systems, the odds in a pelota market
are established when the wager is made, and bets are arranged by middlemen. However,
unlike conventional forms of bookmaking, for a bet to be placed one bettor bets on one
team and another bettor bets on the other team; the middleman does not bet at all.
There is a similar betting system that has been implemented on the Internet, online
betting exchanges. The betting system followed by betting exchanges is similar to the
pelota betting system in that bettors can make as many bets as they want provided there
is another bettor on the other side, and the market maker takes a percentage of the
money as a commission. As we have noted, the main difference with the pelota betting
system is the odds scale.
In this chapter, we have positioned the pelota betting system within the framework
of the economic literature and we have presented the results obtained applying three
different concepts of efﬁciency (deﬁned in Sauer 1998) in this betting market: constant
return of bets, absence of proﬁt opportunity, and equilibrium pricing function. First, we
conducted an examination of the market using orthodox methods, in particular, an
analysis of the general odds rule followed in the pelota betting system under certain

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the efficiency of pelota betting markets
191
assumptions. Although these may be somewhat heroic assumptions, they have been
invoked in studies of other wagering markets. Thus we start by assuming that bettors
are expected value maximizers. A condition for equilibrium is that the expected value
of a bet on the reds must be equal to the expected value of a bet on the blues because,
if not, all bettors prefer to bet on the color with the higher return. We also discussed
the probability inferred from the market odds assuming equal returns on each bet and
found that there is a difference between the probability inferred from market odds
and the theoretical probability of a team winning the match. Low probabilities are
overestimated while high probabilities are underestimated. Therefore, in the pelota
betting market we ﬁnd evidence of the long-shot bias.
Second, in these markets there are commissions, so the equilibrium condition of
equal returns on bets implies that each bet has a negative expected return. Thus it
seems more convenient to introduce the less restrictive restriction of not allowing prof-
itable bets in the market. We checked what the probability inferred from market odds
is to satisfy this less restrictive restriction of no proﬁtable bets, that is, to satisfy the
condition of expected value of a bet lower than or at most equal to zero. We found
that the probability inferred from market odds must be in an area satisfying equations
(10.4) and (10.5). Under the assumption of no proﬁtable bets there are odds at which
subjective probabilities differ from real ones. Thus there are odds in the market at
which proﬁtable bets could be made; when the odds differ by 40, 50, or 60 euros,
it is proﬁtable to bet on the favorite. We would like to point out that the theoreti-
cally positive expected value bets that we found are relatively small. It is nonetheless
an achievement to ﬁnd any positive expectation bets in a game with a 16 percent
commission.
Thirdly, the chapter also contains an empirical analysis of the efﬁciency of this
market based on a standard assumption of equilibrium in an explicit model assum-
ing identical bettors. Llorente and Aizpurua (2008), assuming all bettors are identical
rank-dependent expected utility maximizers, found evidence in the market of under-
estimation of the favorite’s chances of winning, supporting the well-known long-shot
bias. More accurately, the effect found is a kind of long-shot bias. However, it is a bit
different from the long-shot bias in horse racing. In horse racing, the long-shot bias
gets more extreme as p gets smaller. The pelota bias found reaches a maximum in the
medium long-shot range and then gets smaller again for extreme long shots.
Finally, we also provide some insights on hedging strategies.
Notes
1. Data obtained on-line from the paper“Origen y desarrollo de las distintas modalidades del
juego de la pelota vasca” on the website of the Confederación Internacional del Juego de la
Pelota; http://www.cijb.info.
2. I am grateful to a referee for showing me this connection and for his detailed explanation
of it.

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Gonzalez, Richard, and George Wu. 1999. On the shape of the probability weighting function.
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Güth, Werner, Loreto Llorente, and Anthony Ziegelmeyer. 2009. Inconsistent incomplete
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Henery, Robert J. 1985. On the average probability of losing bets on horses with given starting
price odds. Journal of the Royal Statistical Society 148(4):342–349.
Lane, Daniel, and William T. Ziemba. 2008. Arbitrage and risk arbitrage in team jai alai. In
Handbook of sports and lottery markets, edited by Donald B. Hausch and William T. Ziemba.
Amsterdam: Elsevier, 253–271.
Llorente, Loreto. 2007. A proﬁtable strategy in the pelota betting market. In Optimal play:
Mathematical studies of games and gambling, edited by Stewart N. Ethier and William R.
Eadington. Reno: Institute for the Study of Gambling and Commercial Gaming, University
of Nevada, 399–416.
Llorente, Loreto, and JosemariAizpurua. 2008. A betting market: Description and a theoretical
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Quandt, Richard E. 1986. Betting and Equilibrium. Quarterly Journal of Economics 101(1):
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Sauer, Raymond D. 1998. The economics of wagering markets. Journal of Economic Literature
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Vaughan Williams, Leighton, and David Paton. 1997. Why is there a favourite-longshot bias
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chapter 11
........................................................................................................
THE LURE OF THE PITCHER:
HOW THE BASEBALL
BETTING MARKET IS INFLUENCED
BY ELITE STARTING PITCHERS
........................................................................................................
rodney j. paul, andrew p. weinbach,
and brad r. humphreys
1 Introduction
.............................................................................................................................................................................
The starting pitcher plays a pivotal role in the sport of baseball. Pitchers are the key
defensive player on the baseball diamond, and their abilities can drastically alter the
outcome of games. Even poor teams can be bolstered by a great starting pitcher, and
excellentoffensiveteamsmaylosegamesandchampionshipsduetoweaknessinstarting
pitching. Unlikemanyotherteamsports,asingleplayer,thestartingpitcherinabaseball
game, can have a signiﬁcant impact on the outcome of games. This may also affect
outcomes in betting markets.
Although most starting position players on a team remain the same over the course
of a 162-game baseball season, the starting pitcher differs from day to day; modern
professional baseball teams generally use a ﬁve-man rotation, so a starting pitcher
typically plays in every ﬁfth game. Teams often play each other on consecutive days
over the course of a three-game or four-game series. Although the same two teams may
play each other several days in a row, the betting odds on these games vary considerably
due to the starting pitcher matchups. Excellent starting pitchers playing against weaker
opponents often command betting odds of -250, -300, or greater, implying that favorite
bettors must lay out $250 or $300 to win $100. The favored team often differs over the
course of a three- or four- game series between the same two teams due to the relative
abilities of the starting pitchers in each game.
Starting pitchers receive their due respect on the betting boards in Las Vegas and
on online betting outlets around the world. Unlike for other sports, when a baseball

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the lure of the pitcher
195
game is listed at a sportsbook, the starting pitcher for each team is identiﬁed along
with the betting odds on the game’s outcome, called sides in the Las Vegas sports
betting jargon, and the over/under, a bet on the number of runs scored by both teams
for the given game, called totals betting in Las Vegas. Even in other sports, such as
hockey, where a key defensive player, the goalie, can have an important impact on game
outcomes, the starting goalie in each game is not identiﬁed on the betting board. In
baseball, the names of the starting pitchers appear clearly for all bettors to see. Typically,
sports bookmakers allow bettors to place a bet on “listed pitchers” (or just “pitchers”)
compared to the“action”option on games. If a bettor chooses to place a wager on“listed
pitchers”and either or both of the starting pitchers changes, the full bet is returned and
there is no betting action on the game. In the “action” option, the bettor places a wager
on the team no matter which starting pitchers appear in the game. Starting pitchers in
baseball games occupy a unique position in betting markets.
Evidence shows that sports betting markets are weak-form efﬁcient in that betting
odds reﬂect all public information about game outcomes (Sauer 1998). In baseball
betting markets, the posted odds should reﬂect the expected effect of the starting
pitchers on game outcomes. However, recent research on the economics of betting
markets has moved beyond the analysis of prices and game outcomes to examine
variation in the volume of bets placed on games and betting on the total number of
points scored in games, called over/under betting. The goals of this new line of research
are to determine the extent to which gambling has both ﬁnancial and consumption
motives, as in the model developed by John Conlisk (1993), and to look for evidence
of behavioral biases in the decisions of bettors and bookmakers. In this chapter we
develop evidence that starting pitchers affect the volume of bets placed on games, the
amount of money bet on favored teams, and the amount of money bet on the under,
the proposition that a game will be relatively low-scoring. We ﬁnd that the volume of
bets placed on games, the fraction of bets placed on the favored team, and the fraction
of bets placed on the under proposition can all be explained by the presence of high-
proﬁle starting pitchers in a game, other things being equal. These results indicate that
betting on baseball games can be motivated by both ﬁnancial and consumption beneﬁts
and that behavioral biases exist in this market.
2 Previous Research on Baseball
Betting Markets
.............................................................................................................................................................................
The focus of previous research on baseball betting markets has been the favorite-
longshot bias or the reverse favorite-longshot bias. Evidence of a favorite-longshot
bias, where favorites are underbet and longshots overbet by gamblers, has been found
in some research on horse race betting. Linda Woodland and Bill Woodland (1994)
showed that a reverse of this bias exists in baseball, where favorite odds are too high,
resulting in underdogs winning more than implied by market efﬁciency. J. M. Gandar

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sports betting
et al. (2002) showed that the original analysis by Woodland and Woodland (1994) did
not properly account for a unit bet on favorites and underdogs and illustrated that
the reverse favorite-longshot bias was not statistically signiﬁcant for all underdogs in
baseball, only for slight underdogs and home underdogs.
The contribution of this chapter is the inclusion of starting pitchers in econometric
estimation of a bet volume equation in baseball, which allows for the analysis of bettor
behavior in a more detailed way than simply observing the betting market odds on
games. Our approach is important because of recent ﬁndings rejecting the long-held
belief in the balanced book hypothesis. The balanced book hypothesis assumes that
sportsbooks set point spreads to balance the betting action evenly on each side of a
proposition, favorites and underdogs in sides betting, over and under in totals betting.
With respect to ﬁxed-odd betting, used in baseball, hockey, soccer, and other sports,
the balanced book hypothesis predicts that odds will be set to proportionally balance
the betting dollars across outcomes.
The balanced book hypothesis has recently been challenged by Steven Levitt (2004)
in a study of the NFL betting market through a limited betting market tournament. He
concludedthatsportsbooksdonotbalancethe bettingaction,butsetpricestomaximize
proﬁts by exploiting known bettor biases. The result concerning the rejection of the
balanced book hypothesis was conﬁrmed in the study of actual online sportsbooks
in the NFL (Paul and Weinbach 2007), the NBA (Paul and Weinbach 2008), college
football (Paul and Weinbach 2009), the NHL (Paul and Weinbach 2012b), and Major
League Baseball (Paul and Weinbach 2012a). Although the balanced book hypothesis
could clearly be rejected, with bettors consistently favoring favorites (road favorites
in particular) in sides betting and overs in totals betting, the alternative hypothesis
of Levitt (2004) was only supported in the NFL. In other words, only in the NFL
did the sportsbook appear to price to exploit known bettor biases (which are clear
across the sample of all sports) by setting prices where underdogs won more often
than favorites. In all of the other sports studied, despite the consistent imbalance
of bets, win percentages on favorites in sides betting were found to be statistically
indistinguishablefrom50percent. Thisresultimpliesthatsportsbookspriceasaforecast
of game outcomes despite consistent and clearly predictable bettor biases. This behavior
by the sports bookmaker likely prevents informed bettors from entering the market (as
they cannot exploit simple proﬁtable betting strategies) and still earns the sportsbook
a proﬁt from the commission collected on losing bets in the long run.
3 Data Description
.............................................................................................................................................................................
This chapter uses detailed data on betting percentages and volume to examine the
impact of elite starting pitchers on the baseball betting market in the 2009 MLB season.
The data were purchased from Sports Insights, a company that collects detailed betting
market data from four online bookmakers located in the Caribbean. These online

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the lure of the pitcher
197
bookmakers have been in operation for a number of years and are well established
in the online betting industry. They take bets from a large number of customers and
can be considered representative of the online betting market. Sports Insights collects
a large amount of game-speciﬁc data on the baseball betting market, including odds,
game outcomes, and bet volume, on both sides and totals betting
Sports Insights collects betting market data from four online sports bookmakers:
5Dimes.com, a licensed, bonded online sports bookmaker based in Costa Rica in
operation since 1998; BetUS.com, a licensed and bonded sports bookmaker recognized
in both Costa Rica and Canada in operation since 1994; CaribSports.com, a licensed
online sports bookmaker based in Belize in operation since 1997; and Sportsbook.com,
a licensed online sports bookmaker and casino based in Costa Rica since 1996. These
four sports bookmakers handle a large number of bets on a variety of professional and
amateur sports worldwide.
Table 11.1 contains summary statistics for the three dependent variables, the volume
of bets, the percentage bet on the favored team in the sides market, and the percentage
bet on the under in the totals market, as well as the explanatory variable of interest,
games in which one or both of the starting pitchers was one of the ﬁve top vote-getters
in the 2008 and 2009 CyYoung Award voting. We have data on betting market outcomes
for 2,372 MLB games played in the 2009 regular season. This does not include every
game, since volume data are not available for every regular season game. The average
number of bets on baseball games in the sample was almost 11,700. On average, more
bets were placed on the favored team in these games, and more bets were placed on the
over in the total market.
High-quality starting pitchers can be identiﬁed in many ways. The primary methods
include performance-based identiﬁcation methods based on common statistics, such
as earned run average (ERA) and wins, among others, and on voting outcomes, such
as the number of All Star votes players receive from fans. The simplest and most
straightforward method to identify an elite pitcher, in our opinion, is to use pitchers
who received votes for the Cy Young Award,1 the annual award for the best pitcher
in each league in MLB. Each year, the top ﬁve pitchers receiving votes for the Cy
Young Award in each league are identiﬁed at the end of the season. Baseball writers, a
group widely viewed as experts on baseball, vote for the Cy Young Award. The top ﬁve
Table 11.1 Summary Statistics
Variable
Mean
Std. Dev.
Min.
Max.
Number of bets placed on game
11692
5630
826
115409
Percentage bet on favorite
64
16
16
94
Percentage bet on under
43
13
7
87
Games started by Cy Young candidates
0.14
0.34
0
1

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sports betting
vote-getters can be objectively viewed as high-quality pitchers. Therefore, to keep the
identiﬁcation of elite pitchers as simple and objective as possible, we created a dummy
variable identifying games started by these pitchers in the 2009 season; 14 percent of
the games in our sample involved one or more of these starting pitchers. Note that
rotations tend not to change once set, so there is little possibility that these starting
pitchers would be assigned in a way to make them correlated with the equation error
term. Once a starting rotation is set, the starting pitchers generally pitch every fourth
or ﬁfth game throughout the season.
We examine three key elements of the betting market for Major League Baseball.
First, we investigate the role of the elite pitcher in the determination of betting volume.
If many bettors enjoy wagering on the best pitchers, betting volume may reﬂect these
preferences. If baseball betting has a major consumption element and fans follow the
best pitchers, the games involving the elite pitchers may also be the games that attract
the most interest from bettors.
Second, we examine the role of the elite pitchers in relation to the percentage bet on
favorites and underdogs. Given that the baseball betting market has been shown to be
imbalanced (not proportional to sportsbook set odds), there is the distinct possibility
that elite starting pitchers play a key role in betting percentages. The best pitchers may
attract the most betting action, which will be reﬂected in both betting volume and in
the percentage bet on the team with the elite pitcher.
Third, we examine the role of the elite pitcher in the totals market. Typically, in totals
betting, the over has been shown to be a much more popular proposition than the
under, perhaps because fans ﬁnd high-scoring games more entertaining. Across many
different sports, bettors, like fans, prefer more scoring to less. This is reﬂected by a large
percentage of the bets accumulating on the over in totals betting. Given that the starting
pitcher plays a pivotal role in baseball and in the wagering market, the baseball betting
market may provide an instance where the under is preferred to the over. If baseball
bettors like to wager on the best pitchers, they may also wish to wager on the under,
because when the best pitchers perform well they prevent their opponent from scoring
runs, reducing the total number of runs scored in the game. If found, this result would
not necessarily imply that baseball bettors have different utility functions and prefer
less scoring, but it does show the role of consumption in betting markets, as marquee
pitchers lead bettors to hope that their teams will win and that the pitchers will shut
down their opponents, which (in the minds of bettors) will lead to more unders in
these games.
All three of these empirical issues extend the existing research on gambling markets.
The efﬁcient markets hypothesis, the balanced book hypothesis, and the existence
of behavioral biases in betting markets are all addressed in this study. In short, we
further explore how popular baseball players, in this case elite starting pitchers, affect
sports betting markets. We hope to further illustrate the role that consumption-based
gambling motives play in this market.

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## Page 220

the lure of the pitcher
199
4 Empirical Analysis
.............................................................................................................................................................................
We examine the relationship between variation in three betting market outcomes, bet
volume, the fraction of bets placed on the favored team, and the fraction of bets placed
on the under, as well as variation in the quality of the starting pitchers in the game,
controlling for other factors that affect betting market outcomes. We estimate regression
models of the form
OUTCOMEijt = b1GAMEijt + b2TEAMijt + b3PITCHERijt + eijt,
(11.1)
where OUTCOMEij is one of three betting market outcomes for a game involving
home team i and visiting team j on date t; GAMEijt is a vector of game characteristics,
is a vector of team characteristics, is a vector of variables that capture the quality of
starting pitchers in the game between home team i and visiting team j on date t; and eijt
is an unobservable random variable capturing all other factors that affect the betting
market outcomes. We assume that eijt is an independent and identically distributed
random variable with zero mean and potentially nonconstant variance. Because eijt
may be heteroskedastic, we use the White-Huber “sandwich” correction to adjust the
standard errors for potential heteroskedasticity. b1, b2, and b3 are vectors of unknown
parameters to be estimated. We estimated these parameters using the Ordinary Least
Squares estimator.
The Impact of Starting Pitchers on Betting Volume
The ﬁrst set of regression results uses the number of bets placed on each game as the
dependent variable in the regression model described by equation (11.1). Again, this
variable is the total number of bets placed at the four online sports bookmakers tracked
by Sports Insights. Independent variables include an intercept, the months of the year,
the days of the week, dummy variables for elite pitchers (both visitor and home), the
absolute value of the odds on the game, a dummy for road favorites, and the win
percentages of both the home and road teams going into the game.
The months of the baseball season are included to control for any seasonality in
betting volume. This seasonality could manifest itself as bettor excitement early in the
year, effects of the start of football betting on baseball betting volume at the end of
the season, or other reasons. The omitted monthly category is the ﬁrst month of the
season, April.
Weekdaysarealsoincludedasdummyvariablestoaccountforpossibledailyvariation
in betting volume. The dependent variable is betting volume per game, so there could
be impact where bettors may place more wagers on days when there are fewer games
(especially when we consider baseball gambling as purely an activity of consumption).
Mondays and Thursdays typically have fewer baseball games, as these serve as travel days

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200
sports betting
for teams. If bettors choose to wager on baseball as a form of consumption, due to fewer
games on these days, individual game betting volume may increase on Mondays and
Thursdays. Weekend effects also are possible, as more bettors may engage in gambling
on the weekend as compared to weekdays. Tuesday is the omitted category of the days
of the week.
The“CyYoungVoted Pitcher”variable (both home and road) is the proxy for the elite
pitchers as mentioned in the introduction. The top ﬁve starting pitchers who received
votes for the Cy Young Award in each league (NL and AL) are given a value of one,
while all other pitchers are given a value of zero. The ﬁrst regression speciﬁcation uses
pitchers from the previous season (2008) who met this criterion, while the second uses
the current year to create the dummy variable, and the last speciﬁcation combines the
two years (if a pitcher appeared once or twice on the list he is given a value of one). We
will use the previous season dummy as the main point of discussion of the results, but
if one believes that elite pitchers can easily be identiﬁed during the season, new elite
pitchers are likely to receive attention as the season progresses. Although this is a simple
version of identifying an elite pitcher, we believe it will give a good representation of
the importance of the pitcher in the minds of bettors of Major League Baseball.
The absolute value of the odds on the game is also included as an explanatory
variable. This variable has been shown to affect the percentage bet on the favorite in
Major League Baseball (Paul and Weinbach 2012a) in a positive and signiﬁcant manner
and is likely to affect betting volume as well. We use the absolute value of the betting
odds due to the presence of home favorites and road favorites, which additionally is
addressed by the inclusion of a road favorite dummy variable. Road favorites have been
shown to be very popular bets across virtually all sports (due to a likely underestimation
of the home ﬁeld advantage—it appears that bettors are getting a “value” by betting on
the good road team at a lower point spread or odds). With respect to betting volume,
it is likely that road favorites attract a greater number of bets. The absolute value
of the odds has a positive expected sign (bigger favorites are more popular betting
propositions, as they likely are the best teams) and the road favorite also has a positive
expected sign.
The winning percentages of both the home team and the road team also are included
as independent variables in the regression model on betting volume. Assuming con-
sumption plays a pivotal role in sports betting, good teams are likely to attract more
bets, thereby increasing betting volume when they play. This may partially be captured
by the absolute value of the point spread, but it is important to remember that low
betting odds on the favorite could be a function of two similar teams of any quality
playing in a game. We expect games between two good teams to attract more betting
attention than games between two bad teams; therefore we expect the sign on both of
the win percentage variables to be positive.
Table 11.2 presents the regression results for the betting volume model. T-statistics
are shown in parentheses below the parameter estimates. The month of the year dummy
variables are relative to the omitted month, April. The month of May saw a positive
and signiﬁcant jump in volume, while the later months of the year saw a signiﬁcant

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the lure of the pitcher
201
Table 11.2 Baseball Bet Volume Regression Results, 2009 Season Dependent
Variable: Betting Volume per Game
Variable
Pitching
Dummies—Previous
Season (2008)
Pitching
Dummies—within
Season (2009)
Pitching
Dummies—Both
Seasons (2008–2009)
Intercept
−1744∗
(−1.74)
−1782∗
(−1.77)
−1694∗
(−1.69)
May
1847∗∗∗
(4.74)
1839∗∗∗
(4.71)
1827∗∗∗
(4.70)
June
230
(0.669)
209
(0.60)
196
(0.57)
July
−693∗∗
(−2.07)
−690∗∗
(−2.05)
−693∗∗
(−2.07)
August
−1728∗∗∗
(−4.00)
−1746∗∗∗
(−4.03)
−1741∗∗∗
(−4.03)
September
−4358∗∗∗
(−10.53)
−4387∗∗∗
(−10.56)
−4390∗∗∗
(−10.63)
October
−7971∗∗∗
(−15.59)
−8006∗∗∗
(−15.74)
−8000∗∗∗
(−15.68)
Sunday
293
(0.664)
288
(0.65)
298
(0.67)
Monday
863∗
(1.86)
860∗
(1.86)
871∗
(1.88)
Wednesday
−20.74
(−0.04)
−55.46
(−0.10)
−29.12
(−0.05)
Thursday
923∗∗
(2.05)
937∗∗
(2.09)
917∗∗
(2.05)
Friday
419
(0.98)
403
(0.94)
416
(0.97)
Saturday
796∗
(1.75)
792∗
(1.74)
793∗
(1.75)
Cy Young voted
pitcher—Visitor
1275∗∗∗
(2.77)
1327∗∗∗
(3.60)
1342∗∗∗
(3.99)
Cy Young voted
pitcher—Home
1172.8∗∗
(2.55)
770∗∗
(2.04)
900∗∗∗
(2.67)
Absolute value—Betting
odds
41.38∗∗∗
(12.14)
41.57∗∗∗
(11.98)
41.21∗∗∗
(11.91)
Road favorite dummy
variable
1198∗∗∗
(4.98)
1129∗∗∗
(4.64)
1116∗∗∗
(4.60)
Home win percentage
going into game
7832∗∗∗
(7.08)
7804∗∗∗
(7.01)
7742∗∗∗
(6.98)
Road win percentage
going into game
7636∗∗∗
(7.12)
7723∗∗∗
(7.18)
7576∗∗∗
(7.07)
R2
0.222
0.222
0.225

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## Page 223

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sports betting
decrease in the volume of bets on baseball. Through August, September, and October
baseball betting volume dropped considerably as the regular season came to a close.
Likely reasons for this are the start of football season and some teams being eliminated
from playoff contention, which could lessen interest in those games (assuming betting
as a consumption activity).
In terms of daily betting patterns, Monday, Thursday, and Saturday all saw signiﬁcant
increases in betting volume per game compared to the omitted day, Tuesday. Monday
and Thursday likely saw signiﬁcant increases due to there being fewer games per day,
as these days often serve as travel days for teams going from one city to another. The
increase on Saturday is likely due to the opportunity cost of time on the weekend
with more people being willing to place wagers (and likely watch) baseball games on
Saturday afternoons and evenings.
The elite pitchers in the league had a positive and signiﬁcant effect on betting volume.
Both the home and road pitcher were shown to positively affect volume. Elite pitchers
at home increased betting volume by over 1,100 bets per game, while elite pitchers on
the road increased betting volume by over 1,200 bets per game. Both results were found
to be signiﬁcant at the 1 percent level. This implies that many bettors are wagering on
the best pitchers, leading to considerable increases in volume when these athletes take
the mound.
Similar to what was shown previously for baseball in Paul and Weinbach (2012a),
the absolute value of the odds on the game was shown to have a positive and signiﬁcant
effect on betting volume. Bigger favorites were shown to generate more bettor interest in
the game. In addition, road favorites were shown to be more popular with bettors across
the board, as games involving a road favorite led to well over a thousand additional
bets on the game. Records of the teams also played a signiﬁcant role, as bettors placed
more wagers on games between better quality opponents. Both the home and road win
percentages of the teams (heading into that day’s game) were shown to have a positive
and signiﬁcant effect on betting volume.
Overall, these results underscore the major role that consumption plays when betting
on baseball. Quality of the teams, days of the week, months of the year, and elite pitchers
all attract more bettors to wager on baseball games.
The Impact of Starting Pitchers on Percentage Bet
on the Favorite
To illustrate the effect of elite pitchers on the sides (betting on a particular team)
market, we use the percentage bet on the favorite as the dependent variable in this
regression model. To distinguish between home and road favorites, we run two separate
regressions,one consisting entirely of home favorites,the other of road favorites. Results
appear on table 11.3.
The independent variables are closely related to those included in the regression
model on betting volume, with month of the year dummies, day of the week dummies,

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the lure of the pitcher
203
Table 11.3 Sides Regressions—Home Favorites and Road Favorites—2009 Season
Dependent Variable: Percentage Bet on the Favorite
Variable
Home Favorites
Road Favorites
Intercept
−4.045
(−0.92)
14.60∗
(1.79)
May
0.565
(0.49)
−0.201
(−0.10)
June
0.477
(0.365)
−1.225
(−0.64)
July
2.947
(2.43)
1.835
(0.94)
August
1.384
(1.16)
−1.772
(−0.99)
September
1.507
(1.30)
0.616
(0.35)
October
−0.559
(−0.32)
−10.19∗∗∗
(−3.37)
Sunday
−0.036
(−0.03)
1.623
(1.10)
Monday
0.835
(0.669)
−0.298
(−0.171)
Wednesday
−1.142
(−0.95)
1.616
(1.055)
Thursday
−1.058
(−0.85)
1.817
(1.18)
Friday
1.348
(1.21)
0.813
(0.53)
Saturday
0.168
(0.15)
1.433
(0.82)
Cy Young voted
pitcher—Visitor
−6.537∗∗∗
(−2.96)
1.975
(1.42)
Cy Young voted
pitcher—Home
0.214
(0.18)
−11.55∗∗∗
(−2.68)
Percentage bet on
favorite implied by
closing odds
1.250∗∗∗
(20.71)
1.091∗∗∗
(8.29)
Home record
17.88∗∗∗
(3.65)
−26.47∗∗∗
(−4.97)
Road record
−35.17∗∗∗
(−8.81)
12.34∗∗
(1.99)
R2
0.402
0.285
Note: Pitcher dummy variables are based on Cy Young voting from previous season (2008) only. Other
results are available upon request from the authors.

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## Page 225

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sports betting
Cy Young vote-getting pitcher dummies, and team win percentage variables included
for most of the same reasons as described above. We include the days and months to
account for ﬂuctuations that occur over time during the week and the season; team
win percentage variables are likely to inﬂuence which teams are the most popular in the
betting market, as good teams are more likely than poor teams to attract betting action
(based on consumption value and purpose in the minds of bettors), and we expect the
elite pitcher dummy variables to illustrate their impact on the percentage bet on the
favored team.
The main difference between this regression model and the one in the previous
section is that an independent variable is constructed to represent the percentage bet
on the favorite that is implied by the closing betting market odds. Since the baseball
market operates in an odds-based format, rather than through a point spread, we expect
the favorite (and underdog) to attract betting percentages reﬂective of the odds on the
game rather than assume a 50/50 split under the balanced book hypothesis in point
spread–based markets. Therefore, based on the midpoint of favorite and underdog
odds, we can determine the percentage that would be expected to be bet on the favorite
(and underdog) if the sportsbook was behaving in a way to avoid being an active
participant in the wager. This variable, constructed from the closing game odds, is then
included as an independent variable in the regression. A value of one would indicate
that the sportsbook is pricing to clear the market, while a value greater than one would
suggest that the sportsbook is willing to accept a higher percentage of bets on the more
popular side of the betting proposition, the favorite.
In relation to the sides regressions for home favorites and road favorites, the months
of the year and the days of the week had little to do with the percentage bet on favorites
(except for the few games in October with respect to road favorites). Not surprisingly,
winning percentages of the teams played a statistically signiﬁcant role in the percentage
bet on favorites, with the signs on the variable being as expected (positive for the
favored team and negative for the underdog). The percentage that should have been
bet on the favorite, derived from the closing odds on the game, was found to have a
positive and signiﬁcant effect on the percentage bet on the favorite, as expected. The
actual percentage bet, however, was found to be greater than the expected percentage
bet (based on the odds), as the coefﬁcient on these variables was found to be greater
than one in both regressions.
Elite starting pitchers also played an important role in the percentage bet on the
favorite. The signiﬁcant results, however, were found with respect to the underdog
pitcher. If an elite pitcher was an underdog in the game, bettors wagered a considerably
greater amount in these contests. The percentage bet on home favorites dropped by
6.5 percent when an elite visiting pitcher was on the mound. In the rarer case where
the elite home pitcher was the underdog, the percentage bet on the favorite fell by more
than 11 percent. Bettors appear to be quite sensitive to situations where elite pitchers
are underdogs. These situations appear to entice bettors, who are given the opportunity
to wager on an excellent pitcher with the added bonus of receiving odds back in their
favor if the underdog team wins the game.

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the lure of the pitcher
205
The Role of the Pitcher in the Totals
(Over/Under) Market
As mentioned above, the presence of an elite starting pitcher in a game likely affects the
totals betting market. In the totals market, commonly referred to as over/under betting,
bettors wager on the total number of runs that will be scored in a game. Bettors can
place a wager of either over (more runs scored by both teams) or under (fewer runs
scored by both teams) relative to the posted total.
To investigate this, we used the percentage wagered on the under as the dependent
variable in the regression model deﬁned by equation (11.1). The results are shown in
table 11.4. Again, we used monthly dummies, weekday dummies, win percentages of
both teams, and the elite pitchers dummy variables in the regression. The independent
variable that differs in this regression model is the inclusion of the total (as opposed to
the odds on the game). We used only the total itself (not the odds adjustment—which
at most is -130 in either direction) in the regression to attempt to determine whether
bettors are more willing to wager on the over in expected higher-scoring games (higher
totals). This tendency has been shown to exist in the NFL, college football, and the NBA
in point spread markets as well as in the NHL and previous studies of Major League
Baseball.
The dummies to account for the pitchers who received Cy Young votes are expected
to have a positive and signiﬁcant effect on the percentage wagered on the under if fans
like to bet on the best pitchers to prevent the other team from scoring runs. The pitcher
is one of the few cases in North American sports where a notable player’s key role is
defensive (in the case of pitchers—to prevent runs scored). Therefore, we believe that
many bettors who wager on speciﬁc good pitchers are also likely to wager on the under
in these games, as they are cheering for the pitcher to win the game and keep the other
team from scoring. If this premise is true, the elite pitchers will have a positive and
signiﬁcant effect on the percentage bet on the under.
From table 11.4, the percentage wagered on the under was shown to respond to the
months of the season, with fewer bets placed at the beginning of the season (the omitted
month of April). Days of the week did not see much of an effect, except for a statistically
signiﬁcant result on Sunday, where more wagers were placed on unders. Team records
were shown to not have a signiﬁcant effect on the percentage bet on the under.
The total itself and the presence of an elite pitcher signiﬁcantly affect the percentage
of bets placed on the under. Higher totals attract fewer wagers on the under, as bettors
appear more willing to bet the over when the total is high (when the expected amount
of scoring is already high). For each additional point of the total, the percentage bet
on the under dropped by around 4 percent. Elite pitchers also played an important
role in the totals market, as the best pitchers were shown to increase the percentage
bet on the under. Whether on the road or at home, an elite starting pitcher led to a
4 percent increase in the percentage bet on the under (8 percent if two elite pitchers
were starting).

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sports betting
Table 11.4 Percentage Bet on the Under Regression—2009 Season Dependent
Variable: Percentage Bet on the Under
Variable
Pitching
Dummies—Previous
Season (2008)
Pitching
Dummies—within
Season (2009)
Pitching
Dummies—Both
Seasons (2008–2009)
Intercept
73.44∗∗∗
(21.19)
69.49∗∗∗
(19.18)
68.65∗∗∗
(19.36)
May
3.792∗∗∗
(4.08)
3.780∗∗∗
(4.08)
3.702∗∗∗
(4.019)
June
10.82∗∗∗
(11.31)
10.88∗∗∗
(11.39)
10.84∗∗∗
(11.39)
July
13.39∗∗∗
(13.39)
13.49∗∗∗
(14.79)
13.48∗∗∗
(14.86)
August
4.771∗∗∗
(5.49)
4.831∗∗∗
(5.59)
4.838∗∗∗
(5.63)
September
10.81∗∗∗
(11.77)
10.86∗∗∗
(11.91)
10.84∗∗∗
(11.92)
October
7.589∗∗∗
(3.77)
7.699∗∗∗
(3.85)
7.668∗∗∗
(3.91)
Sunday
2.653∗∗
(2.41)
2.045∗∗
(2.39)
2.098∗∗
(2.46)
Monday
1.155
(1.21)
1.143
(1.20)
1.175
(1.23)
Wednesday
1.251
(1.40)
1.118
(1.26)
1.217
(1.37)
Thursday
−0.361
(−0.38)
−0.317
(−0.34)
−0.416
(−0.44)
Friday
0.621
(0.72)
0.480
(0.55)
0.554
(0.646)
Saturday
0.054
(0.06)
0.018
(0.02)
−0.003
(−0.01)
Cy Young voted
pitcher—Visitor
4.28∗∗∗
(3.42)
4.430∗∗∗
(4.12)
4.678∗∗∗
(5.09)
Cy Young voted
pitcher—Home
3.699∗∗∗
(3.17)
4.246∗∗∗
(4.14)
4.359∗∗∗
(4.99)
Total
−4.589∗∗∗
(−15.23)
−4.158∗∗∗
(−12.78)
−4.050∗∗∗
(−12.80)
Home record going into
game
1.608
(0.66)
1.343
(0.55)
1.068
(0.44)
Road record going into
game
2.234
(0.93)
2.279
(2.35)
1.782
(0.75)
R2
0.252
0.256
0.262

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the lure of the pitcher
207
The result of bettors favoring the under appears to be solely a function of the elite
pitchers. Although the percentage bet on the over usually exceeds 50 percent by a
considerable margin in this sample, the best pitchers attract a higher percentage of bets
on the under when they are starting. This likely again reﬂects consumption value to
bettors, as many fans of baseball tend to follow the best pitchers. Bettors may not only
wager on these best pitchers when they pitch, but they also appear to have the tendency
to wager on the under.
This result appears to contradict ﬁndings observed in other sports betting markets,
where bettors appear to clearly favor the over to the under. This likely stems from bettor
preferences for more points scored compared to fewer points scored. That factor is still
present in the baseball totals market (as evidenced by the negative and signiﬁcant effect
of the total on the percentage bet on the under), but the pitchers offer an interesting
exception to this rule. When fans/bettors are given an opportunity to watch or follow
a great pitcher, they likely hope this pitcher performs well. When he does, this leads to
very few runs for the opposing team. Bettors express their desire to see this by placing
wagers on the under in hopes of seeing excellent pitching from these stars. When
pitching stars are not present, however, baseball bettors simply revert back to hoping to
see more scoring, as evidenced by the percentage bet on the over rising with each point
of the posted total.
5 Conclusions
.............................................................................................................................................................................
We investigated the role of elite starting pitchers in the Major League Baseball betting
market. Although there are numerous ways to identify an elite starting pitcher we used
a simple explanatory variable to analyze the effect of elite starting pitchers on betting
market outcome: pitchers who received votes for the Cy Young Award, given to the best
pitcher in each league in MLB, were deﬁned as elite pitchers.
Detailed data on outcomes in the baseball betting market, including data on the
volume of bets placed on games, the percentage of bets wagered on favorites, and
the percentage of bets wagered on the under (in the totals market) were analyzed
using regression models. In terms of bet volume, elite pitchers generate a signiﬁcant
increase in the number of bets on a baseball game. Games involving elite pitchers led
to an increase of around one thousand bets, on average, on a game. In addition to
the elite pitchers, favorites (in particular road favorites) and the win percentages of
the teams attract a statistically signiﬁcant increase in bets. Overall, baseball bettors
appear to bet heavily on games involving the best teams and the best pitchers. Proﬁt-
maximizing bettors would wager on games with the highest expected return; utility-
maximizing bettors would bet on the games with the highest consumption value. Unless
the betting odds offered by sportsbooks on games involving the best teams, and the best
pitchers, systematically have a higher expected return to bettors, this pattern suggests
that consumption-based gambling is a major factor in sports wagering markets.

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## Page 229

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Appendix Cy Young Award Voting—AL and NL—2008 and 2009
2008 AL Cy Young
2008 NL Cy Young
2009 AL Cy Young
2009 NL Cy Young
Cliff Lee (Cleveland)
Tim Lincecum
(San Francisco)
Zack Greinke
(Kansas City)
Tim Lincecum
(San Francisco)
Roy Halladay
(Toronto)
Brandon Webb
(Arizona)
Felix Hernandez
(Seattle)
Chris Carpenter
(St. Louis)
Francisco Rodriguez
(LA Angels)
Johan Santana
(Mets)
Justin Verlander
(Detroit)
Adam Wainwright
(St. Louis)
Daisuke Matsuzaka
(Boston)
Brad Lidge
(Philadelphia)
CC Sabathia (Yankees)
Javier Vasquez
(Atlanta)
Mariano Rivera
(Yankees)
CC Sabathia
(Milwaukee)
Roy Halladay
(Toronto)
Dan Haren (Arizona)
Based on our analysis of variation in the percentage bet on the favorite in baseball
games, elite pitchers were also shown to have a signiﬁcant effect on this wagering.
Although bettors prefer the best teams, elite pitchers on the underdog team attracted a
signiﬁcant number of bets. When an elite pitcher appears as an underdog, many bettors
jump at the opportunity to wager on the best pitchers with the possibility of earning
odds back in their favor if their wager is successful. The balanced book model suggests
that sports bookmakers set odds to equalize the faction of bets on either side of a game,
given all information about that game. Since bettors prefer to bet on elite pitchers, even
if they pitch for an underdog team, this unbalanced betting could indicate the presence
of bettors who want to bet on speciﬁc pitchers no matter what odds are set on the game.
This would represent a type of behavioral bias in this market.
Elite pitchers also played a key role in the totals market in baseball. Although Major
League Baseball bettors enjoy betting the over in far greater numbers than the under,
likely due to a preference for scoring compared to a lack of scoring, the elite pitchers
serve as a key exception. In games involving elite pitchers, a statistically signiﬁcant
increase in bets on the under was observed. The efﬁcient market hypothesis suggests
that the total set by sportsbooks should reﬂect all available information about the game,
includingthequalityof thestartingpitchers. Whenthebestpitchersarepitching,bettors
appear to want to see these pitchers perform well. If these pitchers are successful, few
runs are scored for the opposing team. This leads them to wager on the under, revealing
a preference for the lack of scoring compared to the normal preference for scoring.
This result is likely not due to a desire to see defensive ability to the star power of the
elite pitchers and the under being associated with a winning outcome on the part of
their performance. Again, this could indicate the presence of bettors who would bet the
under when elite starting pitchers appear in a game, no matter what total is set by the
sportsbook. This could also be explained by behavioral biases in this market. It would
be useful to explore these possible explanations.

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## Page 230

the lure of the pitcher
209
Notes
1. The pitchers in the top ﬁve in votes for the Cy Young Award are listed in the appendix.
References
Conlisk, John. 1993. The utility of gambling. Journal of Risk and Uncertainty 6:255–275.
Gandar, J. M., Richard A. Zuber, R. S. Johnson, and W. Dare. 2002. Re-examining the betting
market on Major League Baseball Games: Is there a reverse favorite-longshot bias? Applied
Economics 34(10):1309–1317.
Levitt, Steven D. 2004. Why are gambling markets organised so differently from ﬁnancial
markets? The Economic Journal 114:223–246.
Paul, Rodney J., and Andrew P. Weinbach. 2007. Does Sportsbook.com set pointspreads to
maximize proﬁts? Tests of the Levitt Model of sportsbook behavior. Journal of Prediction
Markets 1(3):209–218.
——. 2008. Price setting in the NBA gambling market: Tests of the Levitt Model of sportsbook
behavior. International Journal of Sport Finance 3(3):137–145.
——. 2009. Sportsbook behavior in the NCAA football betting market: Tests of the traditional
and Levitt models of sportsbook behavior. Journal of Prediction Markets 3(2):21–37.
——. 2012a. Behavioral biases and sportsbook pricing in Major League Baseball. In The
Oxford handbook of sports economics: Volume 2, Economics through sports, edited by Stephen
Shmanske and Leo H. Kahane. New York: Oxford University Press, 302–320.
——. 2012b. Sportsbook pricing and the behavioral biases of bettors in the NHL. Journal of
Economics and Finance 36(1):123–135.
Sauer, Raymond D. 1998. The economics of wagering markets. Journal of Economic Literature
36:2021–2064.
Woodland, Linda M., and Bill M.Woodland. 1994. Market efﬁciency and the favorite-longshot
bias: The baseball betting market. Journal of Finance 49(1):269–279.

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## Page 231

chapter 12
........................................................................................................
INFORMATION EFFICIENCY IN
HIGH-FREQUENCY BETTING
MARKETS
........................................................................................................
j. james reade and john goddard
1 Introduction
.............................................................................................................................................................................
The betting industry has been transformed by the Internet. Growth of person-to-
person betting, mediated through online betting exchanges, has been a key element
of this transformation (for a review see Smith and Vaughan Williams 2008). Betting
exchanges enable traders to either back (buy) or lay (sell) bets on a wide range of sport-
ing events. Betfair, launched in June 2000 and ﬂoated on the London Stock Exchange
in October 2010 with a market valuation of £1.4 billion, has established its position
as the dominant online betting exchange.1 Customers deposit funds with Betfair via
bank transfer or credit card, and Betfair adjusts the customer’s account each time a
transaction is initiated or completed. Betfair generates revenue by charging a commis-
sion of between 2 and 5 percent on its customers’ net winnings. Customers with a
positive balance can withdraw funds at any time. Betfair publishes the three best prices
currently being offered by customers wishing to back any particular bet, the three best
prices offered by customers wishing to lay that bet, and the total stakes available at those
prices.2
Given its capability to update instantaneously as individual customers enter and leave
the market, it is natural that Betfair has been at the forefront of the development of
in-play betting markets, in which bets can be backed or laid continuously while the
sporting event in question is under way. Traditionally bookmakers offered bets only
until an event began but more recently have adapted to provide in-play betting.3 As
such, these continuously operating online betting markets have ensured the transition
of the use of high-frequency data from the ﬁnancial setting into the betting market

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information efficiency in high-frequency betting markets
211
context. A high-frequency dataset records prices that are traded continuously at as
high a frequency as possible, usually at the minute-by-minute level and often even
second-by-second.
Betting markets have traditionally attracted academic interest, particularly from
economists interested in the efﬁciency of markets: Leighton Vaughan Williams (1999)
provided a survey of research on information efﬁciency in betting markets, mostly
before the growth in online betting and the exchange-led revolution. As opposed to
ﬁnancial markets, where insider information can make timing of information breakage
unclear and the true value of an asset is rarely ever revealed, sports betting markets
offer nonexperimental opportunities to observe cleanly breaking information on assets
whose value is revealed when the sporting event in question ﬁnishes, which can often
be just minutes or seconds away. It is to these studies using these kinds of datasets to
which we refer in this review of high-frequency investigations of information efﬁciency.
This chapter is organized as follows: section 2 provides an introduction to betting
exchanges such as Betfair and high frequency data on in-play betting markets, section 3
considers how the value of bets is determined in-play, and then the concept of infor-
mation efﬁciency is brieﬂy introduced in Section IV. We will then consider a number of
papers that have used high frequency data from betting markets to investigate informa-
tion efﬁciency in Section V, splitting our review into weak-form efﬁciency (Section V.1)
and semi-strong and strong form efﬁciency (SectionV.2). Finally, SectionVI concludes.
2 Betfair and In-Play Betting
.............................................................................................................................................................................
In the 2010–2011 ﬁnancial year revenue from football accounted for 42.3 percent of
Betfair’s sports gambling net revenues, narrowly overtaking for the ﬁrst time horse
racing, with its share of 42.1 percent. The United Kingdom accounted for 53 percent
of Betfair’s total “core” net revenue. The rest of Europe accounted for 42 percent of the
total, and the rest of the world accounted for 5 percent. Betfair’s ability to trade in any
country is heavily dependent on the regulatory and taxation system applicable to the
betting industry. The U.K. government adopted a relatively benign regulatory stance
at an early stage of Betfair’s historical development. Betting exchanges in the United
Kingdom are subject to the conditions of a regular betting license with several additional
restrictions imposed: for example, betting exchanges are not permitted to participate
in bets; monies belonging to customers must be ring-fenced from the exchange’s own
resources; and the parties to any bet must not be identiﬁed to one another. Importantly,
however, the licensing of individual customers is not a requirement. At the time of
this writing, a number of other European countries were still developing a regulatory
framework for online gambling. Regulatory and taxation arrangements, which can vary
markedly from country to country, will have a major bearing on Berfair’s prospects for
future growth outside the United Kingdom. During the 2010–2011 ﬁnancial year Betfair

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212
sports betting
encountered severe regulatory difﬁculties in France and Italy, and the company ceased
trading altogether in France in May 2010.
In addition to sports betting, Betfair offers a number of non–sports betting prod-
ucts, including poker, online casino games, and proprietary exchange games. Revenue
from these core Betfair products in the 2010–2011 ﬁnancial year was £330 million.
This revenue ﬁgure reﬂects growth of 36 percent on the corresponding 2007–2008
ﬁgure of £242.3 million. Betfair claims to have had 949,000 active customers in 2011
(increased from 522,000 in 2008), accounting for 7 million betting transactions per day
in 2011 (increased from 3.9 million in 2008). The Betfair Group’s total revenue for the
2010–2011 ﬁnancial year was £393 million. In addition to its core products, the group
generates revenues from its other investments. These are: TVG (Betfair US), an online
racetrack betting service that owns the TVH racing channel shown in 35 million U.S.
homes, acquired by Betfair in January 2009; and LMAX, a platform for online retail
ﬁnancial trading, launched by Betfair in October 2010.
Betfair’s growth in market share relative to the traditional High Street bookmakers
has been driven by effective competition on price, facilitated by the lower transac-
tion, information, and infrastructure costs associated with the online betting exchange
business model. By exerting downward pressure on the bookmaker’s overround, Bet-
fair claims to be able to offer its customers more competitive prices than traditional
bookmakers. In particular, the phenomenon of the favorite-longshot bias (with bets at
long odds offering a lower average return than bets at short odds) is less apparent in
Betfair prices than in those of the traditional bookmakers (Smith, Paton, and Vaughan
Williams 2006). Mark Davies et al. (2005) cited the growth of Betfair as a manifestation
of Moore’s Law, that is, that the number of transistors on a microchip doubles every
18–24 months, resulting in a doubling of the speed of microprocessors. Before the
2000s the computing power needed to process the millions of transactions handled by
Betfair daily would not have been available, and the company’s subsequent growth has
paralleled the growth in its technological capacity to process data.
Relative to its competitors, Betfair enjoys a positive network externality deriving, in
part, from its ﬁrst-mover advantage (Davies et al. 2005; Koning and van Velzen 2010).
By virtue of the fact that Betfair has more customers than any other betting exchange,
a trader is more likely to see his or her position matched on Betfair than on any other
exchange. Accordingly, there is an incentive for all customers to trade using Betfair. This
inducement may be decisive, even if other exchanges charge lower commissions than
Betfair. Consequently the short history of the online betting industry has been punc-
tuated by a series of high-proﬁle closures, including Cantor Index Limited’s SpreadFair
online spread-betting exchange in December 2008 and Bet Bull Holdings’ Betbull.com
exchange in February 2009.
Through the transmission of new forms of betting market data, and by offering
greater ﬂexibility, including the facility to develop hedged positions by backing and
laying, Betfair has been particularly successful in attracting business from sophisti-
cated bettors. It is widely documented that from the mid-2000s onward, the traditional
bookmaker ﬁrms have themselves made increasing use of betting exchanges, rather

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information efficiency in high-frequency betting markets
213
than racecourse bookmakers, for hedging their exposures. Unsurprisingly, however,
the traditional bookmakers have been among the most vocal critics of Betfair and bet-
ting exchanges in general. Criticism has focused on the negative effect of the erosion
of the traditional bookmakers’ overround on the level of subsidy that ﬂows from tra-
ditional bookmaker ﬁrms to the horse racing industry as well as on the danger that
the facility to lay bets, in particular, creates opportunities for illegal trading on the
part of sports industry insiders (especially in the case of horse racing) with privileged
access to nonpublic information. Betfair has argued, on the contrary, that its unique
technology places it in in a better position than that of the traditional bookmakers to
identify suspicious betting patterns and take appropriate steps when the integrity of a
betting market appears to be in jeopardy.
In-play, high-frequency, datasets embody several distinctive characteristics that we
introduce by providing a graphical depiction of a particular high-frequency dataset
before providing a more technical review. In this section, we consider prices from
bookmakers and Betfair for a particularly interesting Euro 2008 match between Turkey
and the Czech Republic. We speciﬁcally focus on the match outcome market rather
than any of the other in-play betting opportunities now offered; later on in this section
we discuss a number of alternative types of in-play markets. Before considering the
evolution of prices across different online gambling markets, we ﬁrst introduce the
user interface for each market, beginning with Betfair. Figure 12.1 shows a screenshot
from Betfair’s match outcome market, which is the focus of all Betfair studies described
in this chapter, for a match between Spartak Moscow and Chelsea in October 2010. A
trader on Betfair can choose to back (buy) or lay (sell) contract i for event j at decimal
odds DOij. If event j occurs, then the seller (layer) of the contract pays the backer
(buyer) DOij. On Betfair, backers and layers make it clear how much money they wish
to back or lay, and this is revealed underneath each decimal odd on Betfair such that
figure 12.1 Screenshot from www.betfair.com illustrating how the betting exchange appears to
a consumer (accessed Oct. 19, 2010).

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sports betting
any other bettor could choose to back or lay bets up to that particular amount. If $x is
matched between a backer and a layer at decimal odds DOij then if event j happens the
layer pays the backer xDOij. Thus in the context of the clash between Spartak Moscow
and Chelsea, a user could have backed Chelsea at decimal odds of 2.18, meaning that
for each dollar staked at these odds the user would have received $2.18 and that up to
$9,881 was available to stake at these odds. A user exhausting all this available liquidity
would stand to win $21,540.58 if (as happened) Chelsea won.
An alternative market structure is provided at Intrade.com, where contracts that pay
out $10 if event j happens are traded at a price $P.4 Assuming the Law of One Price
and an Absence of Arbitrage, the price $P that the contract trades at can be viewed as
the probability of the event occurring. Figure 12.2 provides a screenshot of the Intrade
market for the reelection of President Barack Obama; the price of the most recently
traded contract at the time of the screenshot was $5.08, implying a probability of
50.8 percent that Obama would be reelected in 2012, as happened, taking 51.02 percent
of the popular vote.5 Users of Intrade could either buy or sell such contracts,as indicated
by the green and red buttons, and when the event expired post-election, the buyer of a
contract received $10 from the seller. The equivalence between market structures like
TradeSports and Betfair is the reciprocal of the price; hence P = 1/OD; on both markets,
the availability of contracts at particular prices is listed. The jargon differs somewhat,
but the structures are essentially identical; bettors can go long (buying a contract or
backing the event) or short (selling a contract or laying an event) and hence can cover
their initial positions by taking opposing trades at a later stage.
Figure 12.3 returns to the previously mentioned Euro 2008 match between Turkey
and the Czech Republic, plotting the implied probability, or the inverse of the decimal
figure 12.2 Screenshot from www.intrade.com market on the reelection of President Barack
Obama (accessed Nov. 21, 2012).

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information efficiency in high-frequency betting markets
215
odds, for a Turkey win. Prices from Betfair as well as the two largest traditional
bookmakers, William Hill and Ladbrokes, are plotted. In this particular game, the
Czech Republic scored the ﬁrst two goals, which are noted on the plot as “1–0” and
“2–0”and correspond to discrete shifts in the implied probability of a Turkey win. After
the second goal, the decimal odds were such that the implied probability of a Turkey
win was essentially zero. However, Turkey scored three goals in the ﬁnal 15 minutes to
win 3–2, and again these goals are marked on the plot. The third Turkey goal came so
late that the Ladbrokes price never actually adjusted to it, remaining with an implied
probability of around 15 percent until the end of the match (though punters would
have been unable to back this event at this price). Betfair and William Hill did adjust,
and the Betfair implied probability converged essentially to unity, implying a certain
event, as would be expected in an efﬁcient market.
Apparent in ﬁgure 12.3, relative to bookmakers, is the volatility of the Betfair series.
The best back price available on Betfair is plotted, and naturally as bets are matched,
and more offered for backing or laying, the price that is the best back or lay price
will change; Karen Croxson and J. James Reade (2011b) found that, on average, $527
of bets are matched per second on Betfair during football matches, showing just how
quickly the best back price can change.6 Also apparent from the inset in ﬁgure 12.3 is
the rapidity of the adjustment to goals on Betfair relative to the bookmakers. In the
inset, Betfair’s market is suspended for 7 seconds, and within another 10 seconds of the
William Hill 
Ladbrokes
Betfair
70500 71000 71500 72000 72500 73000 73500 74000 74500 75000 75500 76000 76500 77000 77500 78000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Turkey 3-2 Czech Republic, implied probability of Turkey win
1-0
2-0
2-1
2-2
2-3
William Hill 
Ladbrokes
Betfair
figure 12.3 Graphical representation of information arrival in the market for a win by Turkey
in the Euro 2008 match between Turkey and the Czech Republic.

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sports betting
market reopening, the price has settled at its new level, toward which the bookmakers
move around half a minute later.
3 Valuation of In-Play Betting Odds
.............................................................................................................................................................................
The valuation of in-play betting opportunities, conditional on the state of the match
at the time a particular betting opportunity is available, requires the enumeration of
probabilities for the occurrence of the outcome that is the subject of the bet in ques-
tion. This section reviews two approaches that have been suggested in the academic
literature for the computation of the required probabilities. Stephen Dobson and John
Goddard (2011) employed Monte Carlo simulations to derive probabilities for ﬁnal
match result outcomes (in home win/draw/away win format) conditioned on the state
of the match at any particular point within the regulation 90-minute match duration.
An empirical model for the in-play arrival rates of player dismissals and goals was esti-
mated based on prior data. Following a modeling approach similar to that of Mark
Dixon and Michael Robinson (1998), it was assumed that the arrival rates of goals and
player dismissals can be represented as Poisson processes, such that the probability that
a new arrival occurs is independent of the time that has elapsed since the previous
arrival. A competing risks model comprising hazard functions for four events (a goal
being scored by the home team or the away team and a home team or an away team
player being dismissed) was estimated. These hazards are linear in a set of covariates
including team-quality measures (which do not vary while the match is under way)
and a set of dummy variables that reﬂect the state of the match at any point, deﬁned
as the difference between the two teams in goals already scored (if any) and the differ-
ence between the two teams in players already dismissed (if any). Additional dummy
variables controlled for variations in the goal-scoring and player-dismissal hazards
during the ﬁrst minute after kickoff at the start of each half and after a goal has been
scored, and during the ﬁnal recorded minute of each half, which usually extends for
several minutes to include time added on to compensate for stoppages in play during
the half.
The in-play home win, draw, and away win probabilities conditional on the current
state of the match (again deﬁned by the relative team-quality measure and the current
differences between the teams in goals scored and players dismissed) are calculated
from stochastic simulations of player dismissals and goals, which start from the current
minute and continue over the remaining duration of the match, and are assumed to be
generated in accordance with the estimated hazard functions. Simulated occurrences
of the relevant events (goals and dismissals) are simulated by ﬁring random numbers
at the hazard functions.
The in-play probabilities are the proportions of home wins, draws and away wins
obtained at the end of each simulated match, over 10,000 replications of this procedure.

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information efficiency in high-frequency betting markets
217
For example, consider a match between two teams that are equally balanced in terms
of quality, such that the home win/draw/away win probabilities (allowing for home
ﬁeld advantage) are of the order 0.44/0.28/0.28. If the match has remained level
until the 15th minute, the simulations suggest that these probabilities should have
drifted to around 0.42/0.31/0.27. An opening goal scored by the home team in the
15th minute then tilts the probabilities in the home team’s favor, to 0.70/0.19/0.11.
Conversely, an opening goal scored by the away team tilts the probabilities to
0.20/0.27/0.53.
Naturally the later in the match that the opening goal (or any goal that establishes
a lead) is scored the bigger the value (expressed in terms of the shift in the probabili-
ties) of the goal to the scoring team. An opening goal scored by the home team in the
75th minute tilts the probabilities rather dramatically in the home team’s favor, from
0.22/0.63/0.15 to 0.81/0.17/0.02. The corresponding probabilities immediately follow-
ing a 75th minute opening goal for the away team are 0.03/0.21/0.76. Although the
Dobson and Goddard Monte Carlo simulation method is computationally demanding,
it does provide a scientiﬁc basis, grounded empirically in the observation of past in-play
match data, for the evaluation of the probabilities required for an objective assessment
of the “correct” betting odds at any stage of the match.
As A. D. Fitt, C. J. Howls, and M. Kabelka (2006) pointed out, the range of available
in-play betting opportunities extends to various spread betting markets. In contrast
to ﬁxed-odds betting or person-to-person betting via an online exchange, the possible
payoffs to the bettor (both positive and negative) from a spread bet may be unbounded.
For spread betting via an online bookmaker, the bookmaker quotes a spread (B, T),
and the bettor has a choice of either “buying the spread at T” or “selling the spread at
B.”If the realized value of the index at the end of the event is S, the payoffs to the bettor
for a unit stake are S −T if the bettor bought the spread or B −S if the bettor sold the
spread. If the payoff is positive the bookmaker pays the bettor; if the payoff is negative
the bettor pays the bookmaker.
Fitt, Howls, and Kabelka examined the valuation of spread bets on various out-
comes of football matches, assuming that the arrival rates of goals, corners, bookings
and sendings off can be modeled as Poisson processes. Commonly traded spread bets
include total goals, total corners, multicorners (the product of the number of corners
taken in each half of the match), and four ﬂags (the time in minutes when corners have
been taken from all four corner positions). They illustrate the calculation of payoffs
to the bettor and bookmaker and assess the fair value of a range of bets. The assump-
tion that the arrivals of goals and corners can be modeled as Poisson processes was
found to provide a good approximation to the reality, but the arrivals of bookings and
sendings off appear to be at variance with this assumption.
Below we describe in some detail the methodology employed by Fitt, Howls, and
Kabelka to value two speciﬁc in-play spread bets: “total goals” and “multicorners”.
“Total goals” is the total number of goals scored by the home and away teams;
“multicorners” is the product of the numbers of corners taken in each half of the
match.

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sports betting
For any event, the probability of observing N(a, b) occurrences during the time
interval (a, b) can be written as follows:
P (N (a,b) = n) = μ(b −a)ne−μ(b−a)
n!
,
(12.1)
where μ is the expected number of occurrences over the entire match. Applying this
formula to a“total goals”spread bet, the expectation at duration t (where t = 0 denotes
the start of the match and t = 1 denotes full-time) of the total number of goals scored,
conditioned on r goals having been scored between duration 0 and duration t, is as
follows:
C (t) = Et (N|N (0,t) = r) =
∞

n=0
(r + n)(μ(1 −t))ne−μ(1−t)
n!
= r + μ(1 + t).
(12.2)
C(t) is interpreted as the center spread for the spread bet on the total number of goals
scored in the entire match. The center spread takes the value μ at the start of the match.
As the match progresses the center spread decreases linearly by μ/90 in each minute
in which no goal is scored and increases by a jump of one on each occasion a goal is
scored.
For a “multicorners” spread bet, let X denote the product of the ﬁrst-half and
second-half corner counts, and let N(a, b) denote the number of corners taken
during the period (a, b). We can write X = N(0, 1/2)N(1/2, 1), and E0(X) =
E(N(0, 1/2)N(1/2, 1)). Let μ denote the expected number of corners taken (by both
teams) in the entire match. E(N(0, 1/2)) = E(N(1/2, 1)) = μ/2, and E0(X) = μ2/4.
The expectation at duration t in the ﬁrst half of X, conditional on r corners having
already been taken between duration 0 and duration t, is as follows:
C (t) =
 ∞

n=0
(r + n)(μ(1 −t))ne−μ(1−t)
n!

× E(N(1/2,1))
= [r + μ(1/2 −t)]
μ
2

= μ2
4 −μ2t
2 + μr
2 .
(12.3)
The expectation at duration t in the second half of X, conditional r corners having
already been taken between duration 0 and duration t, R1 of which were taken in the
ﬁrst half, is as follows:
As before, C(t) is interpreted as the center spread for the multicorners spread bet.
The center spread takes the value μ2/4 at the start of the match. During the ﬁrst half
the center spread decreases linearly by μ2/180 in each minute in which no corner is
taken and increases by a jump of μ/2 each time a corner is taken. During the second

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information efficiency in high-frequency betting markets
219
half the center spread decreases linearly by μR1/90 in each minute in which no corner
is taken and increases by a jump of R1 each time a corner is taken.
Similar procedures are used by Fitt, Howells, and Kabelka to calculate fair prices
for a wide range of in-play spread bets. The time paths of the valuations over the
duration of particular football matches are compared with the time paths of the quoted
spreads in order to evaluate whether the spread betting prices are fair and whether the
betting markets in question are informationally efﬁcient. Clearly the assumption that
the arrival rates follow Poisson processes with constant means over the entire match
duration is a simpliﬁcation: it is widely documented, for example, that more goals
are scored during the later stages than during the early stages of matches and that the
rates at which bookings and sendings off accrue likewise increase over the duration of
the match. Nevertheless, the use of mathematical modeling grounded in probability
theory provides a useful starting point for the valuation of a wide range of in-play
spread bets.
Fitt (2009) applied Markowitz portfolio theory to the selection of spread bets. In for-
mulating a spread-betting strategy in a situation where multiple betting opportunities
are available, Fitt suggested that the bettor faces a choice analogous to the choice faced
by the risk-averse investor in portfolio theory. The investor (bettor) seeks to create a
portfolio of assets (bets) that either maximizes the expected return for any given target
level of risk or minimizes the risk for any given target expected return. Risk is measured
by the variance of the return on the portfolio of assets (bets). In the case of betting
on football, all of the risk is concentrated into 90 minutes of play, and no alternative
risk-free asset exists that would offer a meaningful return over such a short period. The
bettor’s sole decision is the selection of the unique optimum portfolio of risky bets.
For any array of bets the computation of the optimal portfolio is a mechanical task.
Theoretically there is only one unique combination out of any available selection of
bets that any bettor need ever consider.
4 Information Efficiency
.............................................................................................................................................................................
The informational efﬁciency of markets is a fundamental concept in economics; the
contention that the market price is the most effective distributor of information to
the greatest number of people is a central tenet of economic theory.7 Friedrich Hayek
(1945, p. 526) captured the idea as follows: “The mere fact that there is one price for
any commodity ... brings about the solution which ... might have been arrived at by
one single mind possessing all the information which is, in fact, dispersed among all
the people involved in the process.” The idea is highly controversial, not least because
of the risk thus in ﬁnancial markets that market participants with greater amounts of
information may proﬁt at the expense of those with inferior information. However,
if a market is efﬁcient, it is argued, its price will instantaneously and fully adjust to

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any such new information, thereby ruling out the possibility of well-informed traders
beneﬁtting at the expense of those with less information. The concept is perhaps most
commonly associated with Eugene Fama 1965, 1970, 1998) though also further back to
Louis Bachelier (1900).
Fama delineated three levels of information efﬁciency that vary in stringency. The
ﬁrst level, weak-form efﬁciency, stipulates that current prices embody all informa-
tion contained in historical prices. Thus no trading strategy is possible based on
past price levels and movements that can yield a positive expected return. A partic-
ularly important implication of this is that betting at particular prices, or ranges of
prices, should not yield different expected returns to betting at any other price or range
of prices. A violation of this would be what is referred to in betting markets as the
favorite-longshot bias (FLB), where the odds offered on favorites and outsiders are sys-
tematically biased. Various studies have investigated FLB, and they will be discussed in
section 5.1.
The second level outlined by Fama is semi-strong form efﬁciency (SSFE), which
requires that market prices reﬂect all publicly available information; hence proﬁtable
trading strategies based on publicly available information cannot be possible. With
SSFE, Vaughan Williams (1999) noted the implication that across different providers
of bets (bookmakers, betting exchanges) it should not be that expected returns differ
and also pointed out that the response of markets to information is crucial. If market
prices are known to over- or underreact to news events then this information could be
used to construct a proﬁtable betting strategy.
The third and strictest notion of information efﬁciency is strong-form efﬁciency,
which requires that market prices reﬂect all information whether publicly or privately
held. Considering strong-form efﬁciency where private information is factored in, it
should not be possible for any participant trading on superior information to make
abnormal returns. Furthermore, prices set later in a market, after trading has taken
place based on private information, should not incorporate any more information
than that set earlier in the market. In particular, insider trading constitutes a central
focus of investigations of strong-form efﬁciency.
We shape our review of the literature investigating information efﬁciency in high-
frequency betting markets around these three levels of efﬁciency.
5 Information Efficiency in
High-Frequency Betting Markets
.............................................................................................................................................................................
We now review investigations into information efﬁciency in high-frequency markets
by considering the three levels of efﬁciency outlined in the previous section; in section
5.1 we review investigations into weak-form efﬁciency before, in section 5.2, we look at
studies of semi-strong and strong form efﬁciency.

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information efficiency in high-frequency betting markets
221
5.1 Weak-Form Information Efﬁciency
As mentioned in section 4, weak-form information efﬁciency has often been assessed by
investigating the favorite-longshot bias, which states that bets placed at different prices
yield different expected returns. Testing for FLB in betting markets has been carried
out by many authors in the context of explaining the phenomena; Linda Woodland
and Bill Woodland (1994) tested in the context of U.S. baseball markets, ﬁnding a
reverse FLB; Erik Snowberg and Justin Wolfers (2010) attempted to explain FLB as
a misperception on the part of bettors using pre-event data from U.S. horse races;
Michael Smith, David Paton, and Leighton Vaughan Williams (2006) considered U.K.
horse racing pre-event and concluded in favor of an information explanation for FLB;
bettors face real or perceived costs of information accumulation, meaning that they
accept the prices offered by bookmakers that embody FLB as a proﬁt maximizing
strategy (Levitt 2004). Smith, Paton, and Vaughan Williams (2006) found in particular
that the person-to-person betting exchange prices exhibit substantially less FLB than
do bookmaker prices.
A common calibration test (employed by, for example, Woodland and Woodland
1994 and Franck, Verbeek, and Nüesch 2010) asks whether a contract priced such that
the implied probability of the event occurring is x ∈[0, 1] pays out 100x percent
of the time and is usually conducted via some form of limited dependent variable
regression involving the observed outcome for event i, yi ∈{0, 1}regressed on the
implied probability from market m for event i, pm,i:
yi = β0 + β1pm,i + εi.
(12.4)
Because ∂yt/∂pm,i = β1 it would be expected that an efﬁcient market is such that
β1 = 1: the actual (or frequentist) probability of an event, and the market’s subjec-
tive probability of it, move one-for-one. In addition, no wedge would be expected
between the actual probability and the market’s subjective probability such that β0 = 0
also. Hence the absence of any bias implying that β0 = 0 and β1 = 1 so that the
event is accurately predicted by the implied probability from market m. It is perhaps
useful to note that β0 = 0 is thus, in essence, simply a paired difference in means
test between the actual event outcome probability and the subjective one, and the
β1 = 1 test is one of proportional movements in these two entities. While it might
be asserted that other information surely exists that is correlated with both yi and
pm,i, hence likely causing omitted variable bias in the calculation of β1, it ought to
be the case that this information in an efﬁcient market has already been factored
into pm,i, hence that additional information should not actually affect coefﬁcient
estimates.
The Franck, Verbeek, and Nüesch study (2010) compared bookmakers and Betfair
pre-event and found evidence that Betfair exhibits less FLB than do bookmakers and
thus is more efﬁcient, though the study also provided evidence against semi-strong
form efﬁciency in the betting market more generally.

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sports betting
Croxson and Reade (2011a) considered high-frequency data for bookmakers and
Betfair during the Euro 2008 football tournament. They thus extended the calibration
testing from the cross-section-style setting of pre-event prices into a more panelesque
environment in which numerous events were considered (N) but also many obser-
vations through time (T) during these matches. Due to the nature of matches lasting
slightly different lengths (injury time), but also due to technical difﬁculties of collecting
the data, the authors derived different T’s for each N and hence have an unbalanced
panel. However, because, as pointed out by Woodland and Woodland (1994), the aim
with equation (12.4) is not so much to provide a model with high explanatory power
as to test how well calibrated is the market, the authors did not treat equation (12.4)
as a panel model. Not least, each panel would have a dependent variable without any
variation, but additionally this would involve restricting the dataset over which cali-
bration is assessed; the entire premise of calibration testing is to test over as large a
number of observations as possible whether contracts priced at a particular implied
probability pay out that often. Croxson and Reade (2011a) upheld the results found
by both Smith, Paton, and Vaughan Williams (2006) and Franck, Verbeek, and Nüesch
(2010) in non-high-frequency data settings: Betfair is more accurate, exhibits lower
FLB, but nonetheless still exhibits some bias.
Croxson and Reade (2011b) also considered weak-form efﬁciency in a considerably
larger dataset graphically; their dataset contains second-by-second information from
1,206 football matches across nine different competitions at both domestic club level
and international team level, including the Euro 2008 matches referred to above.8
Figure 5 in Croxson and Reade (2011b), reproduced here as ﬁgure 12.4, displays a
graphic representation of the calibration test described above. On the horizontal axis
is the win probability implied by the Betfair price of a contract, while on the vertical
axis is the proportion of contracts priced at this level that pay out. A calibrated and
hence weak-form efﬁcient market would have all such proportions equal to the implied
probability of the price, hence plotted along the 45-degree line; in this situation the
expected returns from consistently placing bets at particular ranges of prices would be
the same. From ﬁgure 12.4, by and large this is the case for this high-frequency market;
the implied slope of the plotted points is 1.04, implying a slight, and visible, FLB, as
deviations from the 45-degree line are slightly below the line when the probability is less
than 0.5 and generally above the 45-degree line when the probability is greater than 0.5.
Samuel Hartzmark and David Solomon (2008) investigated NFL matches via betting
contracts traded on the U.S.-focused betting portal TradeSports.com and considered
one speciﬁc departure from SSFE known within the behavioral ﬁnance literature as
the disposition effect. TradeSports.com operates somewhat differently from Betfair, as
described in section 2. Hartzmark and Solomon produced a plot similar to ﬁgure 12.4 in
their ﬁgure 2, plotting the frequency with which contracts priced at particular implied
probabilities pay out. Hartzmark and Solomon noted not that the points appear to
suggest presence of the FLB, as the implied slope of the points is greater than unity,
but that they actually appear to follow an S-shaped pattern. At the lower end of the
range of implied contract probabilities points are generally below the 45-degree line

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information efficiency in high-frequency betting markets
223
1.0
0.9
0.8
0.7
0.6
0.5
Win frequency (%)
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
20000
Number of contracts in probability interval (bars)
10000
5000
figure 12.4 In-play calibration test.
Source: Figure 15 from Croxson and Reade (2011b).
but converge back to the line as the probability approaches zero, and likewise at the top
end of the range, again as the event converges on certainty, so does the actual frequency
of payouts, and hence rather than being a linear relationship, what is observe is an
S-shaped curve.
Hartzmark and Solomon suggest that this S-shaped pattern is supportive of a dispo-
sition effect interpretation rather than the FLB interpretation discussed thus far. The
disposition effect states that traders close out winning positions earlier than they ought
to and hold on to losing positions longer. This may manifest itself in the post-news
period in price movements; if a favorite has scored, those that hold positions with the
favorite (they bought contracts that pay out in the event the favorite wins) may seek
to sell contracts at this point to exploit the now substantially higher price that such
a contract will secure. Such selling pressure will exert a downward pressure on the
implied probability (or TradeSports.com price) of such a contract, and indeed this is
exhibited in the markets Hartzmark and Solomon study, as for a ﬁxed probability of
winning (vertical axis) prices are pushed to the left for favorites (contracts implying
probability above about 60%). Equivalently if a news event occurs that makes a team
less likely to win than it was previously, many traders who hold contracts on that team
face a losing position and should seek to sell such contracts to cover any losses. Thus
if the disposition effect exists we might expect to see an absence of selling pressure
after a negative news event for that team, pushing its price up, as people hold on to
these losing positions in the hope they recover. Again, this can be observed in both
Hartzmark and Solomon’s ﬁgure 2 and ﬁgure 12.4 in this chapter; for a contract that
has a low probability of paying out, the price is pushed down (hence rightward on the

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sports betting
horizontal axis). Hence we would ﬁnd that when a price (or implied probability) has
reached the upper end of the scale, very near to unity, then prices are pushed back
down relative to what they would otherwise be (upward biased due to the FLB) and
vice versa for very unlikely events where the implied probability has reached near zero.
It is important to point out that these price distortions are argued to be short term, and
as such, over a longer time period it would be expected that prices would return to the
level at which they should be. It is this aspect of the disposition effect that the authors
use to identify it from other potential explanations (such as the standard explanations
for the FLB outlined in Snowberg and Wolfers 2010 and Smith, Paton, and Vaughan
Williams 2006).
As well as estimating the S-shaped curve using nonlinear least squares and boot-
strapping to get standard errors to investigate the signiﬁcant of the S-shape, they ran a
number of regressions to examine whether price movements do indeed correspond to
their hypothesized explanation. They established that there is signiﬁcant price reversal
for favorites after positive news shocks and for outsiders after negative news shocks.
Although their attempt to rule out alternative explanations of the S-shape is quite
weak, they nonetheless established yet further the absence of weak-form efﬁciency in
high-frequency betting markets both via the S-shaped curve and by identifying serial
correlation in post-news price movements.
5.2 Semi-Strong and Strong Form Information Efﬁciency
Turning to semi-strong and strong-form efﬁciency, these two concepts explore the
reaction of markets to new information, with the former considering only public infor-
mation and the latter public and private information. At the high-frequency level,
Ricard Gil and Steven Levitt (2007) considered betting prices from Intrade for the
2002 FIFA World Cup, while Croxson and Reade (2011b) used prices for more than
one thousand football matches from many competitions worldwide and Buraimo, Peel,
and Simmons (2008) considered a signiﬁcant sample of English Premiership football
matches between 2006 and 2008.
Gil and Levitt (2007) tested information efﬁciency using the 2002 FIFA World Cup
and Intrade markets, attempting to test SSFE with what is essentially a dynamic cali-
bration test; they tested the hypothesis of rapid updating of prices to new information,
which they deﬁne to be goals in football matches. Table 1 from Croxson and Reade
(2011b) makes it clear, as does ﬁgure 12.3 graphically, that goals are the big news
events in football matches. All of these studies add that the football setting makes the
testing of SSFE that much cleaner; even though match outcomes can be anticipated
(legally or otherwise), the exact timing of goals is essentially random such that even in
the seconds before a goal no market participant can be certain that a goal will occur.
Furthermore, once a goal has happened, the news is immediately spread; all online
betting portals now have facilities through which events can either be viewed visually
or followed via audio feeds, and in addition, Betfair suspends its market the moment a

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information efficiency in high-frequency betting markets
225
goal is scored such that it is obvious to all market participants that a material event has
occurred.
These three papers each individually propose different methods to counter the joint
hypothesis problem because despite the ﬁxed endpoint and value for betting contracts,
the problem remains. Speciﬁcally, while a match is in-play, each second and minute
that pass provide new information independent even of events that took place in the
preceding minute; the information is that less time exists in which either team can
inﬂuence the outcome of the match. As such,in-match offered and implied probabilities
always drift toward either zero or unity depending on whether at that point that event
was what the match scoreline reﬂected (i.e., if the score was a draw or one team was
favored over the other). This is displayed graphically in ﬁgure 12.3; while Turkey is not
winning, its implied probability drifts toward zero. The problem thus is ascertaining
whether the drift post-goal is caused by the information embodied in the goal or
in the subsequent seconds and minutes that pass. The method that Gil and Levitt
(2007) employed is calibration testing; by averaging over all goals they arrived at the
objective (frequentist) and subjective (Intrade) probabilities of the contract outcome.
They essentially repeated this test for 15 minutes before a goal happened and 15 minutes
after; the hypothesis of information efﬁciency was thus that post-goal there should be
no drift in the subjective probability (and neither pre-goal for efﬁciency). Hence this
method of testing removes the drift problem using the information embodied in the
ﬁxed endpoint value of each contract, the property of sports betting markets noted in
section 1.
Gil and Levitt included dummy variables for each of the 30 minutes in their sample
and tested the signiﬁcance of these dummies both pre- and post-goal. Speciﬁcally, they
ran the regression model:
pm,c,w,t = β0 +
15

g=−14,g̸=0
βgGoalm,c,w,t+g + εm,c,w,t ∼IID(0,σ 2),
(12.5)
where p denotes the volume-weighted average price and the subscripts m, c, w, and t
denote the particular match, contract traded (we consider home win and away win
contracts), goal“window,”and minute of time considered.9 Goal is an indicator variable
corresponding to a particular minute which is equal to unity when a goal is scored in
favor of the contract and zero otherwise. Hence the null hypothesis of their test for
information efﬁciency is that βg = βh, g ̸= h, g, h > 0; that post-goal there is no drift
up or down in prices.
The result of their test is perhaps best displayed graphically; the estimates for all
β coefﬁcients in equation (12.5) are displayed in Gil and Levitt’s ﬁgure 1. Post-goal
(average) prices drift upward and are much more volatile than pre-goal. This sug-
gests that the news of a goal has a substantial and long-lasting impact on the market,
indicative of an absence of SSFE.
It should be emphasized again that this drift should not be confused with the drift
that would be observed in any individual match price as the event neared its conclusion.

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sports betting
Nonetheless, there are problems with the Gil-Levitt test, notably an absence of liquidity.
In their markets there were few participants (on average just 75 individuals per match),
trades were relatively infrequent (on average 100–200 per match), and the overall vol-
ume of money traded was very low, at about $1.5 million across all matches in the
World Cup, while their sample of matches at 50 is rather small in terms of a calibra-
tion test. Buraimo, Peel, and Simmons (2008) went on to criticize the econometric
speciﬁcation of equation (12.5), noting that it does not accommodate the likely het-
eroskedasticity caused by the bounded nature of subjective and objective probabilities.
Model misspeciﬁcation need not be a moot point here; as Gil and Levitt considered
market prices, if they are efﬁcient then they all satisfy a random walk, meaning that the
ﬁrst lag of the price would be highly signiﬁcant and its omission could cause spurious
signiﬁcance. Buraimo, Peel, and Simmons (2008) raised the additional concern that
Gil and Levitt did not calibrate the time of trading on Intrade (GMT) and the time of
goals scored (minutes in match), meaning that there may be discrepancies between the
two, discrepancies that could explain the prolonged upward shift around minute zero
(when the goal happens) found by Gil and Levitt.
Croxson and Reade (2011b) and Buraimo, Peel, and Simmons (2008) studied SSFE
in the context of Betfair betting markets on match outcome, and despite different
methodologies appear to have arrived at similar results. Croxson and Reade considered
more than one thousand football matches from various competitions (see their table
A.3), while Buraimo, Peel, and Simmons considered 296 Premiership matches between
2006 and 2008.
Croxson and Reade adopted a dual strategy for investigating efﬁciency, both using
unit-root testing and investigating the existence of feasible and proﬁtable trading
strategies.
They attempted to circumvent the joint-hypothesis problem by considering only
the half time interval rather than general in-play prices. This removed information
related to the passage of time from the observations they considered because during
halftime, or at least for the ﬁrst few minutes of halftime, the clock stops and little
if any newsworthy events that are publicly known occur; teams are in their dressing
rooms, and TV stations are on advertising breaks. Hence the information causing the
drift during play ought not to exist at this point, and in-match plots of prices/implied
probabilities, such as ﬁgure 12.3, generally reveal this visually (see the observations
around 74500). In particular Croxson and Reade considered whether the event of a
goal on the cusp of halftime (within a minute of the end of play) has any impact
on the evolution of prices during halftime relative to matches where no goal events
happen. They adopted a panel unit root testing approach and in order to cope with fat-
tailed error distributions simulated critical values. They reached somewhat ambiguous
results, with some panel test variants suggesting a rejection at the 5 percent level but not
the 1 percent level (see their table 3). Responding to this ambiguity they investigated
potentially proﬁtable strategies: either laying one of the contracts at the start of halftime
and backing it ﬁve to ten minutes later to exploit any upward drift or, vice versa, to
exploit downward drift. They found, using a paired difference in means t-test, that

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information efficiency in high-frequency betting markets
227
neither strategy would have yielded a positive return on average (see their tables 4
and 5) and hence determined that while the statistical evidence may be mixed, there
were no feasible trading strategies possible to exploit any drift or inefﬁciency during
the halftime interval and hence concluded in favor of SSFE.
Interestingly, on their substantially larger dataset Croxson and Reade ran the model
of Gil and Levitt and found instead of an upward drift an insigniﬁcant hint of negative
drift (see their ﬁgure 9). In addition, with such a larger dataset, the reduced volatility of
the different β estimates is notable. These results further emphasize their conclusions
in favor of SSFE.
Buraimo, Peel, and Simmons alternatively considered, a la Gil and Levitt, the imme-
diate time after a news event has been occurred and asked how soon the market would
respond. As the title of their study suggests, they found that within about 60 seconds
all information has been impounded into the market price. They also asserted that
the nature of information contained in each goal can be dramatically different if the
goal is scored early or late, or happens when the scores are level or one team is several
goals ahead, and suggested that Gil and Levitt did not account for this (and neither
did Croxson and Reade). However, arguably Gil and Levitt did via their averaging over
all goals in their dataset to consider the objective and subjective outcome probabilities
surrounding these goals, and equally did Croxson and Reade in the sense that they
allowed for different-sized jumps in their autoregressive testing via the error/residual
term.
Buraimo, Peel, and Simmons developed a model that accounts for the different mag-
nitude of jumps in price for goals of differing importance and, as such, also attempted
to control for the heteroskedasticity problem. Speciﬁcally they proposed that the true
probability of an outcome, p, evolves according to:
dp = p

1 −p

u,
(12.6)
where u is news. Hence if p = 0.5 then the impact on the true probability is largest and
decreases as the probability nears zero or unity in order that a news event cannot push
the probability outside the unit interval, on which it is bounded. The authors then used
a discretized version of (12.6) as their dependent variable:
Yt =
pt −pt−1
pt−1

1 −pt−1
.
(12.7)
They identiﬁed news events by considering the extremes of the distribution of residuals
from an AR(1) model of Yt from (12.7):
Yt = α0 + α1Yt−1 + μt.
(12.8)
Hence Buraimo, Peel, and Simmons did not simply consider goals to be the only news
events but instead attempted to identify all news events empirically via ut in (12.8),
considering residuals in the very tails of the distribution (top and bottom 0.025%)
to be news events. This led them to identify considerably more than just goals: they

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uncovered 1,445“newsbreaks,”of which only 454 corresponded to goals. While goals are
infrequent events, Croxson and Reade’s sample (more than one thousand matches from
multiple competitions, domestic, European, club level and international level) contains
on average 2.55 goals per game; this would imply about 755 goals in Buraimo’s sample,
and hence it would appear that their strategy missed a number of goals,most likely those
that occurred with a team already signiﬁcantly ahead and late in the game, therefore
not registering as a news event.
Speciﬁcally Buraimo, Peel, and Simmons tested for weak-form efﬁciency by testing
that in the aftermath of a goal Yt is not serially correlated; that is, news isn’t serially
correlated and instead its impact happens in just one period. This would appear to
be more of a test of SSFE than of weak-form efﬁciency, and hence we treat it as
that. The test is a simple t-test of the signiﬁcance of α1 in (12.8). Buraimo, Peel, and
Simmons considered six time frequencies to test SSFE: 2 seconds, 5 seconds, 10 seconds,
30 seconds, 1 minute, and 2 minutes and hence aggregated their data for each case. They
measured the time from the news event, and hence if the Betfair market was suspended,
then the 2- and 5-second regressions will miss some news events since at 2 or 5 seconds
later the market is still suspended. Nonetheless, their table 3 reports the results of the
t-test on α1 for these varying time frequencies. For 2 and 5 seconds the t-statistics are
greater than or equal to 1.96 and hence signiﬁcant, indicating that at such short time
horizons the market is not efﬁcient, not absorbing news instantaneously. However the
t-statistics decrease with the time interval, and for 10 seconds the t-statistic is already
below 1.96; hence it might be concluded that for time intervals of 10 seconds and longer
the market fully processes any new information.
Buraimo, Peel, and Simmons did also uncover evidence against weak-form efﬁciency,
pre-match, by noting that betting strategies involving backing home teams that were
outsiders generated signiﬁcantly higher (positive) returns (16.95%) than did backing
home teams that were favorites (4.87%), while backing away team favorites incurred
smaller losses (−11.7%) than did backing away team outsiders (−31.6%). In-play,
however, after news events, they found that all strategies resulted in losses, though
again they found that returns differed for different types of bets, arguing against weak-
form efﬁciency, though in favor of strong-form efﬁciency since no information, public
or private, could be used to generate positive returns.
Continuing with strong-form efﬁciency, as mentioned in section 4, insider trad-
ing is a particular aspect of this; were a market strong-form efﬁcient, insider trading
would not be proﬁtable, as the market would reﬂect any private information already
held. Betfair has attracted signiﬁcant controversy by allowing market participants to
lay bets; although those associated with a particular horse are not allowed to lay (to
bet against or to act as the bookmaker for a bet on) a particular horse, they can
provide information to others regarding horses. Anecdotally Betfair is much more
transparent than traditional bookmakers regarding user accounts, and a number of
successful investigations have been carried out against suspected suspicious activity
noticed by Betfair.10 That Betfair has a team of employees working speciﬁcally on
detecting suspicious activity suggests that it does exist and hence that substantially

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information efficiency in high-frequency betting markets
229
positive expected returns must exist, arguing against strong-form efﬁciency (again, only
anecdotally).
5.2.1 Information Efﬁciency across Betting Market Formats
As mentioned in section 4, Vaughan Williams (1999) noted that different expected
returns found across different providers of bets can provide evidence against SSFE in
the betting market as a whole. The high-frequency comparison of bookmakers and
betting exchanges in (Croxson and Reade 2011a) thus provides insight into whether
SSFE exists in betting markets more generally than just in Betfair. Via their tables 8–11
and ﬁgure 12 they clearly showed that the expected returns on Betfair for winning bets
are statistically signiﬁcantly higher than those available from traditional bookmakers;
in addition, they investigated the size of the bet for which this ceases to be the case
on betting exchanges by calculating the average return possible once one wishes to bet
more than is available at any given price on Betfair. It is only for bets of over $450 in size
that traditional bookmakers begin to become competitive on average with the returns
provided by Betfair. As such, this would appear to provide evidence against SSFE.
Croxson and Reade (2011a) also investigated the process of information arrival
on betting exchanges, making use of the cointegration methodology applied by Joel
Hasbrouck (1995) to stocks listed on multiple exchanges in ﬁnancial markets. It would
be expected that in terms of information discovery, and hence efﬁciency, Betfair would
lead due to its disaggregated nature; anyone with information can trade, and because
there are sufﬁcient numbers of traders, if the new information is initially mispriced
this inefﬁciency will quickly be arbitraged away. Conversely, bookmaker odds are set
and altered by some small group of experts operating within the bookmaker, and
hence it would seem plausible that these would be unable to react with the speed and
accuracy of Betfair. Figure 12.3 would appear to graphically make the case that it must
be Betfair leading information discovery: after a goal happens in the zoom inset, the
Betfair market is suspended for about seven seconds before reopening, and it appears
that within ten seconds of restarting the price at Betfair has reached its new level,
around which it then ﬂuctuates. The two bookmaker prices, conversely, do not appear
to adjust to their new level for around a minute (William Hill) and almost three minutes
(Ladbrokes). This plot would suggest that Betfair displays quite notable SSFE, adjusting
almost instantaneously to new information (the goal), while the bookmakers do not;
furthermore, it suggests that information discovery is clearly led by Betfair rather than
the bookmakers.
Of course this is but one example of one goal in one match, yet it provides quite
a clear picture of the process of information arrival in the betting market: Betfair
appears to adjust much more quickly than the bookmakers to the news of a goal.
Croxson and Reade then attempted to test this formally using the cointegrated VAR
methodology of Søren Johansen (1995), a method that allows the identiﬁcation of
stationary steady-state relationships between nonstationary variables (such as between
prices from the different betting companies) and also, importantly, the adjustments

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sports betting
to these relationships. If a ﬁrm’s price does not adjust, it implies that that ﬁrm leads,
or drives, the relationship between the prices and hence leads information discovery. It
would be expected then that the remaining prices adjust to the relationship, meaning
that the information is then transmitted from the leading price to the following ones.
However, ﬁgure 12.3 does hint at some of the difﬁculties with attempting to sta-
tistically model raw data series like these; the bookmaker prices are constant for long
periods with discrete jumps, and furthermore the odds are exponential in their behav-
ior, converging slowly to unity (certain event) but also exploding to very high values
as an event becomes increasingly unlikely, while if probabilities are used then they are
constrained to lie on the unit interval hence inducing heteroskedasticity, as Buraimo,
Peel, and Simmons point out. In addition, as noted earlier by Croxson and Reade, Bet-
fair returns (hence odds) are statistically signiﬁcantly better than bookmakers, and this
also can be observed in ﬁgure 12.3; although all three implied probabilities adjust to the
news, they appear to converge to slightly different values. Reﬂecting these difﬁculties,
the cointegration results provided by Croxson and Reade are somewhat ambiguous
in the support they offer for the Betfair leadership hypothesis; although the median
values over all 22 matches (they estimate each match separately as opposed to attempt-
ing a panel cointegrated VAR model) are supportive of Betfair leading information
accumulation, all test results reject this idea, ﬁnding that all ﬁrm prices adjust to the
cointegrating vectors (tables A.6–A.11).
6 Conclusions
.............................................................................................................................................................................
In this chapter, we provide a review of recent academic research on the topic of informa-
tion efﬁciency in high-frequency in-play football betting markets. Several studies have
reported evidence that is contrary to the weak-form information efﬁciency hypothesis,
in the form of a favorite-longshot bias in in-play betting prices. However, there is evi-
dence in the literature in favor of the semi-strong form of the information efﬁciency
hypothesis, with in-play betting prices shown to respond rapidly to the arrival of large
news events in football matches, especially goals being scored. One study we reviewed
also reports interesting evidence in support of the strong-form information efﬁciency
hypothesis. As in-play betting markets continue to develop and gain in popularity,
driven in part by further improvements in computing power, we anticipate parallel
growth in research on information transfer and price formation in ﬁnancial markets,
an exciting new area of academic study.
Notes
1. See Betfair (http://betfair.com)
2. See ﬁgure 12.1 for a screen grab from Betfair’s website.

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information efficiency in high-frequency betting markets
231
3. In-play betting is also often described as in-running; in this chapter we refer to betting
while an event is occurring as in-play betting.
4. Intrade’s sports betting portal, TradeSports, which Hartzmark and Solomon (2008)
used for their empirical investigation of the disposition effect, was one of the victims
of the intense competition in the online sports betting industry, closing in November
2008. See Chris F. Masse, “TradeSports ceases its operations,” MidasOracle.org, Nov. 16;
http://www.midasoracle.org/2008/11/18/tradesports-end (last accessed Nov. 21, 2011).
5. Wrade suspended all tradiry in March 2013.
6. This naturally varies depending on the type of match under consideration, and raises to
as much as $2,534 per second during Euro 2008 matches, of which the match plotted in
ﬁgure 12.3 is one (see table A.3 in Croxson and Reade 2011b).
7. Information efﬁciency in markets is often synonymously described in the literature as
market efﬁciency; in this chapter we use the term information efﬁciency.
8. This corresponds to a number of observations well in excess of one million.
9. Gil and Levitt (2007) also demean their price data; since this is a linear transformation its
effect is simply captured here in the constant coefﬁcient, β0. Gil and Levitt omit this term.
10. See “Eddie Freemantle,“How Betfair beat the bookies,” The Observer, March 29, 2009 (last
accessed Nov. 10, 2011) for a number of such examples.
References
Bachelier, Louis. [1900] 1964. Theorie de la speculation. In The random character of stock
market prices, edited by Paul Cootner. Reprint, Cambridge, Mass.: MIT Press, 17–78.
Buraimo, Babatunde, David Peel, and Rob Simmons. 2008. Gone in 60 seconds: The absorp-
tion of news in a high-frequency betting market. Selected works of Babatunde Buraimo,
January; http://works.bepress.com/babatunde_buraimo/17.
Croxson, Karen, and J. James Reade. 2011a. Exchange vs. dealers: A high-frequency analysis of
in-play betting prices. Discussion Paper No. 11-19. Birmingham: Department of Economics,
University of Birmingham.
——. 2011b. Information and efﬁciency: Goal arrival in soccer betting. Discussion Paper No.
11-01. Birmingham: Department of Economics, University of Birmingham.
Davies, Mark, Leyland Pitt, Daniel Shapiro, and Richard Watson. 2005. Betfair.com:
Five technology forces revolutionize worldwide wagering. European Management Journal
23(5):533–541.
Dixon, Mark J., and Michael E. Robinson. 1998. A birth process model for association football
matches. The Statistician 47(3):523–538.
Dobson, Stephen, and John Goddard. 2011. The Economics of Football. 2nd ed. Cambridge:
Cambridge University Press.
Fama, Eugene F. 1965. The behaviour of stock market prices. Journal of Business 38(1):34–105.
——. 1970, Efﬁcient capital markets: A review of theory and empirical work. Journal of
Finance 25(2):383–417.
——. 1998. “Market efﬁciency, long-term returns and behavioral ﬁnance. Journal of Financial
Economics 49(3):283–306.
Fitt, Alistair D. 2009. Markowitz portfolio theory for soccer spread betting. IMA Journal of
Management Mathematics 20(2):167–184.

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sports betting
Fitt, A. D., C. J. Howls, and M. Kabelka. 2006. Valuation of soccer spread bets. Journal of the
Operational Research Society 57(8):975–985.
Franck, Egon, Erwin Verbeek, and Stephan Nüesch. 2010. Prediction accuracy of differ-
ent market structures—Bookmakers versus a betting exchange. International Journal of
Forecasting 26(3):448–459.
Gil, Ricard, and Steven D. Levitt. 2007. Testing the efﬁciency of markets in the 2002 World
Cup. Journal of Prediction Markets 1(3):255–270.
Hartzmark, Samuel M., and David H. Solomon. 2008. Efﬁciency and the Disposition Effect
in NFL Prediction Markets. Working Paper.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1540313
Hasbrouck, Joel. 1995. One security, many markets: Determining the contributions to price
discovery. Journal of Finance 50(4):1175–1199.
Hayek, Friedrich A. 1945. The use of knowledge in society. American Economic Review
35(4):519–530.
Johansen, Søren. 1995. Likelihood-based inference in cointegrated vector autoregressive models.
Oxford: Oxford University Press.
Koning, R. H., and B. van Velzen. 2010, Betting exchanges: The future of sports betting?
International Journal of Sports Finance 4:42–62.
Levitt, Steven D. 2004. Why are gambling markets organised so differently from ﬁnancial
markets? Economic Journal 114:223–246.
Smith, Michael A., and Leighton Vaughan Williams. 2008. Betting exchanges: A technological
revolution in sports betting. In Handbook of Sports and Lottery Markets, edited by Donald
B. Hausch and William T. Ziemba. Amsterdam: Elsevier, 403–417.
Smith, Michael A., David Paton, and Leighton Vaughan Williams. 2006. Market efﬁciency in
person-to-person betting. Economica 73(292):673–689.
Snowberg, Erik, and Justin Wolfers. 2010. Explaining the favorite-longshot bias: Is it risk-love
or misperceptions?” Journal of Political Economy 118(4):723–746.
Vaughan Williams, Leighton. 1999. Information efﬁciency in betting markets: A survey.
Bulletin of Economic Research 51(1):1–30.
Woodland, Linda M., and Bill M.Woodland. 1994. Market efﬁciency and the favorite-longshot
bias: The baseball betting market. Journal of Finance 49(1):269–279.

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s e c t i o n iii
........................................................................................................
HORSE RACE
BETTING
........................................................................................................

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## Page 256

chapter 13
........................................................................................................
ON THE LONG-RUN
SUSTAINABILITY OF TOTE
BETTING MARKETS
........................................................................................................
david edelman
1 Background---Pari-Mutuel
or Tote Betting
.............................................................................................................................................................................
Pari-mutuel wagering, an ingenious method of organizing the betting on horse races
and other predominantly sportsbetting markets, was ﬁrst invented in the late 1800s by
a Catalan entrepreneur named Joseph Oller Roca and has since come to be the main-
stay of state-sponsored wagering worldwide. The primary historical reason for this is
that, as a system, it is inherently equitable and democratic in the sense that people are
rewarded for their ﬁnancial votes or shares in the winning outcomes, without subjec-
tivity, prejudice, or favoritism, and do not require counterparties with special views or
interests, such as bookmakers; neither do they require any risk to be underwritten.
The fact that pari-mutuel markets are particularly well designed to aggregate, reﬂect,
and reveal (Eisenberg and Gale 1959) as well as possibly to distort (Hurley and
McDonough 1995) information has led to increasing attention to it in the academic
literature. In addition, the simplicity of pari-mutuel markets makes them particularly
well suited to such matters as the examination of the role of asymmmetric or “pri-
vate” information in markets (Koessler, Noussair, and Zielgelmeyer 2008; Ottaviani
and Sørensen 2009) and the microstructure of trading in markets generally (Lange and
Economides 2005). Of these aspects, the role of market asymmetry will be emphasized
here, though (unlike as in most of the literature) not from a behavioral or particularly
analytical way, but rather a pragmatic way, exploring the potential consequences of
worst cases to the functioning and future of real-world pari-mutuel markets.

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horse race betting
Mathematically, a pari-mutuel system may be described as follows: bettors allocate
amounts to their various choices, and when the result is known, all bettors having
made the correct choice receive a share of the pool in proportion to their wagers on
the winning combination. For instance, if a pool is 100 units, divided (for simplicity)
among two choices by A:60 and B:40, each unit wagered on A would return (100/60) =
1.67, if A wins, whereas if B wins the unit bet on B would return (100/40) = 2.50.
Of course, pari-mutuel operators do not pay out all of the money wagered, so that
in this example, if the take is 20 percent the dividend for a unit bet on A would be
.8(1.67) = 1.33 and for a unit bet on B would be 2.00.
In totalizator or tote markets throughout the world, the amounts returned per unit
bet are displayed continuously throughout betting until a race begins, and the clever
player will compare his or her estimated probabilities to the prices on offer and decide
which, if any, of the possibilities merits a wager. More sophisticated players will, of
course, consider the impact of their individual wagers on the dividend so as to not
over bet and reduce the dividend unduly. (It is this fact that we shall refer to later as
being a key stabilizing mechanism of pari-mutuel betting.)
More speciﬁcally, the rational player should take risk into account when deciding the
amount to wager. However, in his paper on optimal staking, game theory expert Rufus
Isaacs (1953) evaluated the case in which the primary consideration in deciding how
much to bet is “pool impact” (this corresponds to the case in which the size of the pool
is of a much smaller order of magnitude than the bettor’s wealth).
With a signiﬁcant takeout, one may wonder why anyone would want to participate
in these markets. An explanation of that is beyond the scope of this discussion, but
clearly if the takeout were increased to too large a level turnover would drop quickly. It
is the ﬁrmly held belief (myth?) of many (most?) tote operators and governments that
the primary threat to their long-term sustainability would be if expert players were to
become too plentiful, thereby raising the effective takeout rate for the average player
further and further until the experts were taking most of the money and the more
casual players were increasingly driven away.
It is the primary purpose here to dispel this impression and to prove the limited
potential impact of expert players using simple economic and mathematical arguments.
In fact, it will be shown that under broad assumptions the opposite of this hypothesis
is true; namely, the more expert players there are in a tote market, the less able they will
be to proﬁt collectively from it, given a ﬁxed number of others.
2 A Brief Note on Information
Asymmetry and Sophisticated Play
.............................................................................................................................................................................
For reasons primarily of simplicity and tractability, much of the published literature
in ﬁnance and economics historically has focused on the abstraction of “homogeneous

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on the long-run sustainability of tote betting markets
237
agents” (or, by extension, “representative agents”), where all participants in a market
are assumed to have (or may be considered to have) similar risk-return preferences and
(more importantly) similar access to relevant information and information processing.
Generally the assumption of “efﬁcient markets” has pervaded, with a strong burden
of proof placed on any attempt to controvert it. We do not attempt here to prove
inefﬁciency in any market; we merely ask the reader to imagine what would happen if
the usual tenets and ramiﬁcations of efﬁciency failed to hold in a pari-mutuel market.
More recently increasing attention has been paid to hypothetical situations such as
this, where customary notions of market efﬁciency fail to hold. In this case, we will
suppose that information asymmetry exists. The simplest formulation of this might be
expressed in terms of information distance (see, e.g., Edelman 2000). Suppose a “true”
(experts’) distribution of outcome p and a “casual” distribution of outcome q exist.
Then information asymmetry is tantamount to the condition that
D(p∥q)

i
pi log
pi
qi

> 0.
(Note that the coincidence of “true” and “expert” is not necessary. One may imagine
an “expert” distribution r as separate from the “true” distribution p, in which case, the
asymmetry condition would be that D(p∥q)−D(p∥r) > 0. However, for simplicity, we
assume here that r ≡p.)
Forhorseracingmarkets,theprimarysourceof inefﬁciencyisarguablytheprocessing
of publicly available information, including the collection of data in electronic form
and the mathematical and statistical modeling which are foreign to the lion’s share of
casual bettors.
3 Limited Capacity for
Sophisticated Play
.............................................................................................................................................................................
In general, casual bettors for a horse race bet in the 20 minutes to half hour preceding
a race, whereas expert players (or sophisticated players as they are often called) will,
either by electronic or other means, have the capability of betting just prior to race start
and later than most of the casual players.
We begin by imagining a “best-case” scenario for the sophisticated player in which
all other wagers occur previous to his or her wagers and in which he or she is the
lone sophisticated player in the market. Then, following Isaacs (1953), we imagine the
example discussed earlier but where the expert has an opportunity to send one last
wager, supposing that his or her probability for horse (outcome) B is 0.60. We shall,
as discussed previously, suppose the expert to be a risk-neutral (expectation-seeking)
investor who would like to maximize the total expected amount of return from wagering

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horse race betting
an amount b, which is
b

.6(.8)(100 + b)
40 + b
−1

,
which is found by simple calculus to be maximum for b ≃7.07, achieving a value of
approximately 0.65 units (i.e., nearly a 10% margin on 7 units). Crucially, if b were
increased beyond this, the expectation would decrease, to 0.64 if 8 units were bet, down
to 0.56 for 10 units, down to a loss of 0.09 if 16 units were bet.
On average, then, the other (here, casual) players can expect to receive back in
aggregate an amount of
80 −0.65 −(.2)(7.07) = 77.94
out of their 100 units of wagers instead of 80 without the expert betting. In effect, then,
for similar races the expert has the effect of increasing the effective takeout rate for the
casual player from 20 to 22.06 percent.
If the takeout rate were small, this best case for the sophisticated player would
correspond to the worst case for the casual player. In this case 20 percent is a signiﬁcant
percentage; hence this equivalence will not necessarily hold, for if the sophisticated
player bet 20 units, then (according to the 0.6 probability assumed here) the return to
the public would be 76.80 (or a 23.2% takeout), a somewhat worse outcome for the
casual player than the case of optimal betting. From the casual players’ point of view,
this latter outcome represents a worst-case scenario irrespective of how many experts
have access to the same information advantage and late-wagering capability.
It seems unreasonable to suppose that, collectively, sophisticated players will tend to
behave in a manner that is close to their collective optimum; it is rather more likely
that the reverse will be true, that the more players there are, the more chance there
will be of their incorrectly anticipating the play of others like themselves, leading to
overbetting (or, conceivably, underbetting) in relation to the optimum which would be
bet in a concerted effort. Thus for a given level of information asymmetry the more
(uncoordinated) expert players there are, the better it is for the casual player.
To ﬁx ideas, suppose a pari-mutuel has a 10 percent takeout rate and a group of
sophisticated players has an information advantage suggesting to them that in a par-
ticular case the probability of a betable event is 25 percent higher than the public
proportion. Then for these values it is possible to gauge the impact of sophisticated
play for single (or, approximately, collectively for many) players as a function of market
proportion. The resulting values can be seen in table 13.1, which presents computed
values of a, the optimal proportion of the pool which would be bet, as a function of
p the market proportion and the resulting total expectation E(R) (equivalently, total
pool Impact) as a proportion of the pool (where basis points “b.p.,” or hundredths of a
percent, are used for the smaller percentages).
For instance, if 10 percent (1 in 9) of the casual bettors favor a certain outcome, and
the sophisticated player(s) is (are) correct in the assumption of the truer proportion
being 12.2 percent (1.25 in 9), the most that may collectively be extracted from the

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on the long-run sustainability of tote betting markets
239
Table 13.1 Maximum Impact as a Function
of Market Proportion
p
a
E(R)
.01
.0007
0.5 b.p.
.05
.0035
2.4 b.p.
.1
.0067
4.0 b.p.
.2
.012
5.3 b.p.
.3
.014
4.4 b.p.
.4
.013
2.4 b.p
.5
.006
<1 b.p.
pool, on average, based on this information is 4 units in 10,000. It appears, then, that
possession of information increasing odds by 25 percent can only result in (at most)
5 basis points (the worst case here occurring when the market proportion is 20%)
or one-twentieth of one percent of the total pool. (This may be comforting to tote
operators who worry about the inﬂuence of sophisticated play in their markets.) The
key point here, following from consideration of pool impact, is that for a given level of
information asymmetry the downside effect to the casual player is limited in aggregate
(and likewise the collective upside to the sophisticated players).
4 Conclusions
.............................................................................................................................................................................
Using a simple mathematical example and a theoretical best-/worse-case argument, we
have established that the discouraging effect of sophisticated play to the casual bettor
must be limited, even in a worst-case scenario, from the point of view of the casual
player. Further, even this theoretical worst case is unlikely to be achieved due to the
friction between expert players.
While the abstraction of sophisticated players being homogenous (with regard to the
nature and quantity of their information advantage), used here for simplicity, could be
challenged, it is clearly also a worst case, since any disagreement between experts would
lead to a ﬁxed level of aggregate losses among the experts in virtually every race, even if
their respective information advantage levels (as measured by D(p∥q) −D(p∥r)) were
all positive. Although we have established the above in a conceptual sense, the actual
behavior of a system with many experts attempting to proﬁt from a pari-mutuel pool
over time would be interesting to attempt to model, as lower proﬁt levels would lead to
experts leaving the market but then perhaps returning periodically whenever the level
of expert betting was perceived to be lower.

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240
horse race betting
It is hoped that the arguments presented here, however simplistic, may prove useful
in the understanding of pari-mutuel markets (even to the extent of preventing panic
in some quarters) and help industry decision makers refocus their energies toward
addressing other factors that may be affecting their business. For instance, might not
the fact that the entertainment industry (including the sporting events on which these
tote markets are based) has undergone a digital revolution over the past 10 years be
the more likely dramatic source of disruption than the manner in which the role of
expertise in tote betting markets may have been playing out over the past 100 years
or so?
Acknowledgment
.............................................................................................................................................................................
This chapter has emanated from research conducted with the ﬁnancial support of the
Science Foundation Ireland under Grant No. 08/SRC/FM1389.
References
Edelman, David. 2000. On the ﬁnancial value of information. Annals of Operations Research
100(1–4):123–132.
Eisenberg, Edmund, and David Gale. 1959. Consensus of subjective probabilities: The pari-
mutuel method. Annals of Mathematical Statistics 30(1):165–168.
Hurley, William, and Lawrence McDonough. 1995. A note on the Hayek hypothesis and the
favorite-longshot bias in parimutuel betting. American Economic Review 85(4):949–955.
Isaacs, Rufus. 1953. Optimal horse race bets. American Mathematical Monthly 60(5):310–315.
Koessler, Frédéric, Charles Noussair, and Anthony Zielgelmeyer. 2008. Parimutuel betting
under asymmetric information. Journal of Mathematical Economics 44(7–8):733–744.
Lange, Jeffrey, and Nicholas Economides. 2005. A parimutuel market microstructure for
contingent claims trading. European Financial Management 11(1):25–49.
Ottaviani, Marco, and Peter Norman Sørensen. 2009. Surprised by the parimutuel odds?”
American Economic Review 99(5):2129–2134.

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## Page 262

chapter 14
........................................................................................................
THE ECONOMICS OF
RACETRACK–CASINO
(RACINO) GAMBLING
........................................................................................................
richard thalheimer
1 Introduction
.............................................................................................................................................................................
The inclusion of casino-style gambling (henceforth gaming) at pari-mutuel racetracks,
beginning in 1990, has changed the landscape of the pari-mutuel racing and wager-
ing industry in the United States.1 To investigate the implications of racetrack–casino
(henceforth racino) betting on the pari-mutuel racing and wagering industry, this
chapterisorganizedasfollows. Section2examineslong-runtrendsinpari-mutuelhorse
race wagering. Section 3 reports results of economic studies of the effects of competition
from state lotteries and casino gaming on the long-run trends in pari-mutuel wagering.
Section 4 considers the rationale for legislation enabling casino-style gaming at race-
tracks and on various characteristics of racinos in the United States. Section 5 reports
key ﬁndings from economic studies of the demand for racino wagering. Section 6
presents a summary and conclusions.
2 U.S. Pari-Mutuel Horse Race
Wagering---Historical Trends
.............................................................................................................................................................................
A review of trends in horse race wagering (handle, turnover), the predominant form of
pari-mutuel wagering in the United States,2 is helpful in understanding the background
against which pari-mutuel racetracks have been permitted by law to have casino-style

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242
horse race betting
gaming. As of 2010, some form of pari-mutuel horse race wagering was conducted in
38 states. Live horse racing was conducted in 34 of these states.3 Betting on live races
simulcast from racetracks conducting live races to other pari-mutuel wagering facilities
was ﬁrst permitted in 1983. Simulcasting is the process by which live races held at one
racetrack, the host track, are transmitted simultaneously to other locations that allow
patrons at the receiving racetrack or off-track betting (OTB) facility, the guest location,
to place wagers on the races transmitted by the host track. The host track charges the
guest facility a fee based on the amount wagered on its races at that location.
U.S. horse race wagering on all racehorse breeds (thoroughbred, harness, quarter
horse) was $3.4 billion in 1960 and had increased to $10.8 billion in 2010 (Association
of Racing Commissioners International 2010). Adjusted for inﬂation, a very different
picture of the historical trend in horse race betting in the United States emerges. Horse
race wagering from all sources (live and simulcast) peaked in 1977 and declined 69 per-
cent over the next three decades through 2010. Over this same period, wagering at
racetracks on live horse racing as a percentage of live and simulcast wagering declined
from 100 percent of the total prior to 1983, when simulcast wagering was ﬁrst intro-
duced in New Jersey, to only 12 percent in 2010 (Association of Racing Commissioners
International 2010). The decline in total all-source horse race wagering has occurred
despite the introduction of market expanding measures such as simulcast wagering
between racetracks or to OTB facilities, and telephone and internet account wagering.
Why then, in light of the market-expanding measures instituted over the past several
decades, has inﬂation-adjusted horse race wagering fallen 69 percent? A large part of the
answer lies in the introduction and growth of competition from other types of gaming,
speciﬁcally casinos and state lotteries. The decrease in wagering from increased gaming
competition has more than offset any increase due to the market-expanding measures
undertaken by the racehorse industry. Competition from casino gaming has been found
to reduce pari-mutuel horse race wagering on the order of 31 to 39 percent. Similarly,
the competition from state lotteries has been found to reduce pari-mutuel horse race
wagering on the order of 10 to 36 percent. For a review of the economic literature on
the effect of competition on horse race wagering see Thalheimer and Ali (2008a).
3 Background of Racino Gaming
.............................................................................................................................................................................
Concern for the decline in handle and revenue of the pari-mutuel horse racing industry,
brought about by competition from other forms of gaming, has prompted a number of
statestopermitcasino-stylegamingatpari-mutuelracetracks. Aconsistentthemeof the
legislation in most states permitting casino-style gaming at racetracks is preservation of
horse and greyhound racing and breeding industries in light of competition from other
forms of gaming, such as state lotteries and casinos. Also mentioned in many of the state
racino statutes is the preservation of live racing, economic development, tourism, job

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the economics of racetrack–casino (racino) gambling
243
creation, and the agricultural nature of the racehorse industry. An important aspect of
enabling legislation in racino states is that in addition to the allocation of a percentage
of gaming revenue to state and local governments and the racino operator, a percentage
of gaming revenue is allocated also to purses for horsemen with horses at the racino.4
Following is a discussion of important aspects of racinos in the United States.
Racino types. In a number of racino states gaming devices at racinos are operated
under the auspices of the state lottery and are placed under the lottery’s regulatory
authority. In those instances the gaming devices are referred to as video lottery termi-
nals (VLTs). In other racino states, the privately owned gaming devices at racinos are
placed under the regulatory authority of a state racing or gaming commission and are
referred to as electronic gaming devices (EGDs) or slot machines. In either case VLTs
or slot machines are equivalent casino-style gaming devices and are transparent to the
customer. The number of slot machines (VLTs) at racinos ranges from around 250 to
5,000, depending on state regulations and market demand (McQueen 2009).
Initially all racinos were limited by legislation to slot machines (VLTs) and were
not permitted to have casino-style table games, such as blackjack, roulette, and craps.
This restriction was lifted beginning with the Iowa racinos in 2004. Following Iowa’s
lead, table games were permitted at racinos in West Virginia (2007), Delaware (2009),
and Pennsylvania (2010). In addition to table games, the Delaware racinos were also
permitted to offer limited sports betting in 2009. Delaware is the only state outside of
Nevada to permit sports betting at gaming facilities.
Racino launch dates and locations. As shown in table 14.1, the number of states
that permitted casino-style (racino) gaming at pari-mutuel racetracks in chronological
order of launch date has grown from 1 in 1990 to 15 in 2011. There were 51 racinos in
those 15 states.
4 The Economics of Racino
Gaming---Empirical Studies
.............................................................................................................................................................................
Racino wagering is a special case of live race and casino-style wagering where the two
products are offered at the same location. There have been a number of non-racino
studies of the demand for pari-mutuel horse race wagering. These studies include:
Ali and Thalheimer (1997, 2002), Church and Bohara (1992), Coate and Ross (1974),
Degenarro (1989, 2009), Gramm et al. (2007), Gruen (1976), Morgan and Vasche
(1979, 1982), Simmons and Sharp (1987), Suits (1979), and Thalheimer and Ali (1992,
1995a, 1995b, 1995c). In addition to studies of the demand for pari-mutuel horse
race wagering, David Forrest, O. David Gulley, and Robert Simmons (2010) examined
the determinants of the demand for non-pari-mutuel (ﬁxed-odds) bookmaker betting
on horse and dog racing in Britain. Finally, Paton, Siegel, and Vaughan Williams
(2004) examined the demand for bookmaker betting on the aggregate of horse and dog

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horse race betting
Table 14.1 U.S. Racino States, 2011
State
Type
Under State
Lottery?
Launch Date
Number of
Racinos
Breed (H, G)∗
West Virginia1
VLT’s/Tables
Yes
1990/2007
4
H,G
Rhode Island2
VLT’s
Yes
1992
2
J,G
Iowa
Slots/Tables
No
1995/2004
3
H,G
Delaware3
VLTs/Tables/Sports
Yes
1995/2009/2009
3
H
New Mexico
Slots
No
1998
5
H
Louisiana
Video Poker/Slots
No
1992/2002
4
H
Alabama4
Slots
No
1993
2
G
New York
VLTs
Yes
2004
9
H,G
Maine
Slots
No
2005
1
H
Oklahoma
Slots
No
2005
2
H
Florida5
Slots
No
2006
5
H,G,J
Arkansas6
Slots
No
2006
2
H,G
Pennsylvania
Slots/Tables
No
2006/2010
6
H
Indiana
Slots
No
2008
2
H
Maryland
VLTs
Yes
2011
1
H
Note: Ohio permitted VLT gaming at its seven racetracks in 2011. One racino was launched in 2012.
Table games were permitted at the Maine racino in 2012. Florida has card rooms at all pari-mutuel
racetracks. Minnesota has card rooms but no slot machines at racetracks. Kansas permits racino
gaming but had not received a license application through 2011. South Dakota, Oregon, and Montana
each have limited gaming at many locations (racetracks and other). Canada has extensive racino
gaming.
Racino gaming revenue, which was nonexistent prior to 1990, had grown to $6.4 billion by 2009
(American Gaming Association 2010).
1 Limited number of VLTs (video lottery terminals) at Mountaineer racetrack on an experimental basis
in 1990. In 1994 statutes were enacted permitting VLTs at all four West Virginia racetracks.
2 Simulcast betting only in 2011. There was no live greyhound racing or jai alai at the two pari-mutuel
facilities in 2011.
3 Table games and sports wagering both were launched in 2009. Delaware racinos are the only ones to
also have sports wagering.
4 Slot machines (Class 2 Indian electronic gaming machines) at racetracks under local authority.
5 Slot machine racinos in Broward and Dade counties only. Card rooms also permitted at all pari-mutuel
racetracks and jai alai frontóns in the state.
6 Arkansas has Electronic Games of Skill (EGS).
Source: Thalheimer Research Associates (TRA, Inc.) and state racing and gaming commissions.
∗(H = Horse, G = Greyhound, J = Jai Alai)
racing, sports, and slot machines (ﬁxed-odds betting terminals) at betting shops in the
United Kingdom. There has been only one non-racino study of the demand for casino
wagering (Thalheimer and Ali 2003). The demand variable in this study was aggregate
slot machine wagering for riverboat casinos and racinos in the Midwestern states of
Illinois, Iowa, and Missouri.5

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the economics of racetrack–casino (racino) gambling
245
While there have been many papers on the demand for pari-mutuel horse race
wagering, only three studies have examined the demand for pari-mutuel wagering
when slot machine (VLT) wagering is offered at the same location. A discussion of
these papers follows.
Racino study 1. The subject of the earliest racino study (Thalheimer 1998) was Moun-
taineer Racetrack and Gaming Resort (Mountaineer) in West Virginia. Mountaineer
was the ﬁrst racetrack in the United States to offer VLT (slot machine) gaming. The
VLTs were placed under the auspices of the West Virginia Lottery with Mountaineer
acting as agent for the lottery.
The daily sample period for this study was 1989 through 1991, during which live
racing was also offered at the track. A limited number of VLTs were placed at the
thoroughbred racetrack in June 1990 as an experimental pilot project under the auspices
of thestatelottery. ThenumberofVLT’swasincreasedfrom70to150by1991. Wagering
attheracetrackonsimulcastsof anentireday’sprogramof races(wholecardsimulcasts)
imported from a few racetracks around the country was launched at Mountaineer in
September 1990.
Three wagering demand models were estimated, one for live horse race wagering, one
for import simulcast horse race wagering, and one for VLT wagering. Each of the three
demand models was speciﬁed as a function of its own-demand variables as well as those
of the other two wagering products. The same set of live race, import simulcast race,
and VLT variables was used in each of the three wagering demand models. This setup
resulted not only in estimates of relationships of each of the three wagering product
demands to its own-demand variables but also to the variables associated with the
demands of the other two wagering products. The price of wagering variables, takeout
rate for pari-mutuel wagering, and win percentage for VLT wagering were constant
over the study period and so were not included in the demand models.
An important ﬁnding of the study involved the interaction between the racing and
gaming sides of the racino. On the racing side pari-mutuel wagering from live and
import simulcast racing combined was found to have declined 24 percent as a result
of VLT gaming at Mountaineer. On the gaming side customers who wagered on horse
racing were also found to wager on the VLTs. Therefore, while existing horse race
customers were found to reduce their wagers on horse racing with the introduction of
the VLTs, new customers attracted by the VLTs, on net, did not bet on the horse races.
Wagering on theVLTs from existing and new customers was enough to more than offset
the estimated reduction of pari-mutuel wagering and to add an additional 21 percent
to total wagering.
The change in revenue tells a different story, however. Revenue from pari-mutuel
wagering is computed as the amount wagered multiplied by the price of wagering, the
takeout rate. The takeout rate is set by state statute as a percentage of total wagering
and is deducted from each bet before any winnings are returned to the patron at the
conclusion of each race. Revenues from the takeout rate are distributed to the state
(pari-mutuel tax), racetrack (commissions), and horsemen with horses at the racetrack
(purses). The effective takeout rate for live and simulcast wagering at Mountaineer

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246
horse race betting
was approximately 20 percent. The price of VLT (slot machine) gaming is the win
percentage. While the takeout rate is known and set by state statute, the win percent
for VLT (slot machine) wagering is not a ﬁxed deduction from each wager. Rather it
is based on the long-run probability of winning and the payoffs associated with that
probability. The expected payoff for lottery-run video gaming terminals is set by state
statute and determined by a random number generator. The effective win percentage
is computed as total wagering less the amount paid out in winnings divided by total
wagering. The win percentage for the VLTs at Mountaineer Park was 12 percent over
the study period.
The revenue per dollar wagered on the VLTs at 12 percent was much lower than the
20 percent from pari-mutuel wagering, which it replaced. As a result, total revenue
increased only 3 percent relative to the 21 percent increase in total wagering from
betting on the VLTs. The ﬁndings of the study suggest that if the number of VLTs is
too small VLT revenue may not be large enough to offset the decline in pari-mutuel
revenue. As the number of VLTs was increased, VLT wagering was found to increase
more than the decrease in pari-mutuel wagering.
Racino study 2. Mountaineer was also the subject of a second racino study (Thal-
heimer 2008). The pilot project begun in June 1990 with a limited number of VLTs
at the racetrack was deemed a success, and in March 1994 the West Virginia Video
Lottery Act (the Act) was passed. The Act gave statutory authority to the West Virginia
Lottery to conduct VLT gaming at all four (two thoroughbred and two greyhound)
West Virginia pari-mutuel racetracks, subject to local referendum. The temporary pilot
VLT project at Mountaineer was ended on September 2, 1994. At that time VLT gaming
was launched at the racetrack on a permanent basis, subject to the requirements of the
newly enacted state statutes. The Act permitted more and different types of VLTs than
the limited number and types permitted during the pilot project. The study period
included 443 weeks from July 1994 through December 2002. Market area population
was 8.4 million over the study period.
Annualized, total VLT wagering increased from $131 million to $2.6 billion over the
ﬁrst through the last year of the study period. At the same time, total on-track pari-
mutuel wagering increased minimally from $38.2 million to $39.4 million. Adjusted
for inﬂation, VLT wagering increased 1,559 percent compared to a 13 percent decrease
in pari-mutuel wagering. Over this period the relative importance of pari-mutuel
wagering fell from 23 to 2 percent of total pari-mutuel plusVLT wagering. In 2002 pari-
mutuel and VLT revenues were $16 million and $221 million, respectively. Pari-mutuel
revenue was 7 percent of total revenue.6
Two weekly wagering demand models were estimated, one for on-track (live plus
import simulcast) pari-mutuel wagering and one for VLT wagering.7 VLT gaming was
conducted daily year-round. Live racing was conducted every month of the year and
varied from 0 to 7 days per week, averaging 4.4 days per week or about 220 days per
year. Import simulcast wagering was conducted every week over the year and varied
from 5 to 7 days per week and from 2 to 21 racetrack programs per day. Following the
earlier study of Mountaineer (Thalheimer 1998), each of the wagering demand models

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the economics of racetrack–casino (racino) gambling
247
was speciﬁed as a function of its own-demand variables as well as those of the other
wagering product. The same set of pari-mutuel and VLT variables was used in each
of the two wagering demand models. Variables for the price of pari-mutuel wagering
(takeout rate) and the price of VLT wagering (win percentage) were constant over the
study period and so were not included in the demand models.
As in the earlier study of Mountaineer (Thalheimer 1998), this study examined the
interaction of the pari-mutuel and gaming sides of the racino. In making this determi-
nation, VLT demand variables were constructed to measure the effect of government
regulations (restrictions) onVLT and pari-mutuel wagering. This was made possible by
the provision by racino management of a unique dataset on the racino ﬂoor layout of
the number and types of VLTs at Mountaineer at various times over the study period.
Restrictions imposed on the VLTs under the statutes included: the number of VLTs,
the type of game and machine, the maximum bet-per-play, and the location of the
VLTs between the racino’s hotel and the racetrack. The 1994 statutes that permitted a
maximum of 400 VLTs were subsequently amended seven times, each time increasing
the maximum number of VLTs allowed at the racino. As a result, the number of VLTs
was increased from 165 before termination of the pilot project to 3,000 by the end of
the study period.
In addition to the number of VLTs, the relationship of VLT wagering demand to the
type of VLT was examined in the study. The provisions of the pilot project prior to
the 1994 Act stipulated that each of the ﬁrst generation VLTs be restricted to offering a
single game (card, keno, or slot). The 1994 Act provided for technologically advanced
multi-game VLTs without a video slot machine option. The Act was amended in 1996
to permit a video slot machine option. There were subsequent amendments to the
Act permitting other game types, such as Las Vegas–type slot machines. Several other
restrictions imposed on the VLTs by the 1994 Act were examined in the study, including
a bet limit of $2 per play, which subsequently was raised to $5, and a restriction on the
placement of the VLTs between the racino’s hotel and its nearby racetrack, which was
changed several times during the study period.
The number of VLTs, the distribution of existing and new VLT types relative to
the pilot period ﬁrst-generation single-game VLTs, the placement of the VLTs, and
restrictions onVLT maximum bet-per-play all were found to be signiﬁcant with respect
to their effect on VLT wagering. The relaxation of restrictions on the number of VLTs
leading to their increase to 3,000 over the study period resulted in a 107 percent increase
in VLT wagering. The relaxation of restrictions on the type of machines that could
be included in the product mix increased VLT wagering by 178 percent. Relaxing
restrictions on VLT placement between the hotel and racetrack increased VLT wagering
by 23 percent. Finally, increasing the maximum bet-per-play from $2 to $5 increased
VLT wagering by 11 percent. The joint or combined increase in VLT wagering resulting
from relaxing all of these VLT restrictions was 687 percent over the study period.
These results demonstrate that allowing management to more freely react to changes
in consumer demand by lifting government restrictions on each of the factors limiting
VLT play resulted in large increases in VLT wagering.

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248
horse race betting
The interaction of the horse racing product with VLT wagering demand also was
found to be signiﬁcant, as in the earlier study of Mountaineer (Thalheimer 1998). VLT
wagering was found to be positively related to live race days and the number of import
simulcast racetracks per day. VLT wagering was not found to be signiﬁcantly related to
average purse or stakes races of national or regional importance.
On the racing side of the racino pari-mutuel wagering demand was found to be
positively related to all of its own-demand variables, including the number of live race
days per week, the number of import simulcasts per day, and the average daily purses
and high-quality stakes races. The live race average purse elasticity was 0.1, indicating
that total (import simulcast plus live) wagering demand is highly inelastic with respect
to a change in live race purse. The ﬁnding of inelastic demand with respect to purses has
also been found in Ali and Thalheimer (2002) and Gramm et al.(2007). The presence
of stakes races of national and regional importance in a given week was found to have
large positive impacts on pari-mutuel wagering. As in the earlier study of Mountaineer
(Thalheimer 1998), pari-mutuel wagering was found to decrease with the introduction
and growth of VLTs. The growth in the number of VLTs to 3,000 by the end of the study
period resulted in a 39 percent reduction in pari-mutuel wagering. Lifting restrictions
on the placement of the VLTs at the hotel versus the racetrack resulted in a 15 percent
reduction in pari-mutuel wagering. Finally, raising the maximumVLT bet from $2 to $5
resulted in a 3 percent reduction in pari-mutuel wagering. The joint effect of relaxing
government restrictions on the number of VLTs, their location, and the maximum
bet-per-play was to reduce on-track pari-mutuel wagering by 49 percent.
The study also addressed the important policy issue of the effectiveness of subsidizing
the racehorse industry by dedicating a statutory percentage of VLT revenues to purses.
The intent of the state legislature to preserve the racing industry is clearly stated in the
West Virginia Video Lottery Act of 1994 as follows (Chapter 29, Article 22 A-2):
The Legislature ﬁnds and declares that the existing pari-mutuel racing facilities
in West Virginia (horse and greyhound) provide a valuable tourism resource for
this state and provide signiﬁcant economic beneﬁts to the citizens of this state
through the provision of jobs and the generation of state revenues; that this valuable
tourism resource is threatened because of a general decline in the racing industry and
because of increasing competition from racing facilities and lottery products offered
by neighboring states; and that the survival of West Virginia’s pari-mutuel racing
industry is in jeopardy unless modern lottery games are authorized at the racetracks.
It should be noted that while purses funded byVLT revenues are an expense to the racino
operator, they constitute revenue to racehorse owners and breeders.VLT revenues to the
racetrack operator fund jobs at the racetrack–casino. Purses fromVLT revenues provide
revenue to racehorse owners and to racehorse breeders to fund their operations.8 These
racehorse industry businesses create jobs associated with the care and maintenance of
horses that compete for purses at the racetrack and reside on breeding farms in the state.
The analysis compares the cost of purses to the revenues they generate. Purses were
$39 million in 2002, $31 million from VLT revenues and $8 million from pari-mutuel

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the economics of racetrack–casino (racino) gambling
249
wagering. The average daily live race purse, which measures the quality of racing,
increased from $23,500 to $163,100 over the study period as a result of revenues from
increased VLT wagering. Adjusted for inﬂation, average daily purses increased 481 per-
cent. As a result of the highly inelastic purse elasticity, pari-mutuel revenue increased
only $1 million. The study also found that VLT wagering did not increase signiﬁcantly
with an increase in purses. For these reasons, the large increase in average purses would
not generate sufﬁcient additional on-track pari-mutuel or VLT revenue to offset their
cost.
There is, however, another effect of theVLT purse subsidy that cannot be overlooked.
Competitive purses are necessary to attract horsemen in order to conduct live racing
at the racetrack. Without the VLT purse subsidy, the level of purses from pari-mutuel
wagering alone would not have been sufﬁcient to fund horsemen’s operations at Moun-
taineer, especially on a year-round basis as required under the statutes. The absence of
live racing at the racetrack would result in a loss of $12 million in live race pari-mutuel
wagering revenue, including revenue from wagering on export simulcasts of live races
at Mountaineer to other in-state and out-of-state locations.9 An important ﬁnding of
this study was that VLT wagering increases on days when there is live racing. If live
racing were to cease there would be an estimated 18 percent loss in VLT wagering with
a corresponding $40 million VLT revenue loss on total VLT revenues of $221 million.10
Assuming that live racing is preserved by the VLT purse subsidy of $31 million, VLT
and pari-mutuel revenues it generates would more than cover the cost of purses and
contribute to racino operating costs.
Racino study 3. Prairie Meadows Racetrack and Casino (Prairie Meadows), a horse
race racino in Iowa, was the subject of the third racino study (Thalheimer 2012).
Thoroughbred, quarter horse, and harness horse wagering were all conducted at the
racetrack. The study period for analysis of the demand for pari-mutuel horse race
wagering at Prairie Meadows included the 168 months from 1993 through 2006. The
market area population was 1.6 million in 2006.
Slot machine gaming was introduced at the racetrack in April 1995. The study period
for analysis of the demand for slot machine wagering at Prairie Meadows included the
period from April 1995, with the introduction of slot machines, through December
2006. The number of slot machines was increased from 1,100 to 1,600 over the ﬁrst and
last year of the study period. A major focus of this study was the effect on pari-mutuel
and slot machine wagering demands due to the expansion of the gaming product at
Prairie Meadows to include casino-style table games such as poker, blackjack, craps,
and roulette in December 2004. Iowa was the ﬁrst state to permit table games at racinos.
Slot machine wagering increased 72 percent, from $1.5 billion to $2.6 billion from
the ﬁrst year to the last year of study period. Adjusted for inﬂation, slot machine
wagering increased 31 percent over the study period. Adjusted for inﬂation, on-track
pari-mutuel wagering, which was $17.8 million in 2006, fell 47 percent from its 1993
level. The number of live race days varied from 54 to 118 and was 95 in 2006. Import
simulcasting was year-round at the racetrack, and the number of import simulcast
racetrack programs per day varied from 2 to 16 over the study period. Due to the

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250
horse race betting
statutory allocation of slot machine revenues to purses, average daily purses increased
from $23,500 in 1993 to $163,100 in 2006.
Following Thalheimer (2008), two wagering demand models were speciﬁed, one for
slot machine wagering and one for on-track (live plus simulcast) pari-mutuel horse
race wagering. Each of the wagering demand equations was speciﬁed as a function
of its own-variables as well as those of the other wagering product. The same set of
pari-mutuel and slot machine variables was used in each of the two wagering demand
models. The price of pari-mutuel wagering (takeout rate) was constant at 21 percent
over the study period and so was not included in the demand models. The price of slot
machine wagering (win percentage) varied from 6 to 8 percent over the study period.
The interaction of racing and slot machine gaming at the racetrack was consistent
with the ﬁndings of the two earlier racino studies (Thalheimer 1998, 2008). On the rac-
ing side of the racino operation, pari-mutuel wagering was found to decrease 21 percent
after slot machines were introduced. For the ﬁrst time in the literature, the effect of table
games on pari-mutuel wagering at a racino was determined. Pari-mutuel wagering was
found to decrease 16 percent after the introduction of table games. In total, pari-mutuel
wagering decreased 34 percent as a result of the combined effect of slot machines and
table games at the racino.
On the gaming side of the racino operation, slot machine wagering declined 8 percent
following the introduction of table games at the racino. This result was consistent with
a study of casino gaming in the Midwest (Thalheimer and Ali 2003) in which slot
machine wagering at the casinos was found to decrease 13 percent as a result of table
gaming. As in the earlier racino studies (Thalheimer 1998, 2008), slot machine wagering
demand was found to be positively related to pari-mutuel wagering demand variables.
In particular, slot machine wagering increased 13 percent in the presence of live horse
racing and 14 percent in the presence of import simulcast horse racing. For comparison,
a study by the Pennsylvania Gaming Control Board (2010) concluded that on days when
there was live racing at the state’s racinos slot machine revenue was 15 percent greater
than on non-racing days. Slot machine wagering was also found to be positively related
to stakes races but not to average daily purses.
Among other ﬁndings of the study, pari-mutuel wagering was found to be positively
related to the number of live horse race days, the number of import simulcast racetrack
programs per day, and average daily purses and stakes races. Pari-mutuel wagering was
found to decrease with competition from nearby casinos. On the gaming side of the
racino operation wagering demand was found to be positively related to the number
of slot machines and negatively related to the price of wagering (win percentage). Slot
machine wagering demand was found to be price inelastic (-0.8) at a win percentage of
8 percent and was found to decrease with competition from a nearby casino.
Finally,thestudyaddressedtheimportantpolicyissueof theallocationof stakeholder
shares from table game and slot machine revenues. The Iowa gaming statutes make no
distinction in the allocation of shares of slot machine or table game revenues to the
stakeholders: government, racino operator, and horsemen (purses). This is not the case
for table game revenues at the West Virginia, Delaware, and Pennsylvania racinos. In

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the economics of racetrack–casino (racino) gambling
251
each of these states the shares of table game revenue to government and horsemen
have been reduced and the share to the racino operator increased relative to their
corresponding shares from slot machine revenue. Stakeholders with lower relative table
game revenue shares may lose gaming revenue (slot machine plus table game) if table
games do not produce enough revenue to offset the expected loss of slot machine
revenue.
Racino study—Gaming side only. A fourth racino study is mentioned here in the
interest of completeness (Thalheimer and Ali 2008b). This study examined the deter-
minants of demand for slot machine wagering at each of the three Delaware racinos.
The study was limited to the slot machine gaming side of the racino operation and so
was in effect a casino wagering demand study. A major ﬁnding of this study was that
slot machine wagering at each of the three racinos was reduced 16 percent as a result
of the introduction of a statewide smoking ban.
5 Summary and Conclusions
.............................................................................................................................................................................
Adjusted for inﬂation, pari-mutuel horse race wagering declined 69 percent from its
peak in 1978 through 2010. Increasing levels of competition from casinos and state
lotteries have been shown to be major causes of this decline. Studies have reported
that casino gaming has reduced pari-mutuel horse race wagering in the range of 31 to
39 percent. Similarly, state lotteries have reduced pari-mutuel horse race wagering from
10 to 36 percent. Recognizing the effect of increased competition on the pari-mutuel
racing industry, a number of states have enacted laws permitting racetracks to offer
casino-style gaming at their facilities. These racetrack-casinos are often referred to as
racinos.
A key theme of the enabling legislation in most states permitting casino-style gam-
ing at racetracks is preservation of the racehorse and greyhound racing and breeding
industries in light of competition from other forms of gaming, such as state lotteries
and casinos. Also mentioned in many of the statutes is the preservation of live rac-
ing, economic development, tourism, job creation, and the agricultural nature of the
racehorse industry.
Racino gaming was ﬁrst launched in 1990 at a racetrack in West Virginia. As of 2011,
there were 51 racinos in 15 states following passage of legislation permitting casino-
style gaming at racetracks, and this number is expected to grow. In a number of racino
states, racino gaming devices are operated under the auspices of the state lottery and are
placed under the lottery’s regulatory authority. In those instances, the gaming devices
are referred to as video lottery terminals (VLTs). In other racino states privately owned
gaming devices at racinos are placed under the regulatory authority of a state racing
or gaming commission and are referred to as electronic gaming devices (EGDs) or
slot machines. In either case VLTs or slot machines are equivalent casino-style gaming

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252
horse race betting
devicesandaretransparenttothecustomer. Initiallyallracinoswerelegislativelylimited
to VLTs or slot machines and were not permitted to have such table games as blackjack,
roulette, and craps. This restriction was lifted beginning with the Iowa racinos in
2004. Following Iowa’s lead, three additional states have been permitted table games
at racinos, and the trend toward permitting racinos to have table games is expected to
continue.
Many studies have been conducted on the demand for pari-mutuel horse race wager-
ing, but only three such studies have examined the demand for pari-mutuel and slot
machine (VLT) wagering at a single location, that is, a racino (Thalheimer 1998, 2008,
2012). Of particular interest to policy makers and racehorse industry stakeholders is the
interrelationship between the pari-mutuel and gaming sides of the racino operation. All
of the racino studies found that placing slot machines (VLTs) at horse racing racetracks
resulted in signiﬁcant reductions in pari-mutuel wagering at the racetrack, on the order
of 21 to 39 percent. On the other hand, these studies also found that slot machine (VLT)
wagering increases signiﬁcantly on days when there is wagering on live, and/or import,
simulcast races at the racetrack. In particular, since enabling racino legislation focuses
on the preservation of live racing, it is of interest that slot machine (VLT) wagering
was found to increase from 13 to 18 percent on live race days. The conclusion that can
be drawn from these results is that the crossover between the racing and gaming sides
of the racino is one way, from racing to casino gaming. Existing horse race customers
place fewer bets on the races and play the slot machines (VLTs) when they become
available. New customers, attracted by the slot machines (VLTs), bet, on net, on the
gaming machines and not on the races. It should be noted that pari-mutuel revenue is
a very small percentage of total gaming and pari-mutuel racino revenue. For example,
consider that in 2002 VLT and pari-mutuel revenues at the Mountaineer Racetrack and
Gaming Resort (Mountaineer) racino in West Virginia were $221 million and $16 mil-
lion, respectively. Therefore, the relatively large percentage reduction in pari-mutuel
revenue from slot machines (VLTs) at racetracks results in a small revenue loss relative
to the very large gain in slot machine (VLT) revenue from a smaller percentage increase
due to the presence of live racing at the racetrack.
Unique to racino legislation is the allocation of a statutorily set percentage of gaming
revenue to purses to support racing and breeding operations in the state. With a few
exceptions for casinos in two racino states (Maryland and Pennsylvania), this is not the
case for casinos in all other states. Purse allocations from racino gaming revenues have
resulted in large increases in purses as intended by the enabling legislation even as pari-
mutuel wagering revenue has continued to decline. In one racino study (Thalheimer
2008), an analysis was made of revenues generated by purses relative to their cost
at Mountaineer. It was shown in this study and others that demand for pari-mutuel
wagering was highly inelastic with respect to purses. As a result, even with the large
increase in purses from VLT revenue, the revenue from pari-mutuel wagering did not
increase sufﬁciently to cover the cost of purses. On the gaming side of the racino
operation, the relationship of VLT wagering to purses was found to be insigniﬁcant.
As a result of the statistically weak relationship between purses and wagering on both

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the economics of racetrack–casino (racino) gambling
253
sides of the racino operation, the change in racino revenue with respect to a very large
increase in purses was not sufﬁcient to cover a meaningful portion of the cost of purses.
There is, however, another effect of the purse subsidy from gaming revenue that
cannot be overlooked. Competitive purses are necessary to attract horsemen in order
to conduct live racing at the racetrack. Without the purse subsidy from gaming revenue,
the level of purses from pari-mutuel wagering alone would not be sufﬁcient to fund
horsemen’s operations at Mountaineer, especially on a year-round basis as required
under the statutes. If year-round live racing were to have ceased at the racetrack, there
would have been an 18 percent loss in VLT wagering and revenue. This loss would have
been greater than the cost of purses. This ﬁnding was based on the estimated reduction
in VLT wagering if live racing were to have ceased. Stated another way, the operation of
live racing at the racetrack was found to generate VLT revenue which would more than
cover the cost of purses. A smaller amount of pari-mutuel revenue is also generated
from wagering on the live races. Total revenue from both sides of the racino operation,
therefore, was sufﬁcient to more than cover the cost of purses from VLT revenue and
to contribute to the operating cost of the racino operation.
Other ﬁndings of racino studies are worth noting. Thalheimer (1998) found that
if the number of slot machines (VLTs) is too small gaming revenue may not be large
enough to offset the decline in pari-mutuel revenue. Thalheimer (2008) later found
that lifting government restrictions on the number and type of gaming machines, the
placement of those machines, and bet limits resulted in signiﬁcant gains in slot machine
(VLT) wagering and corresponding reductions in pari-mutuel wagering. These results
demonstrate that allowing management to more freely react to changes in consumer
demand by lifting government restrictions on slot machine (VLT) play may result in
large increases in gaming revenue. Finally Thalheimer (2012) found that adding table
games to a slot machine racino reduced pari-mutuel wagering by 16 percent and slot
machine wagering by 8 percent.
Based on ﬁndings in the literature the outlook for the pari-mutuel racing industry
is mixed. On a positive note, the presence of live racing has been found to generate
signiﬁcant racino gaming revenues. However, pari-mutuel wagering has continued to
decline, even with large increases in purses funded by racino gaming revenues. Pari-
mutuel revenue at racinos is much less than gaming revenue. The long-run viability
of the pari-mutuel racing industry will depend on the ability of racing to generate
increased revenue from racing customers and thus, cover the cost of racing.
Notes
1. Even though this chapter is restricted to racino gambling in the United States, it should
be noted that racino gambling is also permitted throughout Canada. At this writing no
academic studies on the economics of racino gaming in Canada have been published.
2. In 2010 greyhound (dog) racing was conducted in seven states and accounted for only
6percentof totalpari-mutueldogandhorseracing(Associationof RacingCommissioners

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254
horse race betting
International 2010). Jai alai is conducted only in the state of Florida, and pari-mutuel
wagering on this product is minimal.
3. Live greyhound racing was conducted in 6 of the 34 states that had live horse racing and
in Alabama where there is no live horse racing but where simulcast horse race wagering
does take place.
4. In some racino states a percentage of gaming revenue is also allocated to racehorse
(greyhound) breeder awards.
5. A number of other studies on casino gaming have been published, but in each case the
dependent variable is casino revenue,which is not a demand variable since it is the product
of gaming price (win percentage) and the demand variable, wagering. The price variable
is also a demand determinant (independent variable), which results in biased estimates
of the revenue model coefﬁcients. The interested reader is referred to Thalheimer and Ali
(2003) for a review of the casino revenue studies.
6. Pari-mutuel revenue includes both on-track wagering and revenue from export simulcasts
of Mountaineer’s live races to other in-state and out-of-state locations.
7. Import simulcast races at the racino included thoroughbred, harness, and greyhound
races exported from other in-state and out-of-state racetracks.
8. In an economic analysis of the supply and demand for racehorse breeding stock (year-
lings), Neibergs and Thalheimer (1997) found that an increase in expected purses results
in an increase in yearling prices (i.e., breeder revenue) and an increase in the supply of
horses.
9. Live race revenue equals $16.2 million on-track wagering times 23 percent of the live
race takeout rate plus $268 million in wagering on export simulcasts of live races at
Mountaineer at other in-state and out-of-state betting locations times 3 percent of the
wagering on the host racetrack (Mountaineer) races remitted by those locations.
10. VLT revenue equals $2.6 billion VLT wagering times the 8.5 percent win percentage.
References
Ali, Mukhtar M., and Richard Thalheimer. 1997. Transportation costs and product demand:
Wagering on pari-mutuel horse racing. Applied Economics 29(4):529–542.
——. 2002. Product choice for a ﬁrm selling related products: A pari-mutuel application.
Applied Economics 34(10):1251–1271
American Gaming Association (AGA). 2010. 2010 State of the states: The AGA survey of casino
entertainment. Washington,D.C.:AGA;http://www.americangaming.org/sites/default/ﬁles/
uploads/docs/sos/aga-sos-2010.pdf.
Association of Racing Commissioners International. 2010. Pari-Mutuel wagering 2010: A
statistical summary. Lexington, Ky.: Association of Racing Commissioners International.
Church, Albert M., and Alok K. Bohara. 1992. Incomplete regulation and the supply of horse
racing. Southern Economic Journal 58(3):732–742.
Coate, Douglas, and Gary Ross. 1974. The Effect of off-track betting in New York City on
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DeGenarro, Ramon P. 1989. The determinants of wagering behavior. Managerial and Decision
Economics 10(3):221–228.
——. 2009. New evidence on the link between government subsidies and wagering. Journal
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Gramm, Marshall, C. Nicholas McKinney, Douglas H. Owens, and Matt E. Ryan. 2007. What
do bettors want? Determinants of pari-mutuel betting preference. American Journal of
Economics and Sociology 66(3):465–491.
Gruen,Arthur. 1976. An inquiry into the economics of race-track gambling. Journal of Political
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McQueen, Patricia A. 2009. “Challenging times for mature markets. Casino Journal, Dec.;
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Morgan,W. Douglas, and Jon DavidVasche. 1979. Horseracing demand, pari-mutuel taxation
and state revenue potential. National Tax Journal 32(2):185–194.
——. 1982. Anoteontheelasticityof demandforwagering. AppliedEconomics 14(5):469–474.
Neibergs, J. Shannon, and Richard Thalheimer. 1997. Price expectations and supply response
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Pennsylvania Gaming Control Board (PGCB). 2010. The economic impact of slot machines
on Pennsylvania’s pari-mutuel wagering industry—Benchmarking the industry: 2006–
2009. Harrisburg, Pa.: PGCB; http://gamingcontrolboard.pa.gov/ﬁles/reports/2009_Pari-
Mutuel_Benchmark_Report.pdf.
Simmons, Susan A., and Robert Sharp. 1987. State lotteries’ effects on thoroughbred horse
racing. Journal of Policy Analysis and Management 6(3):446–448.
Suits, Daniel B. 1979. The elasticity of demand for gambling. Quarterly Journal of Economics
93(1):155–162.
Thalheimer, Richard. 1998. Parimutuel wagering and video gaming: A racetrack portfolio.
Applied Economics 30(4):531–544.
——. 2008. Government restrictions and the demand for casino and parimutuel wagering.
Applied Economics 40:773–791.
——. 2012. The demands for slot Machine and pari-mutuel horse race wagering at a racetrack-
casino. Applied Economics 44(9):1177–1191.
Thalheimer, Richard, and Mukhtar M. Ali. 1992. Demand for parimutuel horse race wagering
with speciﬁc reference to telephone betting. Applied Economics 24(1):137–142.
——. 1995a. Exotic betting opportunities, pricing policies and the demand for parimutuel
horse race wagering. Applied Economics 27(8):689–703.
——. 1995b. Intertrack wagering and the demand for parimutuel horse racing. Journal of
Economics and Business 47(4):369–383.
——. 1995c. The demand for parimutuel horse racing and attendance. Management Science
41(1):129–143.
——. 2003. The demand for casino gaming. Applied Economics 35(8):907–918.
——. 2008a. Pari-mutuel horse race wagering—Competition from within and outside the
industry. In Handbook of Sports and Lottery Markets, edited by Donald B. Hausch and
William T. Ziemba. Amsterdam: Elsevier, 3–15.
——. 2008b. The demand for casino gaming with special reference to the effect of a smoking
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chapter 15
........................................................................................................
THE MODERN RACING LANDSCAPE
AND THE RACETRACK WAGERING
MARKET: COMPONENTS OF
DEMAND, SUBSIDIES, AND
EFFICIENCY
........................................................................................................
ramon p. degennaro and ann b. gillette
Introduction
.............................................................................................................................................................................
In 2012 $11.4 billion was wagered in the United States on horse racing. These dollars
affected state revenues, the equine industry, and racetrack income. Competition for the
wagering dollar has become increasingly dynamic and intense with the introduction of
new wagering and gaming venues. On any given day, a U.S. bettor has the opportunity,
via simulcasting and online betting, to place bets on more than one hundred races
across different tracks. In addition, interstate horse race wagering has become more
competitive and complex across racetracks as state legislatures have approved new
betting venues. Legislative prohibitions against most other forms of gambling in the
United States protected the industry until the advent of state lotteries (New Hampshire
established the ﬁrst in 1964) and, later, casinos and other gaming. By the end of 2013
it is likely horse racings monopoly on online betting will be eroded away as three states
have passed legislation for online gambling by in-state customers and ten others have
passed online poker. Now lotteries, casino and sports gambling, and slot machines also
compete for that wagering dollar.
Over the years the horse racing industry has beneﬁted from several types of local,
state, and federal government subsidies. In recent years, with more and more states
having trouble balancing their budgets, these subsidies, funded by varied sources of

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257
state tax revenues, casinos taxes, and gaming, are coming under increased scrutiny.
Racetrack stakeholders often cite viable returns from such subsidies in terms of higher
wagering handles (the total amount of money wagered) and increased employment in
the horse and agriculture sectors that eventually funnel increased revenues into state
coffers.
As of 2010 statistics compiled unofﬁcially from private data by the Daily Racing
Form (DRF) found that racetracks receiving subsidies from slot machines and casinos
generated on average only two-ﬁfths of the betting handle that nonsubsidized tracks
generated, even after accounting for similar average daily purse distributions (Paulick
Report 2011). They also indicated that the off-track simulcast marketplace is becoming
more of a driver of handle, which allows small tracks that are strategically positioned in
the racing schedule to do relatively well in attracting the wagering dollar. Furthermore
they quote Chris Scherf, executive vice president of the Thoroughbred Racing Asso-
ciation, a racetrack trade group, remarked, “The weakness of the subsidized tracks in
the pari-mutuel market could lead legislators to cut off the subsidies” using arguments
that tracks are not supported by the public. Recently Pennsylvania and Indiana have
reallocated some of their horse racing subsidies to compensate for budgetary shortfalls
in areas such as education. Other states are considering following suit.
Walker and Jackson (2011), however, found support for horse racing’s contribution
to state government revenues, relative to other forms of gambling. Using panel data
analyses from 1985–2000 across all 50 states and ﬁve types of gambling industries,
the authors examined the volume of gambling on total state government receipts’ net
of federal government transfer funding. Accounting for competition across states and
both gambling and non-gambling entertainment alternatives for the consumer dollar,
they found that for the typical state horse racing and lotteries tended to increase state
revenues while casinos and greyhound racing tended to have a negative effect. Walker
and Jackson emphasized that their results were for the “average” state since they did
not ﬁnd consistency in the complementary (substitute) relationship among different
gaming options across states. These differences across states arise because of varieties in
the types of gambling industries within a state, types of non-gambling entertainment
industries available, regulations, and relative tax rates on various types of spending.
Another recent study by Forrest, Gulley, and Simmons (2010) using bookmaker data
for horse wagering in the United Kingdom also concludeed that bettors view other
gambling options, such as dog races, soccer games, and numbers betting, as substitutes.
In particular, they found evidence that horse racing bettors are value-sensitive and
respond to changes in relative wagering prices and taxes, although the cross-price
elasticity effects are hard to measure. Earlier studies looked at the effect of a single
gambling industry on horse racing handle and state tax revenues. For example, using
data from 1960–1987 of racetracks on the Kentucky–Ohio border, Thalheimer and Ali
(1995) found that although the lottery reduces the handle at racetracks it increases
overall state tax revenues. The competitive interaction of gambling industries and their
consequent effect on state revenues appears to be a fruitful area for further study.

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258
horse race betting
Complicating estimates of the return on racing subsidies for state taxpayers is the fact
that the ownership of racetracks has been changing. Private investors are increasingly
leasing state-owned tracks and acquiring control of a portfolio of tracks across state
lines. This transfer away from state ownership of racetracks has prompted gaming
venues, whose state surcharges help subsidize racing, to promote the argument that
the horse racing industry should be self-sufﬁcient. For example, in Maryland, this
self-sufﬁciency argument has resonated with the state legislature, which is angry that
out-of-state corporations currently own the Maryland Jockey Club. The Maryland
legislature (and other states) is legislation that would make it more difﬁcult to provide
support for certain players put forth in the industry. After two years of negotiations
between track owners, horsemen, and the legislature the horsemen have ceded some
of their slot revenue to the track management. These events highlight the political
complexities affecting the strategic competition for the racetrack wagering dollar.
The Modern Racing Landscape
.............................................................................................................................................................................
The total economic impact of the equine industry in the United States is $101.5 billion.
The industry contributes $1.9 billion to government taxes and fees, according to the
last commissioned study performed by Deloitte Consulting LLP (2005). The horse
racing industry, which includes racetracks and off-track betting operations, horses
in training and breeding, contributed $10.697 billion directly to 2005 GDP, with an
additional economic impact of $26.1 billion; employed 146,625 individuals in full-
time jobs; and indirectly employed 383,826. Currently 32 states allow horse racing.
The dominant racing breeds and their relative dollar contributions to horse racing
are: Thoroughbred (78%), Quarter horse (6%), and others, including Standardbred or
harness racing (16%).
The United States is the world leader in the number of races run and the num-
ber of registered foals bred for racing but fourth in overall betting handle behind
Japan, France, and Australia. The total betting handle in the United States has declined
steadily in recent years, from a high of $15.180 billion in 2003 to $11.410 billion
in 2010. Today the host track of a race is just one intermediary for betting on
the race, as simulcast and online bets increasingly contribute to the overall amount
wagered. Signiﬁcantly, since 1996, when the Jockey Club began collecting data, the
on-track handle has steadily declined to $1.199 billion from $2.944 billion while
the off-track handle rose steadily until 2004, to $13.239 billion, before dropping
steadily to 1998 levels. Off-track wagering still dominates the share of total wagering at
89.5 percent.1.
U.S.racetracksuseapari-mutuelwageringsystem. Inpari-mutuelbettingthepayoffs
are set collectively. In essence, bettors are betting against each other instead of against
designated odds set by a bookmaker. The takeout is the amount taken by the track

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the modern racing landscape and the racetrack wagering market
259
operators and government and typically runs 15 to 30 percent of handle depending
on the type of wager. At most tracks the takeout is higher for more complex wagers.
Studies have examined the effect of takeout rates on trading volume and, as expected,
have found an elastic price elasticity of demand (for example, Thalheimer and Ali
1995). Interestingly, Gramm et al. (2007) found that the elasticity of track takeout
differs across wager types. This is not surprising since the takeout determines the cost
and the risk-reward tradeoff of placing a given type of bet.
Recent evidence from changes in California takeout rates highlights how online
betting and simulcasting have heightened this elasticity effect. At the beginning of 2012
the California Horse Racing Board implemented a higher takeout on certain wagers.
The response from the racing community was immediate. Players Boycott, an online
group, quickly formed and advocated a boycott on California thoroughbred racing. The
boycott became ofﬁcial when the Horseplayers Association of North America, whose
ﬁfteen hundred members bet $65 million annually, promoted the boycott. By August
racetrack executives had proposed reducing the takeout for these bets.
The variety of bets offered and the allocation of total betting volume across different
types of bets have changed over the past few decades. Intra-race exotic bets and multi-
race exotics at and across racetracks are now offered alongside the standard bets of win
(which requires the bettor to select the race winner), place (which typically returns a
smaller amount if the chosen horse ﬁnishes ﬁrst or second), and show (which typically
pays a still smaller amount if the selected horse ﬁnishes in the top three). Among
exotic bets, the exacta requires the bettor’s two horses to ﬁnish in the exact win-place
order speciﬁed. Trifecta and superfecta wagers extend their selection order to third
and fourth positions, respectively. A quinella bet is an attractive alternative for less
self-assured bettors because it allows the selected horses to ﬁnish in either order. The
tradeoff is a smaller payoff if the bettor wins.
Multi-race exotic bets require the bettor to choose the winner in each of a speci-
ﬁed number of consecutive races, typically called the daily double, Pick 3, Pick 4, and
Pick 6. These multi-race exotics attract even greater wagering pools if there are carry-
overs. Carryovers occur if no one wins a given wager for that day. This happens more
frequently for wagers with a low probability of success, such as a Pick 6 wager. If no
one correctly selects all six winners, then a portion is paid to the bettors who selected
the most consecutive winners without a loss and the majority of the pool (typically
75%) is carried over to the next race day. This continues until there is a winner. This
means that the previous day’s track patrons subsidize the next day’s track patrons. If the
dollar amount of wagers on the exotic bet is constant through time, carryovers increase
the expected return on bets when the carryover is large. Naturally patrons ﬁnd this
attractive.
Ramon DeGennaro (2009) found that in standardbred racing a dollar of Pick 6
carryover is associated with almost a $2 increase in total betting. In particular, he found
that the ratio of the Pick 6 carryover to the total amount bet averaged 0.4 percent of the
amount that gamblers bet on the entire program but ranged as high as 11.1 percent.
He also found that the mean of the amount bet on straight wagers was barely a third

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260
horse race betting
of the mean handle, even though the number of straight wagering opportunities on a
race card is greater than the number of exotic bets available. In thoroughbred racing,
Gramm et al. found that large consecutive carryovers increase handle on all wagers and
that a large Pick 6 carryover tends to increase total betting volume by 25 to 43 percent.
State governments and racetracks are looking for new types of wagering and gaming
venues to attract new gaming dollars as well as ways to keep wagering dollars in state.
Purse levels and distribution can affect the quantity and quality of horses racing at a
particular track and thereby affect total handle. The purse distribution varies across
states, and prior to 1970 most thoroughbred tracks paid only the ﬁrst four ﬁnishers in
a race. In 1975 Florida implemented a novel distribution scheme that pays all ﬁnishers
in the race. Today several states have adopted a similar distribution format and others
have it under consideration. This trend is also evident in standardbred racing, as exem-
pliﬁed by Woodbine Entertainment Group’s announcement that starting December 1,
2011, they would pay all starters in the race a nominal amount. Using experiments,
DeGennaro and Ann Gillette (2013) examined the track choices made by individuals
and racehorse syndicate groups under different racetrack purse distributions. Syndi-
cate ownership is becoming increasingly prominent in the industry. DeGennaro and
Gillette found that in general both individuals and syndicate groups prefer tracks that
pay something to all ﬁnishers something unless there is a signiﬁcant probability that
they have a superior horse. These ﬁndings have implications for the competition for
quality horses across racetracks holding congruent racing meets and, therefore, for a
track’s share of the overall racing handle.
In addition, direct competition for pari-mutuel horse race betting dollars in the
United States has become more intense. For example, pari-mutuel futures markets have
in recent years become common for notable races such as for the Kentucky Derby and
Breeders’ Cup races. Instant Racing, also known as historical racing, is also becoming
more common. Instant racing is a pari-mutuel betting system that allows players to
wager on previously run races at a video lottery terminal (VLT). There are more than
21,000 digitized videos of historic races. Instant Racing was developed in 2000 by
Oaklawn Park in association with AmTote, Inc., and has generated millions of dollars in
purses for the track (Blood-Horse, Aug. 22, 2011). Several states have recently allowed it,
most notably Kentucky. For each historic race played, Instant Racing players are given
handicapping information that does not include the date or location of the historic
race or the names of the jockey or horses. Players use this information to select three
horses they think will ﬁnish in the top three positions. As in live racing players wager
against each other, and winning payoffs are distributed after the takeout from the pool.
Winners receive graduated payoffs for selecting the top three ﬁnishers, the ﬁrst three
horses in any order, the top two ﬁnishers, the winner, or any two of the top three
ﬁnishers.
In 2011 New Jersey became the ﬁrst U.S. state to introduce Exchange Wagering (EW),
a form of Internet betting that is prominent in the United Kingdom and Australia. EW
differs from pari-mutuel betting in that an individual can make a peer-to-peer bet with
just one or more individuals who each agree to the odds before the exchange takes place.

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the modern racing landscape and the racetrack wagering market
261
This type of betting also introduces a “betting-to-lose” category that is not available in
pari-mutuel betting: a lay bet, as it is called. This is controversial, since a jockey can
produce the loss by manipulating the outcome. This integrity issue has raised concerns
with the Jockey Guild, thoroughbred owners, breeders, and track associations.
The Components of Demand for
Racetrack Wagering
.............................................................................................................................................................................
An important question facing the racing industry is how to increase demand for race-
track wagering in today’s dynamic competitive landscape. Classiﬁcation and quality
of races differ and affect betting volume, with higher quality races tending to attract
a larger dollar amount of wagers. Quality of a race is often measured by purse size
or the grade classiﬁcation of the race. Thoroughbred races are classiﬁed into six levels
of descending quality and prestige: stakes, allowances, maiden special weight, starter
allowance, claiming and maiden claiming.
Stakes races attract the best horses and pay out the highest purses. Allowance races
are often run with conditions for entry. For example, they may be restricted to horses
that have yet to win a race other than a maiden race or to certain age groups or sex. Any
horse in a claiming race is eligible to be claimed (bought). In order to claim a horse
owners or trainers must notify, in writing, the racing ofﬁce no later than ten minutes
before the scheduled post time and have the appropriate funds in their racing account.
The transfer of ownership occurs at the beginning of the race, but all purse and prize
monies are retained by the prior owner (in the event of the death of a claimed horse
in a race, the new ownership is ﬁscally responsible, though many racing organizations
provide insurance for such causalities and as of 2013 tracks are reevaluating this liability
transfer.). In the event that two or more owner/trainers claim the same horse a draw is
held to determine the new ownership. Gramm et al. (2007) found that wagering volume
increases with the quality of the race. In particular, stake races attract roughly 15–35
percent greater betting volume relative to their control allowance race group, whereas
mid-level quality races attract 22–26 percent less volume and low-level claiming races
even less, 37–48 percent less.
FurthermoreChou,DeGennaro,andSauer(2000)useddatafromracesatSantaAnita
Park, a major track in California (USA), in 1987 to demonstrate that the dispersion of
the race odds within a race is smaller using claiming races—a price system—than it
is using a command system dictated by a highly skilled planner, the racing secretary.
This approach is the allowance (or conditioned) approach. Chou, DeGennaro, and
Sauer also studied the behavior of horse owners by comparing their self-selection into
these two common methods of controlling the ability of horses entered in races. Under
the claiming approach, the racing secretary sets the claiming price, letting the owners
determine if their horses belong in the race. Horses that enter are explicitly being offered

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262
horse race betting
for sale at the predetermined claiming price. Under the allowance approach the racing
secretary writes a list of restrictions that exclude some potential entrants which are
likely to make for an uncompetitive race because they are either too good or too bad in
comparison to the other entrants. The simplest restrictions typically come in the form
of age and previous racing success, such as earnings or number of wins. Restrictions
may be more complex, though.
A quarter of the races are conditioned races. Chou, DeGennaro, and Sauer speculated
on why they remain common despite producing races with a wider dispersion of betting
odds, which they interpret as being less competitive. They argue that the reason is prob-
ably the wedge between a horse’s current racing ability and its total value. The value of
horses with the potential to produce quality offspring is often disproportionately large
in comparison to their value as racehorses. They give the example of two horses, each
worth $300,000. The value of one of the two is distributed equally between its current
racing value and its future breeding value. The other horse derives its entire value from
its current racing ability. The owner of the ﬁrst horse will not enter a race with a claiming
price of $300, 000 because the horse has little or no chance of being competitive. But the
owner cannot enter a race with a claiming price of $150,000, either, because someone
will claim the horse at a below-market price. Similarly, claiming races are a poor way to
match competitive ﬁelds of older horses against very young horses that have yet to reach
their full with potential with a large portion of their racing earnings to come in the
future. Conditioned or allowance races are better suited to match horses of comparable
ability when the efﬁciency lost to the command or non-price system is smaller than the
wedge between a horse’s value in excess of his or her current racing ability.
Gramm et al. formally investigated the demand for racetrack wagering assuming
that there are two primary types of bettors: an informed bettor who is risk-averse and
whose demand for racetrack wagering is dependent on both race-speciﬁc returns and
information quality and an uninformed bettor who is either risk-neutral or risk-loving
with high costs to gathering and processing information. Gramm et al. focuses on
whether bettors are deterred by lower returns or by noisier information about a betting
interest.
Gramm et al. note that from 1985 to 2002 the total amount wagered on thoroughbred
races in the United States almost doubled despite a concurrent 20 percent drop in
the number of races run. The authors suggest that the rise in handle is primarily
attributable to the ascent of off-track wagering venues. However, they acknowledge
that new exotic bets play a signiﬁcant part. They found that during this time frame,
adjusting for inﬂation, total thoroughbred horse wagering increased 21 percent while
per-race wagering more than doubled, increasing by 53 percent.
Using 2002 fall thoroughbred race data from twelve major racetracks, Gramm et al.
examined the attributes of a given race that may affect a bettor’s preference to wager.
They hypothesized that both types of bettors prefer higher returns but that informed
bettors reduce wagering when information is noisier, whereas uninformed bettors are
unaffected. In their analyses the return on a given wager was related to the track takeout
and whether or not it was a carryover wager. The larger the track takeout, the higher

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the modern racing landscape and the racetrack wagering market
263
the price of wagering (or, alternatively, the lower the expected return), and one expects
the wagering volume to be less. A carryover raises the expected return to that speciﬁc
wager, and one would expect greater interest in wagering.
Gramm et al. hypothesized that risk is increased for a bettor when either there is more
noise in a wager or less information available on a betting interest. The variables they
used to classify as increasing the noise of information to an informed bettor are: larger
ﬁeld size, lower race quality, competitiveness of the race, and poor track conditions.
The effect of race length is uncertain. On the one hand, the longer the race, the more
likely that racing luck can be overcome so that quality dominates. For example, a bad
start that cannot be overcome in six furlongs might be surmountable over 10 furlongs.
On the other hand, a longer race also increases uncertainty because there is more time
for random events to occur during the race. Gramm et al. used ordinary least squares
regressions with heteroskedasticity robust standard errors to regress the log of race
handle on 38 independent variables. Two different regression models using purse size
and race classiﬁcation measures were used to account for the race quality.
They found that for a given race, higher quality races (as measured by purse size or
grade classiﬁcation of race, which is consistent with DeGennaro 1989), more compet-
itive races (as measured by the dispersion of the odds of the race, which justiﬁes the
conjecture in Chou, DeGennaro, and Sauer 2000), and turf races increased the volume
of betting while higher pari-mutuel takeout, poorer track conditions, and the occur-
rence of concurrent simulcast races lowered wagering volume. Most of these results are
intuitive. A higher takeout lowers the expected return, poorer track conditions reduce
the beneﬁt of handicapping skill, and competition for the bettors’ wagering dollar is
sure to siphon off bets.
Interestingly, these race attributes can vary for different types of wagers in a given
race. Speciﬁcally, betting volume by quality of race increases in the show pool but has
little effect on exacta and trifecta pools. We can think of two reasons why the show pool
might increase with race quality more than it does for exotic wagers. First, casual bettors
are probably more likely to bet on high-class horses; to them, the sporting aspect of the
race is relatively more attractive than gambling. If these casual bettors are more risk-
averse, then they are more likely to choose safer wagers. Second, high-class races, drawn
from the upper tail of the distribution of quality, are more likely to feature a horse
that dominates the betting. Coupled with rules mandating a minimum payoff (usually
either 5 or 10% of the amount bet), a dominant horse allows bettors to place large
wagers with higher expected returns than other bets. A horse with a 98 percent chance
of ﬁnishing in the top three actually offers an expected proﬁt, despite the takeout.2
Furthermore, Gramm et al. found that each additional betting interest in a race
(anotherentrant)hadanonlineareffectonbettingvolume. Forrelativelysmallnumbers
of entrants they found that betting volume tended to increase with an additional entrant
but that this began to diminish with around 10 or 12 entrants. Thus the optimal ﬁeld
size for maximizing the size of the wagering pool is 10 to 12. This varies across betting
wagers, although the estimates are not signiﬁcantly different: 10 is the optimal ﬁeld
size to maximize the amount bet on trifectas, 11 for win and place bets, and 12 for

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horse race betting
show and exacta wagers. Gramm et al. suggested that this nonlinear relationship, along
with evidence of lower wagering volume for maiden races, which offer bettors less
information, support the conjecture that informed bettors reduce betting volume in
response to increased noise. They also found evidence that there is less betting volume
in races with race restrictions, such as a restriction to just ﬁllies and mares as well as to
state-bred horses.
To examine the effects that differential returns to wagering have on the volume
wagered, Gramm et al. analyzed track takeout, carryovers, and competition. In their
data, the effects of track takeout differed across wagers. Speciﬁcally, the demand for
wagering was price elastic for straight wagers and exactas but inelastic for trifecta
wagers. Carryovers increased betting pools, as expected. In particular, large consecutive
carryoversincreasedhandleonallwagers,andalargePick6carryovertendedtoincrease
total betting volume by 25 to 43 percent. Betting venues that face competition for race
wagers, such as through simulcasting, tend to experience lower betting volume. For
each additional race run in the same hour, betting volume declined by 3 to 5 percent for
each form of wager. As expected, volume wagered was related to the day of the week,
with Saturdays being the most popular followed by Fridays and Wednesdays.
Moreover, they found that track patrons also bet more on races with higher purses,
typically stakes races, with a purse elasticity of 0.212. This means that on average
for a 1 percent increase in the purse the volume wagered increased by 0.212 percent.
Competitiveness of race (as measured by a modiﬁed Herﬁndahl index of the spread
of odds) did not affect total handle, though it did affect different wagering types for
a given race. To protect the turf courses over extended race day meets, thoroughbreds
race on turf less frequently than on dirt or synthetic surfaces. Interestingly, turf races
typically are associated with increased wagering volume of 6–11 percent. This may be
due to the relative freshness appeal of races run on the surface at a given meet or simply
because there is less handicapping noise because in the United States the pool of horses
typically racing on turf is smaller.
DeGennaro (1989, 2009) explored the determinants of wagering in the standardbred
industry.3 Unique among racehorses, standardbreds race on either the pacing gait or
the trotting gait. Pacers move both legs on one side of their bodies simultaneously.
Trotters move their diagonal legs simultaneously. Trotters and pacers almost never race
against each other. In DeGennaro’s 2009 study, the number of races scheduled for
trotters ranged from zero to six. Weather impairs the track 8.5 percent of the time, and
2.8 percent of race cards are contested on state holidays. The number of races per day
ranges from 8 to 12, with a mean of almost 11. Races for very young horses appear on
11.5 percent of the race cards; for three-year-olds the ﬁgure is 22.7 percent.
DeGennaro estimated the following model:
Ht = a0 + a1 TrackCondt + a2 Subsidyt + a3 Tempt + a4 Racest + a5 Trotst
+ a6 OtherFeaturet + a7 Tuesdayt + a8 Wednesdayt + a9 Thursdayt
+ a10 Fridayt + a11 Holidayt + a12 Pick6t + et
(15.1)

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the modern racing landscape and the racetrack wagering market
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ThevariableTrackcond isabinaryvariablethatequalsoneif thetracksurfaceisimpaired
for any race on the card and zero otherwise. Subsidy is a binary variable that equals one
if a sire stakes is contested on the race card (zero otherwise). Temp is air temperature.
Races is the number of live races held that day. Trots is the number of live trotting
races held that day. OtherFeature is one if a feature race other than a sire stakes is
contested (zero otherwise). The days of the week are unity on the corresponding days
(zero otherwise). Holiday equals unity for weekends and holidays (zero otherwise). In
this speciﬁcation a12 = 0 for the observations for which Pick6 is unavailable.
Economic intuition and DeGennaro’s 1989 results predicted the signs of the coef-
ﬁcients. The coefﬁcient on Trackcond should be negative because an impaired racing
surface almost always traces to bad weather; bad weather keeps some patrons home, and
some of them probably do not wager off-track instead. We defer discussion of Subsidy
until later, noting only that its coefﬁcient should be positive here. High temperatures are
almost never a problem, but cold weather sometimes keeps people at home. Therefore,
the sign on the coefﬁcient of Temp should be negative. The more races contested, the
higher the mutuel handle should be. A feature event probably attracts more betting, just
as the Super Bowl or World Cup ﬁnal attracts more betting than regular season games.
Conventional wisdom suggests that the coefﬁcient on Trots should be negative. Because
potential patrons have more time on holidays and on weekends, the signs on the week-
day dummy variables are likely to be negative, while those on Fridays and holidays are
likely to be positive. DeGennaro assumed that factors such as competition from other
gambling opportunities or sources of entertainment were too small to matter or that
they were uncorrelated with the other regressors and were included in the intercept.
DeGennaro estimated equation (15.1) using 436 daily observations, also using the
280 observations for which Pick 6 was available. The results show that most coefﬁ-
cient estimates are intuitively pleasing and much like those in previous research. The
exception is OtherFeature, which is negative and not close to statistically signiﬁcant.
The economic implications are tiny, as the point estimate implies a decline of less than
1 percent of the average daily mean. The coefﬁcient on the number of races contested
on a program is reliably positive, with each extra race associated with an increased
betting handle of about 16.6 percent. Sundays and Tuesdays have lower handles, all else
being equal (by 13.8%), while Fridays and Saturdays have higher handles (by almost
20%). Breeders’ Crown events dwarf these estimates. A Breeders’ Crown event is asso-
ciated with an increase of almost twice the mean total handle. Having this variable
undoubtedly contributes to the adjusted R2 of 0.725 in the model without Pick6 and
0.637 in the model using the subset of observations for which Pick6 is available. The
time trend is positive in both models and reliably so in the model using all observations,
implying that each subsequent race day tends to be associated with an increased handle
of about 0.04 percent. The Pick 6 carryover is reliably associated with an increase in
handle, and the estimate means that a dollar of carryover tends to increase total betting
by $1.90.
DeGennaro (2009) concluded that the determinants of wagering volume have
remained fairly constant since his earlier study, despite signiﬁcant differences in the

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horse race betting
nature of the data. The two studies used data from racetracks in different countries,
operating on different days of the week, and separated by over 20 years, during which
regulations, betting technology, and institutional features have introduced new com-
petition for gamblers’ dollars. More extensive data allowed him to conﬁrm that the
number of races (constant in his previous study) and high-quality races tend to increase
betting volume. The Pick 6 carryover is a subsidy from previous patrons to current
patrons. Current patrons bet more because the payout is larger, making the expected
return better. One noticeable change in the later study is that nonworking days have
no reliable effect on mutuel handle. Perhaps modern patrons have more ﬂexible work-
ing hours than their predecessors, or perhaps off-track betting makes workdays less
important.
State Breeding Subsidies
.............................................................................................................................................................................
Proponents of subsidization of the racetrack and breeding industry argue that tan-
gible beneﬁts accrue to the state by means of increased tax revenues through larger
wagering handles and agriculture industry job creation (see DeGennaro 1989, 2009).
Popular subsidies are breeder incentives which come in several forms, typically for
performance and residency. For example, the sales taxes paid for breeding a stal-
lion to a mare in Kentucky are used to pay incentives to breeders whose horses have
won races. The amount of incentive varies by type of stakes, with quality receiv-
ing more, and with regard to whether the race is in- or out-of-state. In particular,
rewarding quality with a strong industry marketing appeal, a Kentucky breeder of
the Kentucky Derby and Oaks winners are awarded an incentive of $100,000 each.
Typically conditions for eligibility that support the breeding industry are attached.
Under this particular subsidy the mare must board in Kentucky from live cover until
foaling.
Breeders’Awards programs are also commonplace for other racing breeds. For exam-
ple, the New York Breeders’ Awards program is 10 percent of the state breeding farm
account, which comes from remittances as a percentage of total betting handle from
the state’s harness tracks and off-track betting parlors and a legislatively approved per-
centage of VLT revenues. The stated purpose of the program is to provide an incentive
to promote agriculture through the breeding of standardbred horses in New York State.
Awards are allocated on both performance and residency. Performance based awards
reward for each level of NYSS (New York Sire Stakes) racing, with higher percentages
of payouts going to the higher quality classiﬁcations of the race and to the top ﬁve
ﬁnishers. The residency component of the bonus awards rewards breeders for keeping
their mares in New York State. Eligibility requires the mare to reside in state for at least
180 consecutive days during breeding season.
Yet an important question remains: how much of a return are taxpayers getting for
such subsidies? Using data from standardbred racing, DeGennaro (1989) investigated

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the modern racing landscape and the racetrack wagering market
267
the inﬂuence of sires stakes, races open only to state-bred horses, on the volume of
wagering in standardbred races. He found that assistance to the racing industry in the
form of subsidized purses for horses bred or foaled within a given jurisdiction has
no statistically reliable inﬂuence on the volume of wagering in daily data. If there are
no beneﬁts other than increased wagering handle, DeGennaro concluded, the subsidy
amounts to a direct transfer from taxpayers to the breeding industry.
We have considered DeGennaro’s (2009) research in the context of wagering, but
that analysis also revisited the standardbred sire stakes subsidy. Despite the dramatic
differences between the data in his 1989 and 2009 papers, DeGennaro, using daily data,
found similar qualitative results for the effect of the sire stakes subsidy on total betting
handle. However, using data from individual races (which were not available for his
earlier study), he found that subsidized races do show a small but statistically signiﬁcant
increase in wagering, indicating that the government earns at least some return on its
investment. Despite the statistical signiﬁcance, he concluded that the increase is simply
too small to detect in daily data, and far too small to justify the government subsidy
purely on the economic beneﬁts of increased wagering.
For example, the coefﬁcient on the binary variable Subsidy, which equals one if a sire
stakes is contested on the race card, never has more than about half the inﬂuence of a
feature race other than a sire stake, and in the speciﬁcations with Pick6, the effect of the
subsidy virtually vanishes. By contrast, a dollar of Pick 6 carryover is associated with
almost a $2 increase in total betting.
The data in the 2009 paper are much better suited to study the subsidy because
they include individual race data as well as more than three times the number of
daily observations as DeGennaro (1989), and he uses the national unemployment
rate and a time trend. These allow for changes in the economic welfare of the track’s
patrons (which Ali and Thalheimer 1997 found to be important). DeGennaro also
includes binary variables to control for Breeders’Crown races. Similar to thoroughbred
Breeders’ Cup races, standardbred Breeders’ Crowns are of immense importance to the
sport. DeGennaro’s (1989) data do not include any Breeders’ Crown races.
DeGennaro’s (2009) data include the ages of the horses. This variable was unavail-
able in 1989. This is particularly important because the state subsidizes races only
for two- and three-year-old horses. Younger horses tend to be unproven and more
erratic, reducing the advantage of handicapping skill. Gramm et al. (2007) sug-
gested that informed bettors, having less information to process, would bet less. In
addition, the owners and trainers of these young horses have a larger information
advantage over the betting public. Less informed serious gamblers probably bet less
in the face of this adverse-information problem. Because the state only subsidizes
races for young horses, this adverse-information problem might explain the some-
times negative sign on Subsidy in the daily data. The subsidy might induce patrons
to bet more, but if this is entangled with a tendency to bet less on younger horses,
it might be impossible to detect in the data. Three-year-old horses are less prone to
this than are two-year-olds because most three-year-old horses raced the previous year.
DeGennaro (2009) disentangled the effect of the subsidy from the effect of the age

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horse race betting
group by adding variables to control for unsubsidized races restricted to two- and
three-year-old horses.
The results, though, rule out this explanation for why the sire stakes does not increase
wagering. First, all of the estimates on control variables for age are positive, though
never statistically signiﬁcant. Gamblers do not bet less, and may even bet more, on
unsubsidized races that are restricted to younger horses. In contrast, the coefﬁcients on
variables which measure deviations from the unsubsidized races that are restricted to
the same age groups are negative in four of six cases.
The large increase in exotic wagers does not explain the insigniﬁcance of the subsidy,
either. DeGennaro repeated his tests using only the straight wagering totals and found
no important changes.
DeGennaro’s (2009) results, therefore, mirror his earlier results. After controlling
for several other factors that explain wagering volume, the sire stakes subsidy sim-
ply is not positively correlated with total betting volume on the day these races are
held. The evidence supports previous research showing that this particular govern-
ment subsidy does not generate additional revenue—at least in the short term—to
offset the cost of the subsidy. The loss to the state from the subsidy is not as large as
it ﬁrst appears, though, because the industry itself funds part of the sire stakes’ purse
through stallion assessments, contributions from breeding farms, and from entry fees
paid by horse owners. In addition, a portion of revenues from slot machines located
at the racetrack is directed to the sire stakes program at the racetrack that supplied
the data.
In addition, DeGennaro’s results using individual races are the ﬁrst to show that
the state may in fact recoup part of its investment because the sire stakes subsidy is
associated with increased betting on subsidized races. However, the estimated magni-
tude of the increase is far too small to compensate for the subsidy, and taxpayers can
still ask why states continue to subsidize this aspect of the racing industry. DeGennaro
offers some possible explanations. One traces to public choice theory. Governments
subsidize many things, not just horse racing. Perhaps the better question is why gov-
ernments subsidize racing rather than some other activity. To justify the subsidy on
economic grounds, one must ﬁnd more (taxable) economic activity either in other
areas or in other time periods that trace to the subsidy. For example, because the horses
compete for higher purses, their earning potential is higher, and they sell for higher
prices. This means that the state could recoup part of the subsidy through higher taxes
on horses sold. Another possibility is that the state overtaxes the horse racing indus-
try, and the subsidy is a way to reduce the effective tax rate. It would be simpler and
more efﬁcient economically to reduce the tax that is too high, but this might be politi-
cally less viable. “Subsidizing jobs” makes a better campaign sound bite than reducing
“sin taxes.”
Furthermore DeGennaro conjectures that conceivably the racing industry offers a
politically attractive way to legalize casino games, including table games and VLTs.
Taking the step from no gambling to casino games might be a bridge too far, but adding
gaming to existing gambling opportunities might not be. Preserving horse racing as an

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the modern racing landscape and the racetrack wagering market
269
avenue to institute gaming in the future might make sense. One might also argue that
future tax revenues from gambling are higher because of the current subsidy. Races
with better horses tend to generate more betting than those featuring lesser animals,
and sire stakes horses are better than most others. However, we know of no research that
supports the link between racehorse quality (or subsidies) and higher betting through
time. This represents a fertile ground for additional research.
Promoters of the subsidy could argue as well that the racing industry provides a
public good. For example, perhaps having a racetrack or breeding farm nearby attracts
businesses and tourists, which locate near or visit an area with a racetrack instead of a
competing location. The Kentucky Cabinet for Economic Development produced an
advertisement that reﬂects this (see US Airways magazine, June 2007, p. 129). Breeding
farms and racetracks offer open areas, green areas, and access to animals, which many
people enjoy, and many tracks feature areas for children to play. The atmosphere is
similar to a baseball stadium or even a park or zoo, and for better or worse, states do
subsidize these activities. Viewed this way, racetracks provide non-pecuniary beneﬁts to
the area. Perhaps, then, the state’s subsidy to the racing industry permits it to economize
on other parts of its budget.
Efficiency of the Race Track
Wagering Market
.............................................................................................................................................................................
The efﬁciency of wagering markets is of great interest to researchers, bettors, and
the industry. Many industry players believe that betting on horse racing is similar to
investing in stocks. That is, there is a return for gathering and processing information,
and thus, horse betting is not just pure speculation or gambling. Researchers have
hypothesized that these markets have an opportunity to be more efﬁcient than even the
stock market because the wager value becomes known at a ﬁxed termination point,there
is quick feedback, low cost access through off-track venues, and learning is enhanced
with repeated opportunities to bet the same wager or betting interest Hausch, Ziemba,
Rubinstein (1981). Offsetting this, however, is the inability of bettors to take short
positions. As in the ﬁnancial markets, there is strong interest in how informed bettors,
dubbed the “smart money,” wager and how they place bets.
In the United States, the ﬁnal odds at a racetrack that determine potential winnings
on a race are not known until the betting windows close at post time. Thus payoffs are
unknown to the bettor until after the race starts. Camerer (1998) found that approxi-
mately half the money in his sample was bet three minutes before post time. It is widely
accepted that informed bettors bet near the end of the wagering period. Supporting
this, Asch, Malkiel and Quandt (1982) found that bets made near the end of the wager-
ing period are better predictors of the order of ﬁnish than are the ﬁnal odds. Asch and

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horse race betting
Quandt (1987) examined exotic bets and reported that the smart money systematically
bets on exactas in order to avoid signaling their actions.
Manipulation of markets with large trades is of particular interest in many markets.
Camerer (1998) ran an interesting ﬁeld experiment using pari-mutuel betting on thor-
oughbred racing to examine how information aggregation occurred in these centralized
pari-mutuel markets and to test whether these markets were easily manipulated by large
bets. Bycomputerhestrategicallyplacedlargebetsthatvisiblymovedtheoddsonhorses
(relative to matched-pair control horses in the same race with similar pre-bet odds)
and then canceled these bets before the race was run. The temporary bets were placed
approximately17–22minutesbeforeposttimeandcancelled5to8minutespriortopost
time. Even though there was a slight movement of money toward the horse bet it was
temporary such that the net effect was statistically insigniﬁcant. Camerer found no evi-
dence that bettors systematically responded to his manipulated change in odds relative
to his control sample horse at any time when the temporary bet was“live.”He concluded
that information aggregates well in these pari-mutuel markets and bettors know enough
toignorealargebetbeforeposttimethatisnotbackedbyconsistentlyincreasingwagers.
Other studies have looked for market inefﬁciencies for the possibility of exploitable
wagering patterns. The most notable empirical regularity in racetrack betting markets
documented in both bookmaker and pari-mutuel data is the favorite-long shot bias
ﬁrst documented by Grifﬁth (1949). The favorite-long shot bias suggests that betting
odds are biased estimates of the probability of a horse winning. In particular, longshots
are overbet while favorites are underbet, giving consistently greater returns to favorites
as compared to long shots. Thaler and Ziemba (1988), Sauer (1998), and Snowberg and
Wolfers (2007) provide literature surveys.
Focusing on the post-simulcast era, Gramm and Owens (2006) examined whether
the favorite-longshot bias persists when the ﬁnal odds pool is comingled with bets
from a variety of sources: on-track betting, casinos, off-track betting hubs, phones,
and online betting venues. They found that the favorite-longshot bias still exists and
is more severe in the place and show pools than in the win pool. Interestingly, they
went on to analyze whether one could proﬁtably arbitrage this inefﬁciency and found
it to be unproﬁtable. Since roughly only 60 percent of the ﬁnal pool totals are recorded
when the betting windows close, Gramm and Owens found that late money reduced or
eliminated the inefﬁciencies that appeared exploitable.
Examining the bias from a different signiﬁcance perspective and noting that bets
on longshots account for a small amount of the actual wagers in aggregate, O’Conner
(2007) used the common method of value weighting in ﬁnancial portfolios to inves-
tigate the economic signiﬁcance to bettors in the aggregate of exploiting the longshot
bias. He weighted each horse in the portfolio according to the dollar amount bet on
it instead of assigning an equal wagered amount to all horses. O’Conner found that
the longshot bias is only one-third as strong in a value-weighted portfolio relative to
an equal-weighted portfolio and that it falls considerably as pools increase in size. It
would be interesting to see if future research using different data sets across countries
and time replicated this result.

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the modern racing landscape and the racetrack wagering market
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New Landscape Issues
.............................................................................................................................................................................
Facing a decline in the volume of pari-mutuel wagering in recent years, horse racing
advocates have considered several changes to enhance the sport’s visibility. One recur-
ring discussion centers on the tendency for the most successful racehorses, particularly
stallions, to retire from racing and begin lucrative careers in the breeding shed. The
conventional wisdom is that people, particularly new and potential fans, need time to
build an afﬁnity for the sporting aspect of racing rather than just the appeal of betting.
Keeping top horses on the racetrack longer would probably offer media outlets addi-
tional story lines, too, as last year’s competitors begin training for the upcoming racing
season.
Thoroughbred racing champion Zenyatta is the perfect example of how one horse’s
four-season racing career can captivate not only the nation’s but the world’s atten-
tion. Her unprecedented consecutive wins, signature paddock dancing, and electrifying
come-from-behind ﬁnishes propelled her into the spotlight, but it was also the generous
access and astute decisions of her owners and racing team that allowed her legacy and
popularity to beneﬁt the industry. After becoming the ﬁrst ﬁlly to win the Breeders’
Cup Classic she was brought back from a brief retirement as a six year old to challenge
more industry records. Although it is hard to measure the impact that a superstar
horse has on overall wagering handle, the Daily Racing Form (Nov. 7, 2011) noted that
the total handle for the Breeders’ Cup races was down 5.1 percent relative to 2010’s
record level increase of 15.5 percent when Zenyatta raced for the second time in the
classic.
What is more important for the industry is how she won the hearts of thousands of
non-regular race fans and brought back visibility to thoroughbred racing. Her iconic
popularity is so strong that even the Los Angeles Dodgers baseball team has used her on
billboards for promotion, and she was featured on 60 Minutes among other national
media outlets. Thousands of fans came to her retirement ceremonies at Hollywood
Park and Keeneland Race Track. Her popularity has not waned since retirement, as
she has more than 90,000 fans on Facebook who follow almost daily blogs by racing
manager Dottie Shirreffs, and she continues to raise a great deal of money for several
racing and cancer research charities. Team Zenyatta exempliﬁes what many people feel
the sport of racing should be, and they were recognized with a special Eclipse Award
for extraordinary service, individual achievement, and contributions to thoroughbred
racing. As economists we realize that not all owners are so philanthropic and that the
industry needs to create credible incentives to capture the externality of longer racing
careers. Perhaps one credible way would be to fund valuable multiyear racing career
awards.
Another aspect of concern is racing very young horses, whose developing tissues and
bones are at greater risk for injury. This is a double blow to the sport because not only
does it add risk to owners, but it also is a source of bad publicity—few people want
to see animals injured, and such injuries reﬂect badly on the sport. Particularly for

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horse race betting
standardbred racing, the present structure of races, with the most lucrative contests
restricted to two- and three-year-old horses, provides strong economic incentives to
retire the top stallions to breeding farms, where they have a longer period of time to
sire potentially valuable offspring. In economic terms racing horses beyond three years
of age is a positive externality to the industry, whereas the private beneﬁts are small to
negative for the individual owner.
To address this issue in standardbred racing in the United States, Jeff Gural, chairman
of American Racing and Entertainment (which owns and operates Tioga Downs and
Vernon Downs), has implemented new rules for qualifying to race at his most recent
acquisition, the Meadowlands. Speciﬁcally, he will ban the offspring of stallions that
were four years old at the time of conception from competing in stakes races. Gural
would offer exceptions for stallions that are sick, injured, or otherwise unable to race.
We understand and sympathize with the goals of such proposals. As economists,
though, we know that when prices are subverted in favor of non-price approaches such
as bans, unintended consequences result. Market participants will surely attempt to
game the system to circumvent such a ban. We can think of several possible ways, and
creative minds in the industry are sure to ﬁnd several more. For example, an owner
could pay a veterinarian to diagnose a career-ending illness or injury or, even worse,
create one. Owners of promising young stallions need not breed their horses in states
where such bans exist or even in the United States. Instead, they could ship their horses
to other parts of the country where the ban is not in effect or even abroad to begin
their stallion careers. This would have the perverse effect of reducing media coverage
of the sport at the tracks where the ban is in place. We can imagine that sponsors of
stakes races currently at these three tracks will encounter pressure to move to other
racetracks not subject to the ban. If enough quality owners move to another track then
sponsors will follow. The real winners of such a ban are the current owners of breeding
stock because the ban delays competition from young stallions that current owners of
bloodstock would otherwise face.
As we noted above, statistics from the Daily Racing Form for 2010 found that off-
track simulcast betting now drives wagering handle. This has subtle implications for
the future of racing. Given that even small tracks strategically positioned in the racing
schedule can draw respectable betting volumes, a key driver of a racetrack’s success is no
longer just its location in geographical space but also its location in time. Technology
makes geography much less important for wagering handle than in the past. This
means that racing’s efforts to bring live racing to new areas need to be conscious
of strategically placing the race meet in the wagering market schedule. As a case in
point, during recent legislative hearings in the state of Georgia (USA) horse racing
proponents emphasized not only the beneﬁts of increased employment to the state but
also the strategic geographical advantage that allows them to place short meets within
the racing schedule as horses move back and forth from Florida to other parts of the
country during the different seasons. Not surprisingly, proponents are also seeking a
state constitutional amendment to allow pari-mutuel betting in the state in order to take

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the modern racing landscape and the racetrack wagering market
273
advantage of the simulcasting wagering market revenues while simultaneously arguing
there is no need for other forms of gambling.
Currently 44 of the 109 tracks devoted to thoroughbred racing in the United States
are subsidized by gaming. Many states are also turning to casino gambling to help
revive the racing industry. For example, New York is one of 12 recently allowing casinos
at racetracks, commonly called racinos. In particular the new casino at Aqueduct
Racetrack, Resorts World Casino, brought in an additional $14.8 million to race purses
and $15.96 million to the New York Racing Association in the ﬁrst six months of
operations, 6.5% and 7% respectively of revenues (NewYork Daily News, Sports, March
25, 2012). Higher purse levels attract better quality horses which in turn tend to lead to
higher wagering handles. But even beforeAqueduct’s racino’s fruits can be fully realized,
thedynamicsof competitionforthegamingdollarcontinuestochange. TheShinnecock
Indian tribe has announced that it is contemplating putting a racino at Belmont Park
race course, just seven miles away from Aqueduct. Many players in the gaming industry
believe this concentrates too many venues within too small a geographical space.
Summary
.............................................................................................................................................................................
Horse racing is an important global industry. Along with other forms of gambling this
industry has provided ﬁnancial support for beleaguered state governments. Technology
has changed the way track patrons bet, with the vast and increasing majority of total
bets being made away from live racing. The menu of wagering options continues to
grow with a wide variety of exotic bets, futures wagering markets, program betting,
and on line betting venues becoming more prevalent. We know a fair amount about
the determinants of wagering volume, but our knowledge of the demand for wagering
on these different types of bets within and across venues remains in its infancy. In
particular, different types of informed traders will take advantage of these new venues
to hedge their bets as the new betting exchanges offer different bet types, for example,
limit price betting. As in ﬁnancial markets, these market microstructure issues will
induce changes in the wagering market, constituting fertile ground for future research.
Past studies in standardbred racing found that subsidies to purses, in the form of sire
stakes, to the standardbred racing industry, do not increase wagering nearly enough
to justify their use solely on the growth in handle. Policy makers must make the case
that they help taxpayers in other areas. For example, they might argue that higher
tax revenues will be generated by increased wagering in the future or by attracting
gamblers to other forms of taxable gaming, such as VLTs, or that racetracks provide
a public good. Perhaps, too, the subsidy provides a politically viable way of offsetting
tax rates on gambling that are too high. Future research is needed to value these
positive externalities and to measure whether these same conclusions apply equally to
the thoroughbred and quarter horse racing industries, and in more recent times with
simulcasting.

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horse race betting
Additional research is needed to assess the efﬁciency of wagering in racing markets
in the United States in light of recent types of wagering options coming into the
marketplace. With exchange betting venues having entered the United States for the
ﬁrst time in 2011, and with the relatively recent onset of program betting, it will be
interesting to reexamine the survivability of the favorite-longshot bias. In addition,
increasing numbers of informed bettors with more venues and bet options are likely
to alter the information content and manipulative ability of the on-track pari-mutuel
market odds in interesting ways.
Finally, we described several new issues that will continue to affect the racing land-
scape and avenues to reignite interest in the racing industry, such as longer racing
careers for top horses. One important dynamic that could have a profound effect on
the racing and wagering industry would be the creation of a national racing association.
Many different stakeholders in the industry have promoted such an idea as a way to
control the image and integrity of the industry, with particular regard to drug usage
standards, and to organize the racing schedule to maximize the total wagering han-
dle. With states heavily vested in the subsidization, pricing/taxing of relative wagering
venues and ownership of racetracks, this would involve complex political negotiations
and implications. An interesting area of future research might examine how this tran-
sition might, come about, whether or not this structure would mimic other U.S. sports
leagues and its governance pitfalls.
Notes
1. Data in this paragraph are from the Jockey Club Online Fact Book (www.jockeyclub.com/
factbook.asp).
2. Track patrons call such bettors “bridge-jumpers,” a colorful term referring to the strong
regret that losers of such bets feel.
3. This section draws heavily on DeGennaro (2009).
References
Ali, Mukhtar M., and Richard Thalheimer. 1997. Transportation Costs and Product Demand:
Wagering on parimutuel horse racing. Applied Economics 29(4):529–542.
Asch, Peter, Burton G. Malkiel, and Richard E. Quandt. 1982. Racetrack betting and informed
behavior. Journal of Financial Economics 10(2):187–92.
Asch, Peter, and Richard E. Quandt. 1987. Efﬁciency and proﬁtability in exotic bets. Economica
54(215):289–298.
Bossert, Jerry. 2012. Increased purses from Aqueduct casino seemed like winning bet until
horses started breaking down. New York Daily News, Sports, March 25.
Camerer, Colin F. 1998. Can asset markets be manipulated? A ﬁeld experiment with racetrack
betting. Journal of Political Economy 106(3):457–482.
Chou, Nan-Ting, Ramon P. DeGennaro, and Raymond D. Sauer. 2000. The efﬁciency of the
price system: Evidence from an alternative market. Applied Economics Letters 7:703–706.

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the modern racing landscape and the racetrack wagering market
275
DeGennaro, Ramon P. 1989. The determinants of wagering behavior. Managerial and Decision
Economics 10:221–228.
——. 2009. New evidence on the link between government subsidies and wagering. Journal
of Gambling Business and Economics 3(2):37–62.
DeGennaro, Ramon P., and Ann B. Gillette. 2013. Syndicates’ choices under different payoff
distributions. Kennesaw State University Working paper.
Deloitte Consulting LLP. 2005. The economic impact of the horse industry in the United
States, June.
Gramm, Marshall, and Douglas H. Owens. 2006. Efﬁciency in pari-mutuel betting markets
across wagering pools in the simulcast era. Southern Economic Journal 72(4):926–937.
Gramm, Marshall, C. Nicholas McKinney, Douglas H. Owens, and Matt E. Ryan. 2007. What
do bettors want? Determinants of pari-mutuel betting preference. American Journal of
Economics and Sociology 66(3):465–491.
Grifﬁth, R. M. 1949. Odds adjustments by American horse race bettors. American Journal of
Psychology 62(2):290–294.
Hausch, Donald B., William T. Ziemba, and Mark Rubinstein. 1981. Efﬁciency of the market
for racetrack betting. Management Science 27(12):1435–1452.
O’Conner, Philip F. 2007. The economic signiﬁcance of the longshot bias in horse race wager-
ing. Working paper, June. Hamilton, New Zealand: University of Waikato Management
School.
Paulick Report.
2011.
DRF
study:
Slots tracks drive far less handle,
Aug.
18;
http://www.paulickreport.com/news/the-biz/drf-study-slots-tracks-drive-far-less-handle.
Sauer, Raymond D. 1998. The economics of wagering markets. Journal of Economic Literature
36(4):2021–2064.
Snowberg, Erik, and Justin Wolfers. 2010. Explaining the Favorite-Longshot Bias: Is it Risk-
Love or Misperceptions? Natioanl Bureau of Economic Research working paper 15923.
Thaler, Richard H., and William T. Ziemba. 1998. Parimutuel betting markets: Racetracks and
lotteries. Journal of Economic Perspectives 2(2):161–174.
Thalheimer, Richard and Mukhtar M. Ali. 1995. The Demand for Parimutuel Horse Race
Wagering and Attendance. Management Science 41(1): 129–143.
Walker, Douglas M., and John D. Jackson. 2011. The effect of legalized gambling on state
government revenue. Contemporary Economic Policy 29(1):101–114.

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chapter 16
........................................................................................................
WHAT EXPLAINS THE EXISTENCE
OF AN EXCHANGE OVERROUND?
........................................................................................................
david marginson
1 Introduction
.............................................................................................................................................................................
The advent of person-to-person Internet betting constitutes a radical change in the
nature of gambling. Prior to such “exchanges” as Betfair (www.betfair.com), bet-
tors faced what may be described as wagering asymmetry; it was possible to bet on
something to happen but not to bet on something not to happen. Before the advent
of the exchanges, only licensed bookmakers could lay something or someone to lose.1
Since 2000, however, and because of the exchanges, unlicensed individuals can now
either or both “back” and/or “lay.” The exchanges enable or establish symmetry in
wagering. This symmetry is particularly evident for horse race betting. Punters can
now either back one or more horses in a race to win and/or lay one or more horses in
the same race to lose. Horse race betting is the market focus for this chapter.
The introduction of Internet-based person-to-person betting also represents an
important structural development for horse race and other betting markets. This
structural development concerns the establishment of an order-driven type market to
complementtraditionalbookmaker-led,quote-drivenmarkets. Broadly,aquote-driven
market is one in which dealers or market makers offer to buy or sell assets/securities
to investors (Theissen 2000). All transactions are done with or through the mar-
ket maker (normally at the bid and ask prices quoted by the dealer), who provides
immediacy to the market.2 Bookmaker-led markets are essentially quote-driven mar-
kets. The bookmaker is the market maker, providing immediacy for betting. In turn,
bettors (investors) must bet at the prices offered by the bookmaker who, in reﬂect-
ing quote-driven arrangements, takes the opposite side (as “layer”) of every (betting)
transaction.

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what explains the existence of an exchange overround?
277
An order-driven market operates without specialist market maker intermediation
(Handa, Schwartz, and Tiwari 2003). Instead investors trade directly among themselves.
This direct trading occurs in one of two ways. Any seller (buyer) can place offers
(bids) as limit orders and wait until the order is executed; or, alternatively, seller or
buyer can trade immediately by placing a market order against an existing limit order
(offer or bid).3 Buy and sell prices are publicly displayed, with the transaction price
being the result of the equilibrium of supply and demand (Handa, Schwartz, and
Tiwari 2003).
Internet person-to-person betting exchanges (henceforth exchanges) may be consid-
ered the betting equivalent of an order-driven market. First, the exchanges are similarly
nonintermediated markets; there is no market maker. Put colloquially, the exchanges
represent “betting without bookies” (O’Connor 2007). Second, trading occurs directly
between bettors in essentially the manner described above for order-driven markets.
The terminology is that bets are “matched.”4
An important question that applies equally to both quote-driven and order-driven
markets is that of market efﬁciency; i.e., how efﬁcient is the market? In seek-
ing to address this question, one line of research, often referred to as market
microstructure, has focused on exploring the idea that asset prices need not equal
full information expectations because of a variety of market frictions (Madhavan
2000). Market frictions (inefﬁciencies) include the cost of transacting or trading in
a particular market (Stigler 1967). The most signiﬁcant and observable transaction
cost is the bid-ask spread (Kumar 2004). The bid-ask spread represents the dif-
ference between asset buying and selling prices. Its existence is generally explained
in terms of the effects of inventory holding costs, order processing costs, liquidity,
and adverse selection costs (Levin and Wright 2004). While differing in magnitude,
bid-ask spreads are characteristic of both quote-driven and order-driven markets
(Theissen 2000).
For horse race betting markets, the bookmaker’s overround or “vig” may be viewed
as akin to the bid-ask spread in ﬁnancial markets (Shin 1991). The explanation is
as follows. Consider the market for bets in a horse race comprising n runners. This
market “corresponds to a market for contingent claims with n states, in which the ith
state corresponds to the outcome if the ith horse wins the race” (Shin 1993, 1142).
In this market, the value of the securities (say £1 if a particular state occurs; 0 other-
wise) is determined by betting odds (implied win probabilities). The sum of implied
win probabilities on all race entrants gives the price of a portfolio which pays £1 for
sure at the end of the race (Shin 1993). For operational efﬁciency, sum of implied
win probabilities = 1 (x = 1). Thus if x diverges from 1 (x – 1), an overround
(OR) or market spread exists (Coleman 2007; Law and Peel 2002). Overrounds (ORs)
based on publicly reported starting prices (sum of starting prices – 1) provide a clear,
unambiguous, and readily accessible measure of the size of the (ﬁnal) market spread
(Shin 1993, 1142).5
Since December 12, 2007, Betfair, the leading Internet-based person-to-person bet-
ting exchange (O’Connor 2011), has reported its own horse race starting prices to

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278
horse race betting
rival industry- or bookmaker-determined starting prices. Betfair starting prices are
seen as more “efﬁcient” than industry starting prices, and evidence does suggest that
longshot prices in particular are considerably higher than the equivalent bookmaker
starting price (SP) (O’Connor 2007; Marginson 2010). At the same time, it follows that
the reporting of Betfair starting prices (SPs) helps to establish an equivalent “sum of
Betfair (starting) prices.” To the extent that this sum of SPs diverges from 1, an equiva-
lent Betfair overround is created. A cursory review of the data conﬁrms the existence of
Betfair ORs, both < and >1. The existence of “underrounds” (sum of SPs <1 ) is inter-
esting, not least as it implies that, in theory at least, every participant in a horse race
could be backed to yield a proﬁt, however small. More importantly from an operational
efﬁciency perspective, divergence of sum of Betfair SPs from 1 gives rise to the following
research question: why does this bid-ask spread exist? Put slightly differently, we may
ask: what factors might help to explain the existence of an over/underround in the
Betfair exchange market?
The purpose of this chapter is to examine the reported overrounds on Betfair
in an attempt to explain their existence. The study draws on both the ﬁnance and
horse racing literatures as a basis for identifying possible determinants for investi-
gation. The factors examined include, from the ﬁnance literature on order-driven
bid-ask spreads, balance of investor opinion/activity, trading volume, and adverse
selection costs (Handa, Schwartz, and Tiwari 2003). Drawing on the horse racing lit-
erature, the following are examined: number of runners, grade of race, age limit of
the race (three proxies for adverse selection), last race effect, type of race (handicap
versus nonhandicap), type of race event (Flat vis-à-vis National Hunt), and, given the
increasing association between exchange and racetrack betting (O’Connor 2011), book-
maker overrounds. Hypotheses relating to each are developed and subject to empirical
analysis.
The empirical analysis is based on data collected from 2,184 horse races tha took
place in the United Kingdom between autumn 2008 and spring 2010. The empiri-
cal analysis suggests that Betfair overrounds vary in relation to: balance of activity
(whether weighted toward back or lay), trading volume (monies wagered), grade of
race, and bookmaker overrounds. Signiﬁcant effects (at p < 0.05) are also observed
for type of race (handicap versus nonhandicap), “last race,” and number of runners.
Nonsigniﬁcant results are reported for type of race event and age limit of the race.
Findings support the ﬁnance literature concerning, for instance, the effects of balance
of activity on bid-ask spreads in order-driven markets (Handa, Schwartz, and Tiwari
2003). In contrast, ﬁndings for grade of race and type of race challenge arguments
in the horse racing literature about the effects these two factors are expected to have
on betting overrounds (Vaughan Williams and Paton 1997). Possible reasons for these
ﬁnding are considered. The analysis suggests the need for further research into the
operational efﬁciency of exchange betting markets. More broadly, the present research
suggests that microstructure analysis of order-driven betting markets such as Betfair
offers a potentially fruitful line of inquiry for those interested in understanding market
efﬁciency.

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what explains the existence of an exchange overround?
279
The next section describes exchange betting and explains how an overround con-
tributes to market inefﬁciency. Section 3 develops the study’s hypotheses. Section 4
outlines the research methodology. Section 5 presents the empirical results. Section 6
concludes.
2 Exchange Betting
.............................................................................................................................................................................
“Betting exchanges exist to match people who want to bet on a future outcome at a
given price with those who are willing to offer that price. The person who bets on the
event happening at a given price is the“backer”[or“bettor”]; the person who offers the
price is known as the ‘layer”’ (Smith, Paton, and Vaughan Williams 2006, 674).
For example, someone may wish to lay a particular horse at, say, odds of 3 to 1 to a
maximum stake of, say, £100 (maximum liability is £300). Someone else, the bettor, may
accept these odds and place a bet with the layer, say £100 at 3 to 1. A wager thus occurs
between the two parties. Equally, exchange bettors can indicate (1) the odds at which
they would be willing to bet on a particular horse (say 7–2) and (2) the magnitude of
the wager at that odds level (say £100). Anyone wishing to lay the same horse at those
odds can accept this bet and thereby form a transaction with the bettor. A wager thus
occurs once more—between layer and bettor.
From an order-driven market perspective, the above two betting examples describe
both limit orders and market orders. By specifying both the order/volume (e.g. £100
wager, £300 liability) and the price (e.g.7–2), those bettors who place wagers (lay
or bet) are placing limit orders; they must wait until the wager gets executed. The
wager is executed by those who accept the lay or bet. Accepting is akin to placing
a market order; these bettors are trading immediately with an existing limit order
(lay or bet).
The multiplicity of limit orders on Betfair are displayed under the headings “back”
and lay,” with each category comprising three columns of prices. The term back rep-
resents a situation in which a bettor has placed a limit order about something not
happening. In our example, for instance, the wager (limit order) of the person offering
3–1 against a particular horse winning (stake £100) will be displayed under “back.” In
this context, back represents the response (bet) of the person (bettor) accepting the
limit order (thereby making a market order). The term lay represents the actions of the
participant accepting the limit order placed by the bettor seeking to back the horse to
win at 7–2 (stake £100).
Both “back” and “lay” help to demonstrate the symmetry of betting provided by
the exchanges. At the same time, the development allowing non-licensed individuals
to bet on something not to happen has proved controversial. The main and contin-
uing concern is that, by “allow[ing] punters to bet on horses that lose” (O’Connor
2007), betting exchanges create “the perfect recipe for malpractice, such as race ﬁxing”
(statement by chairman of the Australian Jockeys Association, Oct. 14, 2004). There is

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horse race betting
evidence to support these assertions (Marginson 2010). Such concerns, notwithstand-
ing, exchange betting has proved extremely popular. Betfair, for instance, reported, for
the year 2010, yet another increase in revenue to £340.9 million. While this increase, at
13 percent, is less than 2009’s 24 percent increase, and while gross proﬁt before tax, at
£17.8 million, represents a fall of 63 percent from 2009’s gross proﬁt of £47.5 mil-
lion, Betfair remains by far the biggest Internet-based betting exchange globally
(O’Connor 2011).
The continuing success of Betfair appears to have, in part at least, informed the
company’sdesiretogetinvolvedwithSPs. InOctober2007itwasreportedthatrepresen-
tatives of Betfair had made a submission to the Starting Price Regulatory Commission,
suggesting that Betfair prices should form part of the overall calculation of the SP. This
offer was rejected by the commission. In response, Jack Houghton, a spokesperson for
Betfair, is quoted as saying: “Betfair offered to provide data from its audit trail to assist
in returning an SP that was more equitable, transparent and fair than the incumbent
system ... Betfair’s concern is that the new approach, regrettably, does not prioritise the
interests of punters” (O’Connor 2011).6
The launch of Betfair’s own SP service in December 2007 provided bettors with a
clear way of comparing industry and exchange SPs. As with bookmaker-based SPs, the
production of Betfair SPs is governed by certain rules and procedures. These are pre-
sented on Betfair’s website (www.betfair.com). The algorithms involved can be detailed
and complex, not least because, and controversially for some (see O’Connor 2011), they
allow the incorporation of some unmatched limit orders into the calculation of Betfair
SPs. The reader is referred to Betfair for a full account of how the SPs are calculated.
Perhaps the two key points to mention here are that (1) to a large extent, Betfair SPs
reﬂect the average of the best back and lay odds immediately prior to “the off” and (2)
based on publication of Betfair SPs, it is possible to determine Betfair ORs, calculated
as sum of SPs – 1.
From an efﬁciency perspective, transactional or operational inefﬁciency exists if sum
of prices (SPs) diverges from 1. Normally, for bookmaker-led markets at least, sum
of prices exceeds 1 and may do so by 30 percent or more (Cain, Law, and Peel 2003).
The effect of ORs >1 is to compress prices (implied win probabilities) below their
“true” or objective level, as represented by the frequency of winning outcomes.7 For
example, suppose each horse in a four-runner race is priced at 2/1. This implies that
each should win 33.33 percent of races or, say, 4 races out of 12. But of course, there
are four runners, and so, assuming equal ability (as indicted by the equal prices), the
“true” outcome would be three wins each (out of 12 races), not four. Objectively, this
frequency is represented by odds of 3/1 (25%) and a zero OR. Thus for efﬁciency,
market prices should approximate to their “true” or objective win probabilities. Out-
comes priced at 1/1 should occur 50 percent of the time. Outcomes priced at 100/1
should happen, on average, 1 in 101 cases. In our example, however, each horse wins
25 percent of races, a lower ratio than the 33.33 percent implied in the odds of 2/1.
Not all prices in a given betting market may be affected in this manner. Nonethe-
less, so long as an OR exists, inefﬁciency exists; at least one price does not match its

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what explains the existence of an exchange overround?
281
“true” value.8 (Sum of prices <1 would create a situation where one or more implied
odds are potentially greater than their objective or true odds, as represented by race
outcomes.)
For the sample of 2,184 races used in the present study,9 Betfair sum of SPs (sum
of SPs – 1) ranges from 86 to 112 percent. Thus ORs based on SPs reported by Betfair
range from −14 to +12 percent. This variation is nontrivial; it highlights the extent of
potential operational inefﬁciencies for an order-driven betting market such as Betfair.
This leads us to ask: what might explain the existence of such SP-based ORs on Betfair?
Drawing on both ﬁnance and horse racing literatures, the next section develops testable
hypotheses that seek to answer this question.
3 Explaining Betfair Overrounds
.............................................................................................................................................................................
3.1 Explanations from Finance
The ﬁnance literature posits that three factors in particular inﬂuence the magni-
tude of bid-ask spreads in order-driven markets (see, e.g., Chakravarty and Holden
1995; Chung, Van Ness, and Van Ness 1999; Handa and Schwartz 1996; Handa,
Schwartz, and Tiwari 1998, 2003; Goettler, Parlour, and Rajan, 2009). The factors
are (1) “balance of opinion” based on the proportion of buyers (buying activity)
vis-à-vis sellers (selling activity) in the market, (2) trading volume, and (3) adverse
selection; the risk of trading with informed traders (Handa, Schwartz, and Tiwari
2003). The third factor is also a feature of the horse race betting market literature
(Crafts 1985; Vaughan Williams 2005) and will be discussed under “Explanations from
Finance and Horse Racing.” The following discusses “balance of opinion” and trading
volume.
3.1.1 Balance of Opinion in an Order-Driven Market
Puneet Handa, Robert Schwartz, and Ashish Tiwari (1998) argued that bid-ask spreads
in order-driven markets are related to the activities of buyers and sellers, speciﬁcally
differences of opinion relating to asset values. Fundamentally, markets exist because
investors hold heterogeneous beliefs and opinions (Madhavan 2000). For various rea-
sons, traders reach different opinions based on the same public information. In the
context of order-driven ﬁnancial markets, a “balance of opinion” (equal weighting of
buyers/sellers) is associated with “equilibrium” or widest bid-ask spreads. In contrast,
an imbalance in favor of either buying or selling activity is argued to drive bid-ask
spreads away from equilibrium and toward minimum values (Handa, Schwartz, and
Tiwari 1998).
For instance, suppose two groups of investors, both with access to the same public
information, place different values, Vhigh, Vlow, on a particular security/asset. Vhigh

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horse race betting
investors seek to purchase shares; Vlow investors seek to sell shares. In this context
difference of opinion has two dimensions: (1) divergence of opinion, Vhigh −Vlow,
and (2) the proportion, p, of investors with valuation Vhigh. Handa, Schwartz, and
Tiwari (1998) argued that, for a given Vhigh −Vlow, the difference of opinion reduces
or disappears at extreme values of p (0 and 1) and is maximized at p = 0.5.
Handa, Schwartz, and Tiwari (1998) further argued that differences of opinion trans-
late into or help to establish bid and ask prices, and thereby the magnitude of the bid-ask
spread. Their reasoning is predicated on the notion of a“gravitational pull”effect that a
previously posted buy (or sell) order exerts on an incoming sell (or buy) order. The pull
is the attractiveness of trading with certainty by market order (investors placing limit
orders face the risk that their order may not be executed, in Betfair terms, not matched).
According to Handa, Schwartz, and Tiwari (1997, 49), a spread thereby results because
“any limit order sitting on the book must be far enough away from a counterpart quote
to lie outside the gravitational pull of the counterpart quote.”
Consistent with the gravitational pull effect, market bid, B, and market ask, A,
both depend on the nonexecution risks faced by buyers relative to sellers. Further,
nonexecution risks for each participant depend on the relative proportion of buyers, p
(valuation, Vhigh). For p close to unity, nonexecution risk is high for buyers and low
for sellers (and vice versa for p close to zero). For this reason, the equilibrium spread,
A – B, also depends on p. Handa, Schwartz, and Tiwari (1997, 2003) have shown that
spreads in an order-driven market are widest at p = 0.5 and lowest when p is at either
of its extreme values (0 or 1).10
It is possible to apply the above line of reasoning to betting exchanges. The arguments
are threefold. First, as with ﬁnancial markets, exchange betting markets exist because
bettors, based on the same public information, hold different opinions about the
winning chances of a given race entrant. Those bettors (buyers) holding a relatively
high opinion of a horse’s chances will back the horse to win. Bettors (seller) holding a
relatively low opinion will lay the horse to lose.
Second, similar to order-driven ﬁnancial markets, it also seems reasonable to suggest
that a gravitational pull effect may inﬂuence bettor behavior on the exchanges. The
point is that exchange bettors face similar uncertainties that their limit orders (back or
lay) may not be “matched.” As such, there is an attractiveness to trading with certainty
by matching existing limit orders rather than by placing additional limit orders. And
third, the gravitational pull effect is likely to increase as the proportion of backers
to layers diverges from equilibrium (same proportion of each) toward either extreme
(more backers to layers and vice versa). As the extreme positions are approached,betting
activity is “pulled” toward either the back or the lay prices, depending on the nature of
the imbalance between bettors and layers.
However, while the conceptual arguments may equally apply on exchange order-
driven betting markets, it is argued here that the nature of betting results in a different
effect on the bid-ask spread or OR compared to that proposed by Handa, Schwartz,
and Tiwari (1997), who suggest that order-driven bid-ask spreads are maximized for
p = 0.5, that is, where there is a balance of investor opinion. In contrast, a balance

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what explains the existence of an exchange overround?
283
of opinion/activity on the exchanges (p = 0.5) will result in ORs that are minimized
(closest to zero) rather than maximized (extent of divergence from 1). ORs will be
greatest when p is at either of its extreme values (0 or 1).
Consider a single race entrant; if neither back nor lay activity predominates, there
will be no “pull” on price away from equilibrium. In contrast a preponderance of
betting vis-à-vis laying activity (or vice versa) will either shorten or lengthen the odds
of that race entrant. The cumulative effect (regarding all race entrants) will be to pull
each price, and thereby sum of SPs, either higher or lower, thereby maximizing the
divergence of sum of SPs from 1 (either above or below 1). This leads to the following
hypothesis:
H1: Betfair ORs vary with the balance of betting vis-à-vis laying activity.
3.1.2 Trading Volume/Liquidity
Trading volume or liquidity is generally regarded as a determinant of bid-asks spreads
(Madhavan 2000). Although arguments can differ,11 the enduring view appears to
be that, for both quote-driven and order-driven markets, the width of the bid-ask
spread will vary inversely trading volume/liquidity (Amihud and Mendelson 1980).
This view is supported by empirical evidence (Benston and Hagerman 1974; Chung
and Charoenwong 1998; Stoll 1978) and is predicated on the following two hypotheses:
(1) that market makers/investors normally face more competition with high volume
securities than with low volume securities and/or (2) that it is generally less risky to
make a market in a high-volume security, with the result that spreads for such secu-
rities would be lower, even if there were competing market makers/investors (Smidt
1971, 64). Within ﬁnance/economics, it is seen as a truism that both increasing com-
petition and decreasing risk will reduce market inefﬁciencies, in the present case, by
reducing bid-ask spreads.
The above is generally discussed in relation to a single security; the greater the volume
of trading in a given security, the lower the bid-ask spread. It follows from this that,
for given market of securities, if trading volumes increase for each or all securities,
the lower the market spread. This is simply applying the cumulative or aggregative
effect of the inverse relationship between trading volume and spread widths. Recall
that for horse race betting markets, the market spread for the exchange, Betfair, is
represented as sum of SPs – 1. Considering volume as a potential determinant of sum
of prices, the question is: how might sum of SPs – 1 be affected by trading volume on the
exchanges?
Applying the inverse relationship discussed above, we should expect increasing vol-
ume of trade (monies wagered) for a given race entrant to reduce the spread between
the best back and lay prices. In aggregate, therefore, increasing trade (monies wagered)
on all race entrants would reduce the market spread. At the same time, as the practical
effect of increasing trade would be to increase the back price while reducing the lay
price, the midpoint between the two sets of prices is not necessarily altered and neither
therefore is the sum of SPs.12 To the extent this applies, variation in volume is unlikely

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horse race betting
to alter sum of prices (bid and ask prices may vary, but the mid-point/average of these,
on which SPs are calculated, is not affected). This means that, in effect, and in contrast
to ﬁnancial markets, variation in volume should not affect Betfair ORs. It is therefore
hypothesized that
H2: Betfair ORs are invariant to changes in betting volume (monies wagered).
3.2 An Explanation Shared by Finance and Horse Race Betting
Literatures
3.2.1 Adverse Selection/Information Asymmetry
Studies of ﬁnancial markets and horse race betting conjecture that adverse selection
affects the magnitude of bid-ask spreads. In both cases it is suggested that market mak-
ers (bookmakers) seek to manage adverse selection costs through the bid-ask spread
(overround) (Shin 1991, 1992, 1993; Smith, Paton, and Vaughan Williams 2006). The
basic idea is that the cost of dealing with insiders is passed on to outsides through
higher bid-ask spreads (overrounds) (Law and Peel 2002). In ﬁnancial markets (both
quote-driven and order-driven markets) the cost of dealing with insiders is consid-
ered to increase as liquidity decreases. Market makers respond by increasing bid-ask
spreads.
For horse race betting markets, liquidity tends to decrease as odds increase (that is,
more money is wagered on favorites than on long shots). Increasing odds increases
the payout to the bettor for a given wager. Given these two points, a commonplace
argument is that bookmakers disproportionately compress the odds on long shots
to protect against dealing with insiders (Law and Peel 2002; Schnytzer and Shilony
1995, 2003; Shin 1993; Smith, Paton, and Vaughan Williams 2006). Higher ORs
are needed to allow bookmakers to pass the costs arising from insider activity on
to“outsiders,” that is, recreational bettors who tend to overbet long shots and underbet
favorites (Cain, Law, and Peel 2003; Smith, Paton, and Vaughan Williams 2006). Such
actions create a favorite-longshot bias (Vaughan Williams 1999; Vaughan Williams and
Paton 1997).13
Adverse selection risk is used to explain the observed positive relationship between
OR and number of runners in a given race (see, e.g., Smith, Paton, and Vaughan
Williams 2006); x −1 gets larger as the number of race entrants increases). As Michael
Cain, David Law, and David Peel (2003, 270) argued: “a larger ﬁeld of competitors
leads to higher odds against any individual winning the event and thus higher winnings
for insiders. In these circumstances bookmakers need enhanced margins to protect
themselves.” The effect is that sum of prices, x “increases with the number of runners
as the bookie tries to recoup greater losses to the insider by raising the prices faced by
outsiders” (Shin 1993, 1152).
Totheextentthatbettorsontheexchangesmayseektomanageadverseselectionrisks,
it is reasonable to argue that the effect may be increasing bid-ask spreads. In particular,

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what explains the existence of an exchange overround?
285
back limit orders (offers to lay a given race entrant) may be subject to increasing
pricing constraint as the number of race entrants increases. As with bookmakers, the
point would be to try and limit the payout to insiders as odds increase with increasing
number of race entrants. Moreover, to the extent that any compression of prices occurs
as n increases, the “gravitational pull” effect (discussed above) could be expected to
reinforce any compression of odds. Thus, from the perspective of adverse selection, the
following hypothesis is presented:
H3: Betfair ORs increase with number of race entrants.
The horse race betting literature posits three further manifestations of adverse selec-
tion; bookmaker ORs are expected to vary according to (1) grade of race (Vaughan
Williams and Paton 1997), (2) age of horses competing in a given race (Peirson
and Smith 2010), and (3) type of race (handicap versus nonhandicap) (Vaughan
Williams and Paton 1997). The underpinning argument to (1) is that insider trad-
ing is deemed more or most likely to occur in lower grade races, for which prize
money is less and media interest is often minimal or absent (Smith, Paton, and
Vaughan Williams 2006). Aware of this, bookmakers increase their ORs accordingly
in order to pass on adverse selection costs onto “outsiders.” Regarding (2), the argu-
ment here concerns the relationship between age and publicly available information
about a horse’s ability; younger horses (e.g., two-year olds for Flat racing) typi-
cally have less racetrack experience, and thereby less public form, than older horses,
which, by their greater age, have generally more publicly exposed form.14 Increas-
ing public information is considered to reduce the potential for insider trading; the
horse’s ability is more exposed (Vaughan Williams and Paton 1997). As such, an
inverse relationship is predicted between age and bookmaker OR; lower aged races
attract higher ORs as bookmakers seek to manage adverse selection costs (Peirson and
Smith 2010).
Finally, for reasons similar to those presented for (2) above, bookmaker ORs are
expected to be lower for handicap races compared to nonhandicap races. Insider trading
is expected to be more prevalent in nonhandicap events (see Bruce and Johnson 2003)
because, in such events, some or all of the participants may have little or no prior public
form. There may be a degree of owner/trainer inﬂuence on the race conditions (e.g., via
the assignment of weight in claiming races), the level of media and ofﬁcial scrutiny of
the running of the race is lower, and the magnitude of gains from betting coups relative
to prize money is higher. Each of these factors would, according to Hyun Song Shin
(1991, 1992, 1993), be likely to result in relatively high and low ORs in nonhandicap
and handicap races, respectively.
For (1), (2) and (3) the implication is that bookmakers actively manipulate prices
(in particular, by compressing the prices of long shots) in response to information
asymmetry and adverse selection risks. Bettors placing limit order bets on Betfair
are, as suggested, acting as de facto market makers; they are providing liquidity
and immediacy to the market. Given this, the arguments pertaining to how bet-
tors on the exchanges may seek to manage information asymmetry in relation to
number of race entrants are applied here to (1), (2) and (3) to further test adverse

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horse race betting
selection as an explanation for Betfair SP-based ORs. The following hypotheses are
presented:
H4: Betfair ORs are inversely related to grade of race.
H5: Betfair ORs are inversely related to age limit of race.
H6: Betfair ORs are higher for nonhandicap races than for handicap races.
3.3 Explanations from Horse Race Betting
3.3.1 Last Race Effect
A commonly observed empirical phenomenon in racehorse betting markets concerns
(on-course) bettors’ particular appetite to bet on the last race of the day in order to
recoup losses incurred earlier in the race meeting. This behavior, known colloquially
to bookmakers as “Charlie chasing,” is formalized in both Harry Markowitz’s (1952)
model of utility and more recently David Peel and David Law’s (2009, 253) “general
non-expected utility model” as behavior that is “risk-seeking over losses.” It relates
to the strong probability that, having engaged in regular wagering throughout the
course of a race meeting, bettors will be facing a loss on their trading prior to the last
race. Initial risk-averseness regarding losses is then replaced by risk-seeking behavior
as bettors attempt to retrieve a favorable trading outcome (Peel and Law 2009).
Implicit in this type of behavior is the notion that bettors may not view the menu
of betting opportunities in a particular race as an isolated decision problem but rather
as part of a series of decisions within a larger set of events, for example, the races
constituting a given race meeting. As such, the behavioral inﬂuences on a decision that
form part of a larger set of related decisions may be expected to differ from those that
operate on isolated decisions (see, e.g., Keren andWagenaar 1985; Rachlin 1990). In this
context a number of contributions point to the relationship between declining capital
and increasing risk preference (see, e.g., McGlothlin 1956; Ali 1977; Gilovich 1983;
Asch, Malkiel, and Quandt 1984; Metzger 1985; Gilovich and Douglas 1986; Golec and
Tamarkin 1995), which results in overbetting in the last race, particularly on long shots
(Johnson and Bruce 1993).
To the extent that exchange bettors also view betting as a series of decisions within
the wider context of the race meeting or race day, it is possible to argue that a “last race
effect” also may also arise. Bettors may seek to recoup losses and retrieve a favorable
trading outcome by wagering on the last race. If so, and as laying can only ever represent
an even-money “win” outcome (if the horse loses, the layer retains the stake money),
attempts to recoup losses may push more bettors toward betting to win, particularly
betting long shots to win. This is in order to achieve greater returns for a given wager.
The result will be a greater balance of activity toward betting rather than laying, with
concomitant effects on odds; these will generally shorten, thereby increasing the sum
of prices and OR. It is therefore hypothesized that
H7: Betfair ORs for the last race are signiﬁcantly greater than the OR for prior races at
a given race meeting.

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what explains the existence of an exchange overround?
287
3.3.2 Flat versus National Hunt Races
The study’s ﬁnal hypothesis focuses on the possibility that part of the explanation for
variation in Betfair ORs may lie in differences between Flat and National Hunt (jumps)
racing. The argument is based on the idea that back vis-à-vis lay activity may vary
between Flat and National Hunt (NH) racing. Betting activity may vary because of
the greater number of unpredictable factors for NH racing compared to Flat racing.
The greater number of unpredictable factors may encourage more laying compared to
betting activity, with concomitant effects on prices (lengthened), sum of prices, and
Betfair OR (lower for NH races compared to Flat races).
The increased unpredictability for NH racing includes, for instance, the presence of
hurdles and fences. These introduce the possibility that horses may fall or be brought
down. The longer distances covered and the generally more testing conditions (NH
racing is predominantly a winter sport) mean that it is quite common for horses to
“pull up” (i.e., drop out) without completing the race. The NH season is frequently
badly disrupted by weather-based cancellations, which negatively affects the analysis
and interpretation of form. Finally, there may be an effect relating to the competition for
betting revenue which NH racing has been forced to confront over the past two decades
in the form of all-weather Flat racing. This form of racing, relatively invulnerable to the
vagaries of weather and offering unparalleled consistency in terms of track conditions,
has ended NH racing’s monopoly of horse race betting opportunities during the winter
months. For the reasons outlined above, the study hypotheses that
H8: Betfair ORs are signiﬁcantly higher for Flat racing than for NH racing.
3.4 Control Variable
Bookmakers are known to be active on Betfair (O’Connor 2011). To the extent that
this activity and the experience of bookmakers (e.g., regarding the laying of multiple
runners) inﬂuence prices on Betfair, the study controls for the potential interplay
between bookmaker and Betfair ORs.
4 Data Collection and Measurement
.............................................................................................................................................................................
To test our hypotheses we analyzed data on 2,184 horse races that took place in the
UnitedKingdombetweenautumn2008andspring2010. Sampleracesweredrawnfrom
bothFlatandNHracing(inroughlyequalmeasure)andincludeanapproximatelyequal
number of handicap vis-à-vis nonhandicap races. Data collection was spread across 330
race meetings and all 60 racetracks located throughout the United Kingdom. All days
of the week are involved, including Sunday. For each race in the sample set both grade
of race and age limit were recorded. The sample set includes 330 “last races.” Sample
statistics are presented in table 16.1.

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horse race betting
Table 16.1 Sample Statistics
Variable
Number
Type of race
Flat races and National Hunt (NH) races
1,100
1,084
Type of race event
Nonhandicap races
1,056
Handicap races
1,128
Racetracks
60
Last races
330
Prior races
1,854
Race day
1. Monday
275
2. Tuesday
266
3. Wednesday
243
4. Thursday
250
5. Friday
372
6. Saturday
494
7. Sunday
284
Note: n = 2,184 races.
The study’s focus and dependent variable is Betfair SP-based ORs. Data on these were
collectedviatheTimeformwebsite(www.timeform.com),andcross-checkedusingdata
collected directly from Betfair’s own website (www.betfair.com). The data were also ran-
domly audited and sum of prices calculated to conﬁrm the accuracy of the reported
ORs. No errors were found in the published data, though the reporting to only two
decimal places potentially restricts the sensitivity of the empirical analysis. Bookmaker
SP-based ORs were similarly collected from Timeform and random audited to con-
ﬁrm accuracy. Again, the reporting of ORs to only two decimal places is potentially
restricting.
For the 2,184-race sample, Betfair ORs range from −0.14 (sum of prices: 0.86) to
+0.12 (sum of prices: 1.12), with a mean of 1.0047, standard deviation of 0.0189, and
mode of 1.00 (n = 544 for mode of 1.00). Bookmaker ORs range from −0.04 (sum of
prices: 96%) to +0.42 (sum of prices 1.42), with mean of 1.1834 and standard deviation
of 0.0628.
Betfair provides regularly updated information on monies matched for each
horse race. Total volume traded for each sample race was recording immediately prior
to the start of a given race. Monies wagered “in play” (in running) were excluded from
the analysis. These monies relate primarily to a horse’s “real time” performance and
do not represent “normal” betting activity. Trading volumes for the 2,184-race sample
ranged from £89,160 to £3,592,042, with a mean of £559,706. Given the skewness of
the data, logN of trading volumes was used in the analysis.

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what explains the existence of an exchange overround?
289
For the purposes of this study, a measure of “balance of opinion”/“balance of betting
activity”was calculated as follows. First, for each of the 2,184 races in the sample, Betfair
prices for all race participants were recorded at two points during the betting auction:
at 10 minutes prior to the scheduled start time of the race and immediately at “the
off.”15 The prices were recorded directly from Betfair’s website and included both back
and lay odds for each of the two measurement points.16
Second, from back and lay odds, average prices were calculated for each of the two
measurement points. Third, average price at 10 minutes was divided into average “off”
price in order to determine both the direction and magnitude of any odds change
for each race entrant over the 10-minute period. Finally, for each race in the 2,184-
race sample, race entrants’ price differentials were summated to determine the overall
balance of trading activity. Overall balances in favor of betting were coded 1,lay balances
were coded −1, and equilibrium positions were coded 0.
For analysis handicap races were coded 1 and nonhandicap races 0. Flat races were
coded 0, NH (jumps) races 1. Grade of race was coded as per ofﬁcial grading, from
1 (top grade) to 6 (lowest). To assess possible age limit effects two-year-old Flat races
and three/four-year-old NH races were coded 0 and all other races 1. For each race
meeting prior races (races before the last race) were coded 0, the last race 1. “Number
of runners” is based on the number of starters for each race in the 2,184-race sample
(i.e., withdrawn horses were not included). Numbers range from a minimum of 2 to a
maximum of 22 runners (mean = 9.989; standard deviation 3.48).
5 Analysis and Results
.............................................................................................................................................................................
Table 16.2 presents descriptive statistics, including means, standard deviations, and
Pearson correlation coefﬁcients for the variables examined in this study.
The hypotheses were tested using ordinary least squares (OLS) multiple regression
analysis. Tests for multicollinearity among the predictor variables revealed variance
inﬂation factors and tolerances substantially within acceptable limits (< 1.2 and > 0.85,
respectively).17 These test results conﬁrm no signiﬁcant problems in terms of using OLS
multiple regression analysis to test the study’s predictions (Belsley, Kuh, and Welsch
1980).
The dependent variable for analysis is Betfair OR. For robustness, “Betfair OR” is
operationalized in two related but distinct ways: as sum of prices (SPs) – 1 and as sum
of SPs – 1/runners. The former represents the OR for a given race. The latter establishes
the OR per runner for a given race. This dual operationalization of Betfair OR results
in two regression models, with each taking the following standard form:
Y = β0 + β1 + ···βn + ´ε,
where Y = dependent variable; sum of SPs – 1 (model 1) and sum of SPs – 1/runners
(model 2)

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horse race betting
Table 16.2 Descriptive Statistics, including Pearson Correlation Coefﬁcients
Mean
SD
1
2
3
4
5
6
7
8
9
10
1BetOR
0.005
0.019
-
2IObal
0.085
0.777
0.25
-
3LgMon
13.052
0.505
0.12
0.01
-
4Runa
9.989
3.540
0.22
0.05 −0.14
-
5Grade
4.165
1.298 −0.15 −0.08 −0.33
0.05
-
6Age
3.736
1.428 −0.01
0.00
0.07 −0.14 −0.06
-
7H’cap
0.511
0.500
0.07
0.01 −0.20
0.14 −0.07
0.28
-
8Last
0.152
0.359
0.06
0.01
0.05
0.12
0.19
0.01
0.11
-
9FlatNH
0.494
0.500 −0.02
0.05 −0.15
0.02 −0.21
0.08 −0.05 −0.01
-
10OR
18.341
6.189
0.21
0.03 −0.19
0.79
0.10 −0.07
0.25
0.27 −0.11
-
Note:n = 2,184
BetOR = Betfair sum of prices −1.
IObal = in-out-balance of price movements (in = prices shortening; out = prices drifting).
LgMon = LogN of monies (trading volume).
Run = number of runners in a given race.
Grade = grade of race.
Age = age limit for a given race.
H’cap = type of race (handicap versus nonhandicap).
Last = last race of a given race meeting.
FlatNH = type of race event (Flat versus National Hunt).
OR = bookmaker sum of prices −1.
SD = standard deviation.
Correlations above 0.05 signiﬁcant at p < 0.05 or better.
a Minimum 2 runners; maximum 22 runners.
β1,...βn = independent variables.
The results of the regression analyses are shown in tables 16.3 and 16.4. The results
across both tables support hypotheses 1, 3, and 7. That is, balance of activity, number
of runners, and last race effect all inﬂuence Betfair ORs in the predicted way. For
instance, a balance of activity in favor of backing rather than laying increases the
reported OR. Betfair ORs are also higher for increasing number of runners and for the
last race compared to prior races at a given race meeting.
The results across the two tables also show signiﬁcant effects for trading volume
(logmonies), grade of race, and type of race (handicap versus nonhandicap). However,
ﬁndings here are contrary to expectations. For instance, Betfair ORs increase (rather
than decrease) with both trading volume and grade of race. ORs are also higher for
handicap races compared to nonhandicap races. Nonsigniﬁcant results are reported for
age limit of the race and type of race event (Flat versus NH). The study’s ﬁndings are
discussed in the concluding section.

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Table 16.3 Test of Hypotheses, Betfair Sum of SPs – 1 as Dependent Variable
Variable
Standardized Beta Coefﬁcient
t-value
Inoutbalance (H1)
0.223
7.130∗∗∗
Logmonies (H2)
0.143
4.081∗∗∗
Number of runners (H3)
0.128
2.336∗
Grade of race (H4)
−0.208
−5.811∗∗∗
Age limit of race (H5)
0.037
0.758
Handicap versus nonhandicap (H6)
0.069
1.977∗
Last race (H7)
0.072
2.008∗
Flat versus NH (H8)
−0.070
−1.438
Bookmaker sum of SPs – 1 (control)
0.159
2.805∗∗
Adjusted R2 = 21.0%
F value = 24.556∗∗∗
Note: n = 2,184.
∗p <0.05; ∗∗p <0.01; ∗∗∗p <0.001.
Table 16.4 Test of Hypotheses, Betfair Sum of SPs – 1/runner as Dependent
Variablea
Variable
Standardized Beta Coefﬁcient
t-value
Inoutbalance (H1)
0.214
6.292∗∗∗
LogMonies (H2)
0.116
3.028∗∗
Grade of race (H4)
−0.173
−4.423∗∗∗
Age limit of race (H5)
−0.028
0.549
Handicap versus nonhandicap (H6)
0.081
2.234∗
Last race (H7)
0.084
2.450∗
Flat versus NH (H8)
−0.037
−0.709
Controlb
Adjusted R2 = 11.6%
F value = 14.542∗∗∗
Note: n = 2,184.
a H3 (number of runners) n/a for this analysis.
b Bookmaker sum of SPs – 1/runner omitted due to unusually high value (t-value > 100.00).
∗p <0.05; ∗∗p <0.01; ∗∗∗p <0.001.
5.1 Sensitivity Analysis
Analytical robustness of the empirical examination was assessed via two further tests
of the data. First, to check whether isolating the Betfair OR from sum of prices affects
the analysis, sum of SPs and sum of SPs/runner were substituted for sum of SPs – 1 and
sum of SPs – 1/runner as the dependent variables. The regression analyses were then
repeated as per above. Results are qualitatively very similar to those reported in tables
16.3 and 16.4 except that, for sum of SPs/runner, type of race event shows a signiﬁcant

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horse race betting
effect while grade of race does not. These changes compared to the previous analysis
suggest that both type of race event and grade of race may be sensitive to variation in
the number of race entrants.
Second, therefore, given the above, partial correlation analysis was conducted to test
for possible spurious relationships involving the eight predictor variables and Betfair
ORs. Partial correlation analysis allows examination of the effect of one variable, the
control, on the relationship between two other variables (Meng, Rosenthal, and Rubin
1992). For the present study, the aim was to examine the effect of number of race
entrants (B) on the association between each predictor variable (A) and Betfair OR (C)
by computing a partial correlation coefﬁcient to remove the association that B has with
both A and C (Blaikie 2003).
Results for the partial correlation analysis suggest that, apart from last race effect (the
signiﬁcance of which is reduced), each of the predictor variables found to be signiﬁcant
in the main analysis remains broadly as signiﬁcant (no change in the value of p) when
controlling for variation in the number of race entrants. Put slightly differently, partial
correlation analysis suggests that each predictor variable exerts an effect on Betfair
OR that is independent of the number of race entrants. No spurious relationships are
revealed.
6 Discussion and Conclusions
.............................................................................................................................................................................
The study reported in this chapter sought to explain both the existence and variation
in exchange (Betfair) overrounds. Since December 2007, Betfair, the leading person-
to-person Internet betting exchange worldwide (O’Connor 2007, 2011), has reported
its own starting prices and accompanying overrounds. Based on our sample, we ﬁnd
that Betfair overrounds varied by a factor of 26 percent, from −14 to +12 percent.
The empirical results imply that “balance of activity,” trading volume, number of race
entrants, grade of race, type of race (handicap versus nonhandicap), and bookmaker
overrounds are key determinants of the existence and magnitude of Betfair overrounds.
In contrast, insigniﬁcant results were reported for age limit and type of race event (Flat
versus National Hunt).
The ﬁnding that “balance of activity” may be a key explanatory variable supports
arguments in the ﬁnance literature concerning the determinants of bid-ask spreads in
order-driven markets (Handa, Schwartz, and Tiwari 1998, 2003). The basis of these
arguments is that an “imbalance of opinion/activity,” combined with the “gravitational
pull” effect, will serve to minimize bid-ask spreads, whereas a “balance of opinion”
will maximize the magnitude of spreads. This study has argued that, in the con-
text of exchange betting, an imbalance of activity (for a given race proportionally
greater backing to win/laying to lose) will combine with “gravitational pull” effect to
move Betfair ORs either higher or lower. Results support these theoretical arguments,
suggesting that bettor behavior on the exchanges may, to some extent at least, mirror
investor behavior in order-driven ﬁnancial markets more generally.

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what explains the existence of an exchange overround?
293
The results for trading volume are intriguing, as are the results for type of race,
grade of race, and number of race entrants. Contrary to expectations, the study reports
a positive and signiﬁcant relationship between volume and Betfair OR. It is possible
that increased trading volume may reﬂect increased betting rather than laying activity.
The signiﬁcant correlation coefﬁcients between trading volume and grade of race and
between grade of race and balance of activity (see table 16.2) seem to support this
conjecture; they suggest that a greater proportion of the increasing trading volume may
be directed at betting to win rather than laying to lose, with concomitant effect on
Betfair ORs. The issue merits further attention.
Consistent with hypothesis 3, the study ﬁnds a signiﬁcant positive relationship
between number of race entrants and Betfair OR. That said, results here are minimally
signiﬁcant (p <0.05) and contrast with the strong relationship between bookmaker ORs
and number of race entrants (correlation coefﬁcient 0.79; see table 16.2). Results for
gradeofraceandtypeofracearecontrarytoexpectations.Forinstance,insteadofﬁnding
increasingORsforlowergraderacescomparedtohighergraderaces,resultsshowhigher
Betfair ORs for higher grade races. Taken alongside results for number of race entrants
and type of race, the present ﬁndings raise questions about the nature of betting activity
on the exchanges, particularly bettors’ response to adverse selection risks. In essence,
ﬁndings suggest reasons other than information asymmetry and adverse selection that
mayexplaintheexistenceofexchangebid-askspreads.Again,thesereasonsmightinclude
an increasing tendency to bet to win rather than lay to lose in higher grade races. The
correlation coefﬁcients shown in table 16.2 may help to explain the results for grade of
race; the higher the grade, the greater the volume of monies wagered aimed at betting to
win, which leads to higher ORs on Betfair. The correlations shown in table 16.2 do not
support this explanation for type of race; trading volume is higher for nonhandicaps
vis-à-vis handicaps, yet Befair ORs are higher for the latter compared to the former.
The question of exchange betting behavior in relation to information asymmetry and
adverseselectionrisksisanissuewhichmeritscloserscrutiny. Thepresentresultsprovide
a glimpse into potential idiosyncrasies of exchange-based bettor behavior.
Notwithstanding the above, results for last race effect suggest some familiar bettor
behavior on the exchanges. Results showing a (weakly) signiﬁcant effect support extant
arguments that bettors may often “Charlie chase” on the last race, placing bets aimed
at recovering the day’s losses. Given this observed racetrack behavior, there seems
little reason to think that such behavior would not also feature on the exchanges, with
increasing betting to win activity increasing Betfair ORs on the last race compared to
previous races. Finally, the insigniﬁcant results for type of race event and age limit of
race may suggest that bettors neither differentiate between ﬂat and NH racing nor adjust
their betting according to the degree of public form available for younger vis-à-vis older
race entrants.
Taken as a whole, it appears from the present analysis that betting activity on the
exchanges may show some similarities with investing behavior in order-driven markets
(balance of activity and gravitational pull effect) while also demonstrating behavior
unique to horse race gambling (e.g., last race effect). Extant arguments in both the
ﬁnance and horse racing literatures appear to help explain the existence of and variation

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horse race betting
in exchange (Betfair) ORs. That said, there may be behaviors, such as behavior toward
grade of race, which may be potentially unique to exchange betting. Examining betting
activity on the exchanges appears to offer a potentially fruitful line of inquiry for
researchers interested in empirical tests of the efﬁcient market hypothesis. Additional
microstructure analysis may be especially fertile ground for future research.
Notes
1. Ithasalwaysbeentheoreticallypossiblefor bettorstolay—bybackingallotherpossibilities
to happen. For instance, a bettor could, before the exchanges, lay any given horse(s) in
any given race by backing all other race entrants to win. That said, nontrivial practical
and cognitive difﬁculties have always precluded this form of laying. For two-runner races
it is possible to lay one entrant by backing the other. For three-runner races and above,
however, the practical and cognitive difﬁculties of laying one horse by backing all others
increase exponentially.
2. Immediacy is the ability investors have to buy or sell assets at any time the market is open
(Handa, Schwartz, and Tiwari 1998).
3. The trader placing (buy or sell) limit orders is providing both prices and immediacy to
the market, thereby acting, in essence, as de facto market maker.
4. Exchange betting is discussed further in the following section.
5. Shin (1993, 1142) argued that the measurability of bookmaker overrounds in betting
markets is “in marked contrast to more sophisticated markets, such as the stock market,
in which the spread varies across assets and also across volumes traded.” The magni-
tude of the overround can vary during the period of betting (the betting auction). These
overrounds are observable by racegoers but generally not reported and therefore difﬁ-
cult to access. Overrounds based on starting prices are, however, readily accessible and
measurable through sources such as Timeform and Raceform.
6. The reference to “new approach” relates to changes to the way industry SPs are deter-
mined. Previous to 2007, SPs were determined by the ofﬁcial SP returner(s), who had
the discretion to investigate the entire “betting ring” to ﬁnd the best odds being traded.
The new rules, set by the Starting Price Regulatory Commission, require that (1) a set
number of “pitches” are surveyed (normally 10 and normally to involve the same list of
bookmakers on an ongoing basis) and (2) the “majority price” should be used if prices
among the list of 10 are not uniform.
7. For bookmaker-led markets, divergence from“true value”is typically unidirectional; sum
of prices is usually greater than 1, which means (1) a positive OR and (2) that prices at
which recorded transactions occur tend to be below but not above their objective value.
8. While a horse race example has been used to illustrate the OR and betting market oper-
ational efﬁciency, the points made apply to any event, sporting or otherwise, for which
there is more than one possible outcome and for which betting odds are available.
9. Data collection procedures are described in section 4.
10. The reader is referred to Handa, Schwartz, and Tiwari (1998, 2003) for a thorough
exposition of the arguments and analysis relating to gravitational pull effects on bid-ask
spreads in an order-driven market.
11. Arguments differ in that, on the one hand, if trading volumes are generally low, market
makers will ﬁnd it difﬁcult to adjust their inventory levels and will increase their spreads

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what explains the existence of an exchange overround?
295
to compensate. On the other hand, high trading volumes may suggest investors trading
on superior information. Market makers will therefore increase their bid-ask spreads to
compensate for perceived adverse selection risk.
12. For instance, increasing trade (monies wagered) on a given race entrant will likely increase
the competition among bettors seeking to ensure that their limit order is“matched”and/or
that they are able to execute a market order to match an existing limit order. The effect will
be to bring back and lay odds closer together, potentially reaching the limit of closeness
as determined by the minimum “tick” price available for a given odds range.
13. The favorite-longshot bias refers to the empirical observation that compared to long shots,
implied probabilities for favorites more closely match their objective win probabilities
(Schnytzer and Shilony 1995).
14. In the limit (beginning of Flat race turf season), all entrants in a two-year-old maiden
race will be competing in their ﬁrst race under license. In this context, there is no publicly
available information by which to adjudge a horse’s chances.
15. The time period for recording prices, beginning at 10 minutes before the scheduled start
time, is based on the observation that the vast majority of trading activity on Betfair tends
tooccurinthelast10minutesbeforethestartof arace. Duringthisperiodbettingvolumes
frequently increase at least six-fold, from around £100,000 to in excess of £600,000.
16. Piloting of data collection procedures showed that a maximum of 44 data points (equiv-
alent to 22 runners) could be accurately recorded within Betfair’s automatic “refresh”
period (approximately 25-second intervals). Data collection was therefore limited to
races comprising no more than 22 runners. In turn, creation of a 22-runner race limit
resulted in the omission of several races from the data collection process. In total, because
ﬁeld size exceeded 22 runners, 25 races were omitted from, in total, 23 of the 330 race
meetings. The 2,184-race sample is the net number of races, following the omission of
the 25 races.
17. Basically the closer both values are to 1, the lower the collinearity among the predictor
variables (Blaikie 2003).
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chapter 17
........................................................................................................
INSIDER TRADING IN
BETTING MARKETS
........................................................................................................
adi schnytzer
1 Introduction
.............................................................................................................................................................................
A betting market is a market in which the agents trade bets, where a bet is a contingent
commodity (or portfolio of contingent and, perhaps, regular commodities). One side
to the trade believes that the contingency (or contingencies) will occur while the other
believes it (they) will not. Accordingly, both are willing to enter into a trade that, by
deﬁnition, is subject to either risk (there are known or estimable probabilities associ-
ated with contingencies) or uncertainty (probabilities are unknown and inestimable).
A betting market may be either legal or illegal; this chapter deals only with legal bet-
ting markets.1 Examples of operations in betting markets include betting on two ﬂies
crawling up a wall, buying or selling an option,2 trading in real estate, playing roulette
in a casino, and betting on a horse in the Melbourne Cup.
These examples are sufﬁcient to determine when insiders are likely to be found in
the market and thus determine the boundaries of this chapter. When Australians bet
on which of two ﬂies crawling up a wall will ﬁrst reach the ceiling, they are generally3
betting in a situation where probabilities are neither known nor estimable, and thus
there is no relevant information to determine winning probabilities. Accordingly, there
can be no human insiders and betting on such an event may be termed pure gambling
and will not be discussed further.
Buying or selling options are bets in which payoffs are determined either by the
price of the underlying asset(s) on the expiry date of the option if the option is held
to expiration or by the price of the option when sold if this occurs before expiry. In
either case, there is sufﬁcient information regarding the underlying asset(s) to attempt
prediction of the likely value of the option at some point in the future. Whether such
predictions, if made by outsiders, are economically useful is a matter of debate and
need not be discussed further.4 However, it is undeniable that company insiders who

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insider trading in betting markets
299
are privy to important information not yet publically disseminated are able to predict
the short-term direction in the price of the relevant share.5 Accordingly, this type of
betting market certainly falls within the domain of this chapter. However, since insider
trading in ﬁnancial markets is illegal in the world’s major markets, and since very little
has been published in this area,6 this type of betting, too, will be discussed no further.
It should be noted that these factors are related; illegal insiders will wish to enter the
market in such a way as to be undetectable and given the complexity of derivative
markets,7 this renders data collection by researchers (and the SEC) extremely difﬁcult.
Trading in real estate is similar to trading in derivatives markets in that price predic-
tion is extremely difﬁcult. This difﬁculty is exacerbated by the fact that most properties
are literally unique.8 Also, since the current owner generally has inside information
with regard to the property, the prospective buyer is subject to adverse selection. How-
ever, the exploitation of inside information in this market is virtually immeasurable
and thus, short perhaps of courtroom anecdotes, has not been a subject of considerable
research.9
Playing roulette in a casino is, in some sense, a mirror image of betting on two ﬂies
climbing up a wall. If the latter is pure gambling because the bettors are subject to
uncertainty and no insider can get an edge,10 in roulette all probabilities are known
and so, again, insiders have no edge. Accordingly, insiders do not feature in such
betting markets. To summarize, inside information cannot exist when either all or no
probabilities are known to all participants in a betting market.
This leaves the last example, betting on a horse in the Melbourne Cup, and here the
conditions are ripe for the presence of inside traders and, possibly, for their detection.
First, the only people connected to a runner in the race who are not permitted to bet
on the race are the jockeys. On the other hand, in harness racing, drivers are permitted
to bet and in greyhound racing all the dogs’ connections may bet. Hence in principle
there will be asymmetry of information, with the animals’ connections having a more
accurate idea of the true winning probabilities in the race than the betting public
at large, and the insiders will be able to bet freely should they wish to do so. The
focus in this chapter will thus be on the three racing betting markets, gallops, harness,
and greyhounds.11 A key issue to be addressed is whether the presence of betting
insiders at the track implies that their presence is easily measured. It will be shown
that this is a function of the microstructure of the particular betting market. In some
markets the impact of insider trading is readily measured while in others it has hitherto
proven virtually impossible. The different microstructures of betting markets and the
implications for insider trading and its measurement are presented in the next section.
2 The Microstructure of Betting Markets
.............................................................................................................................................................................
In terms of the functioning of insiders,12 the microstructure of betting markets has
three dimensions, the types of bet offered, the legal betting mechanism(s), and the

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horse race betting
location of available mechanisms—at the track where the race is held (henceforth
on-course) and/or elsewhere (henceforth off-course). While there are many types of
bets available,13 for the purposes of this chapter, only the most common type, win
betting, will be considered.14 The most common betting mechanism worldwide is the
pari-mutuel, also known as the totalizator and henceforth referred to simply as the tote.
The relevant locations for betting are on-course, off-course, and online (Internet bet-
ting). In any country or state that permits betting, it is always permitted on-course, and
it make sense to assume that insiders will generally bet at the track unless considerably
better odds are available off-course, since they may thereby be sure of the state of their
horse or dog shortly before the race.15 The legality or otherwise of off-course betting
varies considerably from country to country and will be considered below wherever
relevant to insider trading.
The tote is a betting mechanism that takes bets on all horses and then, at the end
of betting, removes its proﬁt from the total pool. This tends to be in the range of 12
to 15 percent. The remaining money is then divided among the bets on the winning
horse. Thus if $1,000 is bet altogether on all horses in a given race and the tote take
is 15 percent, then $850 is left in the pool. If $100 of the original $1,000 had been bet
on the winning horse, then each dollar bet would yield a payout of $8.50, that is, a
proﬁt of $7.50 per dollar.16 The only complication that may arise in the tote market is
the case where most of the money is bet on one horse. Suppose, then, that $900 of the
$1000 had been bet on the winning horse. This implies, with a payout of $850 among
the winning bettors, that each dollar bet on a winner yielded a loss of 10 cents in the
dollar!17 To avoid this patently unfair situation, totes guarantee a minimal payout of
either $1.05 or $1.10 for each dollar bet on a winning horse.
The interesting feature of the tote is that it is not a seller of (contingent) commodities
in the classic sense. The owners make a more or less ﬁxed18 rate of return given by the
take and maximize nothing except possibly revenue.19 In particular, the tote owners
do not set winning odds, these being determined entirely by the relative demand for
different horses of the betting population. Hence the owners of the tote are untroubled
by insider trading. There is a tote on every racetrack in the world where gambling is
legal.20
A second betting mechanism related to the tote is known as SP (starting price) bet-
ting in Commonwealth countries and is similar to the mechanism whereby odds paid
on winning bets by bookmakers who operate legally in the State of Nevada (USA)
are determined. Basically this is a mechanism whereby the payouts to winning bets are
determined by the ﬁnal odds available at the end of betting with bookmakers on-course,
in the case of SP betting, and somewhat less than the on-course tote payout in the case
of Nevada betting.21 In such cases, the bookmakers who own the services would appear
to be acting as either a remote tote or a service that provides odds out of their control,
but this is not so. Since these providers may themselves bet with either the tote (in
the United States) or with on-course bookmakers (in the United Kingdom), it can be
shown that they may be able to manipulate And the ﬁnal odds; thus insiders are unlikely
to be interested in this mechanism.22

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insider trading in betting markets
301
The third betting mechanism, and the one that has generated the most research
with respect to insider trading, is the (ﬁxed-odds) bookmaker. Where bookmakers are
legal, they are generally legal on-course. They are also legal off-course in the United
Kingdom and Ireland, while being illegal off-course in Australia. In New Zealand there
are no on-course bookmakers, but the New Zealand tote offers a bookmaking service on
selected races. The crucial difference between bookmakers and the betting mechanisms
described above is that bookmakers offer ﬁxed odds on race outcomes. In other words,
bettors know as soon as they have bet how much they stand to win if their chosen
animal wins.
This provides an obvious advantage for the possessor of inside information because
it enables the holder to make more accurate calculations regarding the expected return
when large sums of money are bet. With an SP-type mechanism, this is impossible,
whereas with the tote it is plausible only if the insider waits until seconds before the
end of betting before placing the bet23 and no other insider has the same idea! It is
thus broadly accepted in the literature that insiders bet with on-course bookmakers
wherever possible. And if there are no legal bookmakers on-course or readily accessible
from the track by phone or online? This question has only rarely been addressed in the
literature.24 However, before presenting some new empirical results on this issue, it will
be useful to consider the literature on insider trading in the presence of bookmakers.
3 Insider Trading in the Presence
of Bookmakers
.............................................................................................................................................................................
The pioneering paper in this ﬁeld is by Jack Dowie (1976), who presented an interesting,
albeit ﬂawed, test of whether there is proﬁtable insider trading in the U.K. horse betting
market. Dowie (1976, 147) deﬁned SP “as the odds at which a sizeable bet could have
been placed at the ‘off’,” in other words as very close to the end of betting, from which
he argued that
SP can be taken to incorporate any superior or inside information that exists in
relation to the event. If inside information plays a signiﬁcant role in horse race
betting markets, then the correlation between the probabilities embodied in the
SP returns and the realized probabilities should be signiﬁcantly higher than the
correlation between the latter and any other set of probabilities assigned prior to
the “off” (and certainly any set assigned prior to betting on the event). If, then,
the correlation between the probabilities embodied in the betting forecasts in a
morning newspaper and the realized probabilities is as high as the SP correlation,
we can conclude that the existence of superior“inside”information is in doubt (149).
Having shown that the correlation between the winning probabilities incorporated
in forecast prices and ex post winning probabilities are no less than those between the

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horse race betting
latter and the winning probabilities implied by SP, Dowie concluded that the market
is strongly efﬁcient.25 The problem with the argument is that these correlations being
tested refer to all horses in Dowie’s sample and not simply to those horses on which
insiders bet. Thus SP might be highly accurate for insider-traded horses and quite
inaccurate for all other horses, whereas forecast odds might be reasonably accurate
overall.
This chapter will provide a simple counter-test to Dowie’s after the behavior of
insiders in such a market are described. Since bookmakers are not required to take bets
of unlimited size, an insider wishing to bet large sums on a horse will spread the bet by
placing acceptable quantities of money on the horse simultaneously with a number of
different bookmakers so as to obtain the best odds possible. This highly visible activity
is called a plunge and is accompanied by an immediate reduction in the ﬁxed odds of
the plunged horse offered by the bookmakers. Since insiders bet at greater odds than
SP, a better test of the presence of insiders in the U.K. betting market would be to check
whether horses whose odds shorten between forecast price and SP would yield proﬁts
were they to have been backed at forecast prices.26 This is the essence of N. F. R. Crafts’s
(1985) attack on Dowie, which he supplemented with interesting anecdotal evidence of
heavily plunged winners. Crafts also showed that horses that drift from forecast prices
to SP tend to belong to “a class of outstandingly poor value bets” (303).
Crafts used these results to suggest that horse betting markets may require more
government regulation than was the case. After all, the sport’s own governing body, the
Jockey Club, was apparently of the same view: “The Jockey Club’s own Committee of
Inquiry argued that‘the public is entitled to be satisﬁed that every precaution is taken to
ensure that racing is fairly conducted and that malpractices are reduced to a minimum”’
(Crafts 1985, 303). Adi Schnytzer and Yuval Shilony (2007) set out to test the implicit
hypothesis provided by Crafts that insiders might have an incentive to mislead the
betting public and bookmakers by having their horses deliberately underperform. This
would provide the insiders with better odds at a later start.
Schnytzer and Shilony presented a simple model that shows the conditions under
which it is optimal for insiders to rig prices by deliberate underperformance in some
races. Using tote27 data for Australian greyhound, harness, and thoroughbred racing
markets, they then showed how an empirical analysis of the relationship between win
and place probabilities in conjunction with observed patterns of betting behavior can be
used to establish the presence of price rigging. It was shown that there is no signiﬁcant
systematic price rigging in these markets. Quite simply, animals that are“not on the job”
do not, on average, underperform other animals. This does not reject the hypothesis
that there is some corruption in these markets, but it does reject the hypothesis that
there is systematic corruption.
Proceeding chronologically from Craft’s contribution in this area, three papers by
Hyun Song Shin28 represent pioneering work on the theory of bookmakers’ behavior
in the presence of insiders. Shin (1991) presented an extensive form game in which
nature ﬁrst chooses the winning probabilities of the horses in a two-horse race.29 This
distribution is observed by a monopoly bookmaker, who sets odds according to this

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303
probability distribution. The single insider then observes the actual result of the race
and decides how much to bet subject to a budget constraint. Outsiders are effectively
noise traders and provide the bookmaker with the means to pay the winning insider
while still allowing the bookmaker a proﬁt. Shin proved that in the unique equilibrium
in this game, the optimal prices set by the bookmaker will display a favorite-longshot
bias30 and that the value of insider trading is a decreasing function of the size of the
insider’s (assumed known to the bookmaker) budget, since as this budget grows, the
implied optimal prices for the bookmaker rise. The maximum value of insider trading
is shown to be one-third, a modest proportion given that the insider always wins, but
is explained by monopoly power of the bookmaker.
Shin (1992) presented a generalization of the previous model to the case of a horse
race with more than two starters and a single bookmaker who, however, has lost his
monopoly power because he must bid against another candidate to set odds on the race.
The game analyzed here has four stages. In the ﬁrst stage two potential bookmakers bid
the sum of prices31 in the race and the lowest bidder becomes the bookmaker in the
race. In the second stage the bookmaker sets prices for each horse in the race, subject
to the constraints that no price is negative or greater than one and that the sum of
prices is no greater than that bid in the ﬁrst stage. In the third stage, nature decides on
the winner of the race and whether the single bettor in the race will be an outsider or
an insider. The difference between insider and outsider is that the former knows the
identity of the winning horse while the latter believes with certainty that a particular
horse (not necessarily, but possibly, the actual winner) will win the race. In the ﬁnal
stage the chosen punter bets and the payout determined. The equilibrium in this game
when the bookmaker is subject to a zero proﬁt condition is that, as in Shin (1991),
prices will reﬂect a favorite-longshot bias.
In order to produce a method of measuring the extent of inside traders operating
at the track, Shin (1993) modiﬁed the previous model slightly and derived an iterative
procedure for determining the extent of insider trading, obtaining a value of somewhat
over 2 percent. He again modeled the behavior of competitive bookmakers facing two
types of bettors, those with and those without inside information, and maximizing
expected proﬁt. The main result is the existence of a favorite-longshot bias if and only
if there is inside money in the market. The model hinges on the absence of any bias in
the participants’forecasts of race results. Shin assumed that the proportion of outsiders
backing any given horse is equal to its true winning probability and that insiders know
the winning horse and always back it. Thus, ex post, the proportion of money bet on
all horses by all bettors is exactly in accordance with the true winning probabilities.
Observing the optimal prices charged by bookies in a race, the model can be used to
solve the underlying winning probabilities and the incidence of insider trading. This
solution cannot be obtained analytically, but numerically, using an iterative process as
described by Michael Cain, David Law, and David Peel (1996).
An interesting result obtained by Shin is that there is a linear relationship between
the sum of prices and the number of horses in a race, and he argued that this is due
to the presence of inside traders. Leighton Vaughan Williams and David Paton (1997)

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horse race betting
showed that the relationship may be due also to bettors counting only a ﬁxed fraction
of their losses. They also showed that the favorite-longshot bias may derive from the
demand as well as the supply side. In other words, while bookmakers may bias their
prices in the presence of insiders, there are other factors explaining the bias.32
In a simple test of Shin’s model against Craft’s idea of the plunge as an indicator
of insider trading, Cain, Law, and Peel (2001b) showed that there is a signiﬁcant
relationship between Shin’s measure of the extent of insider trading and the extent
of plunging in the race. In an alternative test of Shin’s model, Schnytzer and Shilony
(2003) tested whether the Shin (1993) model-derived probabilities correspond to actual
winning frequencies. They showed that bettors display a favorite-longshot and that
accordingly bookmakers would evaluate their expected proﬁts, taking this into account
and setting prices accordingly. However, Shin did not take this correction into account
in his model, and this undermines the essential result of Shin’s model, which is that the
sole cause of the bias is insider trading.
Cain, Law, and Peel (2001a) used Shin model estimates of insider trading in the
betting on individual races to show that the market anomaly observed by Paul Gabriel
and James Marsden (1990), that U.K. tote payments on winning bets consistently
exceeded those paid by bookmakers, is in fact more subtle than originally reported. Use
of more appropriate statistical methods suggests that bookmakers pay more generously
than the tote on winning bets on favorites but less generously on winning longshot bets.
They showed that this new anomaly is associated with the incidence of insider trading
in the betting on each race and argued that it cannot be arbitraged away owing to the
bookmakers’ dominant market position.
In a different application of the Shin model, Law and Peel (2002) tried to distinguish
between insider trading and herding (as evidenced by plunged horses) by arguing that
in races where the Shin measure of the extent of insider trading increases as between
openingpricesandstartingprices,theninsidertradingmaybeimputed,whereasif there
is a reduction in the Shin measure and the horse has been plunged, the plunges would
appear to indicate herding. Law and Peel (2002, 327) found “that signiﬁcant positive
betting returns are achieved when shortening odds are accompanied by a rise in the
Shin measure; when they are accompanied by a fall, returns are negative, suggesting
herd behaviour.”
One difﬁculty with the Law and Peel approach is the implicit assumption that the
reduction in a horse’s odds is due either to insider trading or to herding. While the
authors do provide a brief discussion of various possible triggers for herding, there is
no theoretical model and no empirical allowance for the possibility that a horse might
be plunged by insiders early in the betting and subsequently drift in the betting,allowing
proﬁts to be made by betting late. One reason for this omission might be that Law and
Peel had access only to opening and starting odds and not to odds in the middle of
betting. This lacuna was ﬁlled Schnytzer and Avichai Snir (2008a), who showed that
proﬁts may be made by betting on horses plunged early in the betting, which then
drift, even at starting prices in both the British and Australian on-course bookmakers’
markets. Based on the results obtained, it would seem that, on average, horses which

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305
are plunged late generally trigger herding and that only some of those plunged early
are followed by herding behavior.
The mention of early and late plunges raises the question: when do insiders bet in
a bookmakers’ market? This issue has been analyzed by Schnytzer and Shilony (2002),
who modeled a game of timing where the agents are insiders wishing to bet on different
horses in a race. The basic arguments are as follows. At the opening of the betting, odds
are determined by a cartel and incorporate proﬁt margins so that odds are lower than
the equivalent perceived winning probabilities for all horses. As soon as betting begins,
each bookmaker is on his own, and the cartel collapses.33 Thus, ceteris paribus, odds
tend to rise over time. However, there are risk-neutral informed traders whose estimates
of winning probabilities for the horses with which they are associated are more accurate
than those of the bookmakers. Should the odds be greater than the insiders’ valuation
of the corresponding horse’s winning probability, the relevant insiders will place large
amounts of money on the horse via a plunge.34 This leads to an immediate reduction in
the odds of that horse and an increase in the odds of all other horses in the race. Suppose,
now, that there are two such groups of insiders, each wishing to plunge its own horse.
Since a plunge increases the odds for other horses, each group has an incentive to wait
for the other to plunge ﬁrst. On the other hand, since the information concerning any
given horse is known to more than one person,35 the longer the insiders wait, the greater
the risk that the information will leak to a third party. The recipient of the leak will then
plunge the horse and the group of insiders—except perhaps the one responsible for the
leak—may be left with odds at which betting is no longer worthwhile. This conﬂicting
incentive gives rise to the game of timing. Schnytzer and Shilony showed that the game
has no equilibrium in pure strategies but, for the two-player case,36 derived the unique
equilibrium in mixed strategies. Based on this model, three rather intuitive empirically
testable hypotheses were derived:
1. The lower the level of opening odds, the later any plunge activity will take place.
2. An increase in the number of horses that have insiders associated with them leads
to an earlier optimal plunge time.
3. An increase in the number of horses also leads to an earlier optimal plunge
time.
Using data from the 1997–1998 horse racing season in Australia, the authors showed
that these hypotheses were strongly supported by the data.
Three additional studies complete this survey of the literature on insider trading in
the presence of on-course bookmakers. The ﬁrst is Schnytzer and Shilony (1995), which
found that insider trading takes place in this type of market. A second key study is an
extension of this line of research by Schnytzer, Shilony, and Richard Thorne (2003), and
the third is based on an alternative measure of the extent of insider trading provided by
Schnytzer, Martien Lamers, and Vasiliki Makropoulou (2008 and 2009). The Schnytzer
and Shilony (1995) paper built on Craft’s 1985 insight that plunges provide evidence
of insider trading and used the unique market environment pertaining to horse race

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horse race betting
betting in Melbourne in the 1980s to make the point without access to bookmakers’
odds data and without employing unintuitive theoretical modeling. The argument of
the paper may be summarized as follows:37
The Melbourne horse betting market produces38 data on the betting behavior of two
mutually isolated populations who bet with the tote, one with and the other without
access to inside information. In this market, off-course bettors may place bets with
the government-run tote at ofﬁces located throughout Victoria. During the 1980s the
Victoria government had a legal monopoly in off-course betting.39 In addition to the
public information already available to bettors, all off-course tote ofﬁces provided the
projected odds for the different horses in a race from around 30 minutes before starting
time. There are also tote windows at the racecourse. Some 15 minutes before race time,
the off-course pool is amalgamated with the on-course pool so that the tote payout on
a race is based on the combined pools. Since the size of the off-course pool is generally
more than three times that of the on-course pool, unless the projected odds in the
two pools are very different, changes in projected odds owing to differences in the
betting behavior of the two populations were not easily picked up by off-course bettors
following the amalgamation.
On-course bettors, of course, also may bet with bookmakers. Well over one hundred
private bookmakers competed40 among themselves and with the tote. The important
feature of this market, which facilitated the monitoring of inside information, was that,
with the exception of tote information—whose presentation to bettors was identical
on- and off-course—information ﬂows between these two segments of the market
were restricted. There were no public telephones at the track, and the communication
of race-related information via ofﬁcial phones was forbidden. Bettors were free to leave
the track and pay to return, but since the on- and off-course tote payouts are identical,
they had no (legal) incentive to leave the track. Given that with bookmakers the payout
contingent on a win is known when the bet is placed and that inside information is likely
to be more accurate as race time draws near, it is to be expected that most “insiders”
would bet with bookmakers via plunges. A plunge leads to an immediate reduction
in the odds offered by bookmakers about the horse in question. Since bookmakers
operate in very close proximity to one another, bettors have no difﬁculty in discerning a
plunge. A plunge provides bettors with an indication that a horse’s connections believe
that the true probability the horse will win is higher than that reﬂected in the pre-
plunge available odds. Bettors’ budget considerations and herding aside, the plunge
continues to a point at which the odds have shortened to reﬂect the new subjective
probability that the horse will win. The projected tote odds would now have been
longer than those offered by bookmakers.“Outsiders,”who observed the plunge, would
bet on the plunged horse with the on-course tote to take advantage of this “expected
arbitrage opportunity.” Hence the informed population, on-course tote bettors, used
“secondhand” inside information. However, since plunge information does not leave
the race course, it is not incorporated into the behavior of off-course bettors.
Under these circumstances, testing the hypothesis that inside traders are betting on-
course is fairly simple. First it needs to be shown that the information contained in the

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307
proportions of money bet both on-course and off-course signiﬁcantly contributes to an
explanation of the horses’ ex post winning probabilities. Schnytzer and Shilony (1995)
did this by regressing a win dummy on the proportions bet on-course and off-course
using conditional logit regression41 and found that both explanatory variables received
positive and signiﬁcant coefﬁcients. They remained positive and signiﬁcant when each
was run alone in a separate regression. The interpretation of these variables is that
the proportion of money bet off-course represents the outsiders’ assessment of public
information, while the relative amounts bet on-course represent public information as
modiﬁed by inside information.
Second, and even more convincing, is the following betting simulation: Suppose a
bettor had access to these proportions just before the race and bet on any horse for
which the proportion of money bet on-course exceeded the proportion bet off-course.
This would have yielded a proﬁt, net of the 15 percent tote take, of 29.8 percent over 168
races during the 1984 season. This result makes it clear that, prior to the cellular phone
era, insiders, bookmakers, the tote, and some on-course outsiders were all proﬁting at
the expense of off-course bettors in this betting market.
The connection between on-course bookmakers’ odds and the transmission of
plunge information to the tote is considered in greater detail in Schnytzer, Shilony,
and Thorne (2003). It showed that when the Victoria tote offers bets on races being
held both in Victoria and other states, the transmission of odds information from the
on-course bookmakers to the tote is more efﬁcient for local races, since on-course
punters betting on interstate races are not aware of the precise timing and extent of
all plunges on those races, as local bookmakers ﬁelding interstate races receive only
sporadic information from the relevant interstate betting market.
Prior to a discussion of insider trading in tote-only betting markets, it remains to
present preliminary results on ongoing research that provides an alternative approach
to Shin (1993) to measuring the extent of insider trading at the track. This is the work
of Schnytzer, Lamers, and Makropoulou (2008 and 2009).42 The model is an extension
of that developed by Makropoulou and Markellos (2011), which was applied to the
European soccer betting market. The basic intuition underlying the model is that ﬁxed
odds43 offered by bookmakers at the track are examples of call options and that, while
bookmakers hope to offer only net of premium out-of-the-money options, when they
err by underestimating a particular horse’s true winning probability they are liable to
offer a net in-the-money option, which the insider (who is assumed to know a horse’s
true winning probability) will be glad to snap up. Building on Schnytzer and Shilony
(1995 and 2002), the model tracks the value of the options in the face of plunges and,
using Monte Carlo simulations, estimates the extent of insider trading as between 20
and 22 percent, a value considerably greater than Shin’s (1993) and others applying his
model of 2.5 or so percent. The major reason that Schnytzer, Lamers, and Makropoulou
(2008 and 2009) obtained so high a value is that they did not focus on SP alone and
they relaxed Shin’s two particularly restrictive assumptions, namely, that the proportion
of outsiders backing any horse is equal to its true winning probability and that inside
traders always win.

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horse race betting
4 Insider Trading in a Tote-Only Market
.............................................................................................................................................................................
It is perhaps surprising that very little has been written about the operation of inside
traders in tote-only markets, but the reason is simple: the returns from tote betting are a
strictly decreasing function of the take and the quantity bet on the winning animal while
they are a monotonically increasing function of the amount bet on all losing animals.
Thus the more the insider bets on an animal, ceteris paribus, the lower the return
(whether the animal wins or loses). Further, if the insider plunges an animal relatively
early in the betting and the public spots the plunge,44 the return may be pushed down
further by herding. Hence simple logic suggests that insiders will wait until almost
the end of the betting when returns may be calculated with greater accuracy and the
impact of potential herding minimized. An alternative strategy might be to bet very
small amounts continuously so that no real plunge becomes evident, but this is only
likely to work if the projected payout is sufﬁciently high to provide a high contingent
proﬁt for a relatively small outlay.
One paper that has tested the hypothesis that “smart” money bets late in a tote-only
market is that produced by Peter Asch, Burton Malkiel, and Richard Quandt (1982).
They argued as follows:
We have suggested above that because of the potential signaling effect, bettors who
feel they have inside information would prefer to bet late in the period so as to
minimize the time that the signal was available to the general public. As table 3
[p. 193] shows, the marginal odds of the late bettors appear to be at least as good
as and perhaps better than the ﬁnal odds in predicting the order of ﬁnish. Horses
that win have marginal odds that average 79 to 82% of their morning line odds
(depending on which deﬁnition of marginal odds [p. 190]45 is employed). In other
words, winning horses are especially favored by the late bettors.
This paper concludes with some preliminary evidence on the presence of insiders in
the horse betting market in Hong Kong. The data consist of 4,245 Hong Kong races in
which 54,335 horses took part between the third of September 2000 and the eighteenth
of October 2006. For each horse46 prospective payouts at three different time slices
were observed: at overnight, 5 minutes before race start, and at the close of betting. The
actual win payout and the horse’s ﬁnishing place in the race also are known. The data
are provided for both tracks in Hong Kong: Happy Valley, and Sha Tin.
Using the same data set, Schnytzer and Barbara Luppi (2008) have shown that this
market has two features that are of potential relevance for the tracking of inside traders.
First there was no favorite-longshot bias in the betting at any of the available stages of
betting. This is perhaps surprising since those people betting on the day prior to the
race are most likely “normal” outsiders, and it is these bettors who tend to bet with
a bias in almost all other animal betting markets hitherto studied. The relevance of
this ﬁnding is that such insiders as might be betting in Hong Kong are unlikely to be

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309
arbitraging away biases and thus are more likely to be focusing on speciﬁc mispriced
horses. Indeed, this is likely to be the case also for syndicate bettors, and the model
hinted at by Bill Benter (1994) certainly seems to have been designed with just such a
purpose in mind.
Second, using a linear probability model to regress a win dummy on the price
equivalents of the three sets of prospective payouts and horse-jockey interactions, it
was shown that all three sets of prices contributed signiﬁcantly to an explanation of
horses’ winning probabilities at a one percent level of statistical signiﬁcance. In other
words, odds are changing during the betting but always with the addition of valuable
information. Now, suppose that the (overnight) opening prospective payouts represent
a rough, albeit unbiased, estimate of public information; in that case the subsequent
odds changes seem, at least in part, to reﬂect either insider trading or syndicate expert
betting or both. For the purposes of this chapter, it is not possible to attempt a formal
distinction between the two,47 but the presence of winners in this market is readily
demonstrated. Informally, the one thing that points in the direction of insider trading
is that winning plunges (as shown in table 17.1) are all in the range of middle to
long shots, and to the extent that expert syndicate betting is based on modeling public
information, it is to be expected that some favorite categories would yield proﬁts. Put
differently, public information in the absence of insiders is unlikely to consistently
misprice winning horses at odds greater than 10 to 1.
The results shown in table 17.1 are based on the following simple natural experiment:
Suppose that a better is able to bet when all others bettors have ﬁnished betting but the
race has not yet begun. This bettor places $1 on every horse that has been plunged in
different payout categories and also $1 on each favorite48 and each long shot49 in the
race. When there are two or more equal favorites or long shots in the race, $1 is put on
each. Table 17.1 shows the returns to such betting for favourites, long shots and every
ﬁnal payout category in which a proﬁt resulted. For all other payout groups losses were
incurred and not shown.
Table 17.1 presents results for both tracks together and separately and shows the
number of races in the sample, the number of bets placed, the payout group where
11–20, for example, means that the winning horse paid somewhere between $11 to
$20 inclusive for a dollar bet on the Hong Kong tote, the type of plunge, and the
actual percentage return. There are three types of plunge: early plunged is deﬁned as a
reduction in the prospective tote payout between the overnight and 5 minutes to start
payouts, a late plunge takes place when the prospective payout falls during the last 5
minutes of betting, and throughout indicates that there has been both an early and late
plunge on the horse.
The ﬁrst thing to notice about the results is that backing favorites in Hong Kong is
not a bright idea. While doing so loses considerably less at Sha Tin than betting on rank
outsiders, it fares considerably worse when betting at Happy Valley. This discrepancy
between the tracks may be explained by the relatively high number of bets on rank
outsiders at Sha Tin compared with Happy Valley and by the fact that Happy Valley is
in general a far more difﬁcult track for bettors than is Sha Tin.50

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horse race betting
Table 17.1 Returns to Tote Betting on Plunged Horses in Hong Kong, 2000–2006
Track
Number of Races
Number of Bets
Payout Group
Plunge Type
Return (%)
Both
4,245
4,312
Favorite
-
−0.1934369
Both
4,245
5,934
Long shot
-
−0.4496124
Both
4,245
1,870
21–30
Late
0.1508021
Both
4,245
970
31–40
Late
0.0412371
Both
4,245
1,524
11–20
Throughout
0.003937
Both
4,245
399
21–30
Throughout
0.0100251
Happy Valley
1,428
1.457
Favorite
-
−0.2046671
Happy Valley
1,428
1.593
Long shot
-
−0.086629
Happy Valley
1,428
1.395
11–20
Late
0.0415771
Happy Valley
1,428
423
11–20
Throughout
0.0661939
Happy Valley
1,428
25
31–40
Throughout
0.36
Sha Tin
2817
2,855
Favorite
-
−0.1877058
Sha Tin
2,817
4,341
Long shot
-
−0.582815
Sha Tin
2,817
407
51-max
Early
0.031941
Sha Tin
2,817
1,342
21–30
Late
0.2406855
Sha Tin
2,817
738
31–40
Late
0.1287263
Sha Tin
2,817
315
21–30
Throughout
0.1365079
The results in table 17.1 suggest that insiders are betting on horses in the range 10 to 1
and up. It is also clear that most winning plunged horses are plunged either late only or
throughout, the only exception being the 3 percent proﬁt on early plunged longshots at
Sha Tin. Finally, the returns to betting plunged horses in the winning categories appear
to be both greater and more even at Sha Tin than at Happy Valley, the 36 percent proﬁt
in the 31–40 range at the latter track being for only 25 bets.
In conclusion, it is clear that more research needs to done on the behavior and
impact of insider traders in tote-only markets. While both Asch, Malkiel, and Quandt
(1982) and this chapter provide evidence that insider trades occur late in the betting,
the evidence from Hong Kong is hardly unambiguous, with money being made also
on horses plunged early and throughout the betting. However, a puzzle remains to be
solved: how is it that all proﬁtable plunged odds groups in Hong Kong offered odds at
10 to 1 or greater?
Notes
1. Excluded therefore are any betting markets that are illegal in the jurisdiction(s) in which
they operate. Thus the Australian horse racing markets operated by various pari-mutuels
in that country will be analyzed even though participation in these markets is illegal for
Americans. SP bookmakers who operate illegally in some Australian pubs are, however,
not considered.
2. It makes no difference if it is an American or a European option.

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311
3. It is assumed that either these ﬂies are untrainable or that even if ﬂies can be trained to
race the ﬂies in the market under consideration have not been trained and are unknown
to the bettors in the market.
4. In particular, if the options are on shares and share returns move in accordance with
Brownian motion (as is argued in some texts, e.g., Wilmott 1998), then attempted predic-
tions of future prices would be largely useless. On the other hand, supporters of technical
analysis believe that, under appropriate circumstances, share returns are predictable (see
Bollinger 2002).
5. Accurate prediction of actual share prices over different time horizons is rendered impos-
sible by the fact that exogenous shocks of sufﬁcient magnitude inﬂuence the prices of all
shares to a greater or lesser degree.
6. There is a considerable literature dealing with the impact of legal insider trades in the U.S.
markets, where the insider has reported the trade with the SEC,but these are of no interest
here since such legal trades cannot, by deﬁnition, make use of information unknown to
the public. For an example of a paper that deals with a priori illegal insiders in this market
see Coleman and Schnytzer (2008).
7. For example, an insider who believes that the price of the relevant shares will fall may
sell a range of calls at different strike prices and expiry dates and may also buy various
puts. This is the equivalent of plunging a horse by betting small amounts with many
bookmakers.
8. Even identical new apartments on the same ﬂoor of the same building differ in regards to
position and thus, for example, views.
9. Research into moral hazard in real estate brokerage is unrelated to this topic. For an
example of this literature see Munneke and Yavas (2001).
10. Short of such surreal possibilities as drugging ﬂies.
11. Organized camel racing is popular in the Middle East, but gambling is illegal. Ostrich
racing is popular in Africa and in parts of the United States, and pari-mutuel
betting is legal at the annual Virginia City, Nevada, Camel Races festival (http://j-
walkblog.com/index.php?/weblog/comments/20295), but a discussion of these markets
is beyond the scope of this chapter.
12. For an insightful analysis of the distinction between insiders and experts (an issue
discussed very brieﬂy in section 4), see Pierson (2011).
13. For example, betting on a horse to win a race, betting on it to occupy either ﬁrst,
second, or third place in the race, betting on which two horses will ﬁnish ﬁrst and
second in the race either in the correct order or not are but some of the many
betting options. See http://www.dannysheridan.com/horse-racing/horses-101.php and
http://www.freebettingonline.co.uk/Horse-Racing-Betting/ for information regarding
betting in the U.S. and U.K. markets, respectively.
14. This involves no loss of generality since whether insiders bet and the possibility of tracking
their behaviors are determined by mechanism and location and not by bet type.
15. A trivial example of the importance of being on-course will sufﬁce: when the animal is
brought to the track it may be involved in a minor trafﬁc accident or even simply suffer a
shock from strange trafﬁc noises which would reduce its winning chances in the race. An
insider who is at the track with the animal—and better yet travels with it to the track—is
best placed to monitor the animal’s ﬁtness for racing. One the other hand, in the era of
mobile phones, it may be possible for the insider to remain off-course and still be fully
informed.

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horse race betting
16. Note that most totes round their payouts down to the nearest 5 or 10 cents so that if the
correct payout as described in the text should be, say, $4.29, then either $4.25 or $4.20
would be the actual payout.
17. After rounding, the payout in the example would be 90 cents instead of 94 cents.
18. Subject to ﬂuctuations in proﬁt from rounding.
19. If the tote is privately owned, its take may be ﬁxed by the government, though state-owned
totes might set the take to maximize returns. For more on this topic see Gruen (1976)
and Suits (1979).
20. Dubai features the horse race with the world’s largest prize, but there are no legal gam-
bling anywhere facilities in Dubai. For details and betting facilities online see http://
www.dubai-horse-racing.com/dubai-world-cup-odds.html, where British bookmakers
sell bets.
21. A service that pays full on-course tote odds is available via the Internet in some states,
though winnings may be subject to taxation. See http://www.tvg.com/Default.aspx for
more details.
22. See Schnytzer and Snir (2008b). The authors provide empirical evidence based on U.K.
data that SP betting is a self-enforcing cartel. Outside the United Kingdom there are
Internet bookmakers who offer SP plus betting; that is, they offer odds greater than SP.
As one Australian online bookmaker put it: “If you are currently placing your bets at SP
you really should open an account with Centrebet. They offer SP + odds on all UK horse
racing and greyhounds.” http://www.racing-index.com/bookmakers/centrebet.html.
23. Unless the tote in question does not provide up-to-date data on the amounts bet on the
race, in which case the tote is similar to the SP-type mechanism.
24. See Asch, Malkiel, and Quant (1982), which is discussed in section 4.
25. That is, there is no meaningful insider trading in this market.
26. Of course no one bets at forecast prices, but they may be taken as a reasonable proxy for
bookmakers’ opening prices.
27. Given the presence of both tote and bookmakers on-course inAustralia, it has been shown
that plunges with the bookmakers are reﬂected in tote odds. See Schnytzer and Shilony
(1995), which is discussed below.
28. Shin (1991, 1992 and 1993).
29. For an alternative model of bookmakers faced with insiders and the resulting favorite-
longshot bias, see Schnytzer and Shilony (2005).
30. This well-known bias is discussed elsewhere in this volume.
31. The price is the reciprocal of one plus the odds. Thus for odds of 3 to 1, the price is 0.25.
The price represents the outlay necessary to ensure a total payout of 1 should the horse
win the race.
32. See elsewhere in this volume.
33. This is a reasonable picture of bookmaker odds-setting in the Australian market where
off-course bookmaking was illegal in 1995.
34. See Schnytzer and Shilony (1995), which is discussed below.
35. Owner(s), trainer, jockey or driver, stable hands, perhaps family members and friends, etc.
36. It should be noted that the number of plunges per race for most Australian datasets is
around 2 to 3.
37. The following paragraphs paraphrase closely pages 963–964 of Schnytzer and Shilony
(1995).

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insider trading in betting markets
313
38. The use of the present tense here should be understood as applying to the era prior to
the introduction of cellular phones in Australia. In the description that follows, the past
tense is used wherever the microstructure of this market has changed since the 1995.
39. The Victoria tote has subsequently been privatized.
40. The changing structure of this market has led to a signiﬁcant reduction in the number
of bookmakers who ﬁeld at Melbourne tracks. A discussion of this interesting subject is
beyond the scope of this chapter.
41. McFadden (1973).
42. For the most recent theoretical model in this area see the chapter by Schnytzer,
Makropoulou, and Lamers elsewhere in this volume.
43. For the purposes of this chapter, “odds” means that odds of, say, 5 to 1 represent a net
proﬁt of $5 for every $1 bet on the winning horse.
44. Tote projected payout updates are today very frequent at all tracks.
45. Asch, Malkiel, and Quandt deﬁned marginal odds as the odds implied by those bettors
betting during a particular part of the betting period. They deﬁned the marginal odds
for those betting during the 8 and 5 minutes of betting, respectively, and showed that the
latter bet relatively more on winners than the former, who themselves bet relatively more
on winners than all bettors.
46. Note that the number of starters in a race runs from 7 through 14, with most races having
12 or 14 starters.
47. If indeed this is ever possible, since both would appear to be net winners and because
an empirical distinction between a bettor who has a better estimate than outsiders of
a horse’s winning probability because he knows the horse and one who has an edge
because he is a superior data processor would seem to be difﬁcult to draw, even if the
conceptual differences are self-evident. In the case of the bookmakers’market in Australia
(such as that studied in Schnytzer and Shilony 1995), bettors who make up the plung-
ing agents are invariably observed running from the stables area, suggesting that they
are insiders. Plunging on the tote is observable only via observable prospective payout
changes.
48. That is, the shortest priced horse(s) in the race at the close of betting.
49. The rank outsider(s) in the ﬁeld at the close of betting.
50. This issue is discussed in Schnytzer and Luppi (2008).
References
Asch, Peter, Burton G. Malkiel, and Richard E. Quandt. 1982. Racetrack betting and informed
behavior. Journal of Financial Economics 10(2):187–194.
Benter, William. 1994. Computer based horse race handicapping and wagering systems: A
report. In Efﬁciency of racetrack betting markets, edited by Donald B. Hausch,Victor S.Y. Lo,
and William T. Ziemba. San Diego, Calif.: Academic Press, 183–198.
Bollinger, John A. 2002. Bollinger on Bollinger Bands. New York: McGraw Hill.
Cain, Michael, David Law, and David A. Peel. 1996. Insider trading in the greyhound betting
market. Salford Papers in Gambling Studies No. 96–01. Lancashire: Center for the Study of
Gambling and Commercial Gaming, University of Salford.
——. 2001a. The incidence of insider trading in betting markets and the Gabriel and Marsden
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——. 2001b. The relationship between two indicators of insider trading in British racetrack
betting. Economica 68(269)97–104.
Coleman, Les, and Adi Schnytzer. 2008. Shorting the bear: A test of anecdotal evidence of
insider trading in early stages of the sub-prime market crisis. Journal of Prediction Markets
2(2):61–70.
Crafts, N. F. R. (1985). Some evidence of insider knowledge in horse race betting in Britain.
Economica 52(207):295–304.
Dowie, Jack. 1976. On the efﬁciency and equity of betting markets. Economica 43(170):139–
150.
Gabriel, Paul E., and James R. Marsden 1990. An examination of market efﬁciency in British
racetrack betting. Journal of Political Economy 98(4) :874–885.
Gruen,Arthur. 1976. An inquiry into the economics of race-track gambling. Journal of Political
Economy 84(1):169–178.
Law, David, and David A. Peel. 2002. Insider trading, herding behaviour and market plungers
in the British horse-race betting market. Economica 69(274):327–338.
McFadden, Daniel. 1973. Conditional logit analysis of qualitative choice behaviour.
In Frontiers in Econometrics, edited by Paul Zarembka. New York: Academic Press,
105–142.
Makropoulou, Vasiliki, and Raphael N. Markellos. 2011. Optimal price setting in ﬁxed-
odds betting markets under information uncertainty. Scottish Journal of Political Economy
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Munneke, Henry J., and Abdullah Yavas. 2001. Incentives and performance in real estate
brokerage. Journal of Real Estate Finance & Economics 22(1):5–21.
Schnytzer, Adi, and Barbara Luppi. 2008. Painful regret and elation at the track. Journal of
Gambling Business and Economics 2(3):85–99.
Schnytzer, Adi, and Yuval Shilony. 1995. Inside-information in a betting market. Economic
Journal 105(431):963–971.
——. 2002. On the timing of inside trades in a betting market. European Journal of Finance
8(2):176–186.
——. 2003. Is the presence of insider trading necessary to give rise to a favorite-longshot bias?
In The economics of gambling, edited by Leighton Vaughan Williams. London: Routledge,
14–17.
——. 2005. Insider trading and bias in a market for state-contingent claims. In Information
efﬁciency in ﬁnancial and betting markets, edited by LeightonVaughanWilliams. Cambridge:
Cambridge University Press, 287–312.
——. 2007. The optimality and statistical detection of price rigging in betting markets. Journal
of Gambling Business and Economics 1(1):13–29.
Schnytzer, Adi, and Avichai Snir. (2008a). Herding in imperfect markets with inside traders.
Journal of Gambling Business and Economics 2(2):1–16.
——. (2008b). SP betting as a self-enforcing implicit cartel. Journal of Gambling Business and
Economics 2(1):45–65.
Schnytzer, Adi, Martien Lamers, and Vasiliki Makropoulou. 2008. Measuring the extent of
inside trading in horse betting markets. Working Paper No. 2009-10. Bar-Ilan, Israel: Depart-
ment of Economics, Bar-Ilan University; http://econ.biu.ac.il/ﬁles/economics/working-
papers/2009-10.pdf.
——. 2009. The impact of insider trading on forecasting in a bookmakers’ horse betting
market. International Journal of Forecasting 26(3):537–542.

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Schnytzer, Adi, Yuval Shilony, and Richard Thorne. 2003. On the marginal impact of infor-
mation and arbitrage. In Economics of gambling, edited by Leighton Vaughan Williams.
London: Routledge, 80–94.
Shin, Hyun Song. 1991. Optimal betting odds against insider traders. Economic Journal
101(408):1179–1185.
——. 1992. Prices of state contingent claims with insider traders, and the favourite-longshot
bias. Economic Journal 102(411):426–35.
——. 1993. Measuring the incidence of insider trading in a market for state-contingent claims.
Economic Journal 103(420):1141–1153.
Suits, Daniel B. 1979. The elasticity of demand for gambling. Quarterly Journal of Economics
93(1):155–162.
Vaughan Williams, Leighton, and David Paton. 1997. Why is there a favourite-longshot bias
in British racetrack betting markets? Economic Journal 107(440):150–158.
Wilmott, Paul. 1998. Derivatives: The theory and practice of ﬁnancial engineering. Hoboken,
N.J.: Wiley.

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chapter 18
........................................................................................................
PRICING DECISIONS AND INSIDER
TRADING IN FIXED-ODDS HORSE
BETTING MARKETS
........................................................................................................
adi schnytzer, vasiliki makropoulou,
and martien lamers
1 Introduction
.............................................................................................................................................................................
This chapter examines the decision a bookmaker makes when setting prices under
uncertainty in a ﬁxed-odds betting market.1 We argue that this decision can be mod-
eled in a call option framework to measure the degree of insider trading in racetrack
betting markets. Vasiliki Makropoulou and Raphael Markellos (2011) ﬁrst developed
an option-pricing framework for the pricing of bets in ﬁxed-odds markets and in par-
ticular for the European soccer betting market. In this market the odds are offered
by bookmakers via ﬁxed-odds coupons several days before the game, and they remain
largely unchanged throughout the betting period. Their model deals with expert traders
who either exploit public information in a manner superior to that of bookmakers or
obtain access to new public information sooner than bookmakers do. Our approach
differs in that we focus on racetrack betting, where odds change frequently during
the half-hour betting period. In our context, public information is irrelevant since it
can be incorporated into new odds as soon as it hits the market. On the contrary,
we deal with insiders who possess private information. Of course, the implications of
trading with insiders in the racetrack betting market where the bookmaker frequently
changes the odds can be quite similar to those of trading with experts in a market where
the odds remain unchanged. However, the Makropoulou–Markellos framework could
not be readily applied to the racetrack betting market, due to structural differences
between the two markets. In order to ﬁll in this gap, Adi Schnytzer, Martien Lamers and
Makropoulou (2010) developed a model for the pricing of bets in a market with insid-
ers relying on the Makropoulou–Markellos framework and applied it to the Australian

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pricing decisions and insider trading
317
racetrack betting market. In this chapter, we extend the research of Schnytzer, Lamers,
and Makropoulou (2010) in several aspects. First, we relax their assumption of con-
tinuous arrival of information by employing a more realistic speciﬁcation in which
information arrives in discrete amounts, and therefore the true probability of a horse
winning exhibits quantum jumps and dives. Second, the model is extended to allow
for more periods in which betting takes place. Also, whereas Schnytzer, Lamers, and
Makropoulou (2010) assumed a betting period in which the bookmaker sets prices
once (at opening prices), we extend the model to accommodate more time periods in
which a bookmaker quotes prices. More speciﬁcally, we follow the data at our disposal
and allow for betting by insiders both at opening prices and middle prices instead of
only at one of those. Finally, to derive the probability of insider trading, the zero-proﬁt
condition of the bookmaker does not have to hold for every single horse. This condi-
tion is necessary only for the race, allowing the bookmaker to make losses only on the
horses he or she expects insiders to bet on and to make proﬁts on the horses backed
by outsiders, who bet according to subjective winning probabilities in accordance with
public information as explained below.
The remainder of this chapter is organized as follows. In the second section, we
discuss the general framework. In section 3 we build the theoretical model, which is
then discussed in section 4. Finally, our ﬁndings are presented in section 5.
2 General Framework and
Model Assumptions
.............................................................................................................................................................................
Our objective is to build a model of bookmaker optimal pricing, assuming that there
are two populations of bettors in the market, namely, outsiders and insiders. We begin
by describing the general framework and primary assumptions with respect to the
information possessed by the market agents and their betting criteria along with the
trading process and the pricing response by bookmakers.
Assume there are N horses in a race. The problem of the bookmaker is that of
determining the opening odds. We denote by θj(0) the odds quoted by the bookmaker
at time 0 against horse j winning, where j = 1,...,N. If a bet is successful then, ignoring
taxes, the bettor receives back 1+θj(0) on a one-unit bet. An opening price OP = φj(0)
implies odds θj(0) = 1−φj(0)
φj(0) .
Supposealsothatthehorses’truewinningprobabilitiesatanypointintimet aregiven
byPj(t),j = 1,...,N, where
N
j=1
Pj(t) = 1. Thesetruewinningprobabilitiesareassumed
to evolve according to the ﬂow of information, both public and private, throughout the
betting period until the race starts and are therefore stochastic. Moreover, we assume
that the ﬂow of information is tied to the ﬂow of bets. In this sense new information

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318
horse race betting
is said to have hit the market only if bets arrive in the marketplace in a way that alters
the horses’ winning probabilities, as those were until then perceived by the bookmaker.
The stochastic process for the true winning probabilities could be either continuous
or discontinuous, that is, a jump process or a mixture of the two. Strictly speaking,
the process that affects the true probability should be seen as discontinuous, since the
ﬂow of information from small events that may affect the outcome of the race is not
continuous. Moreover,weassumethattheﬂowof publicinformationduringthebetting
period is negligible, at least compared to the amount of private information that may
hit the market. This assumption makes sense especially if one considers the nature of
racetrack betting and the short betting period (about 30 minutes). Moreover, it implies
that whenever the bets arrive in a way different from the bookmaker’s expectation, it
is due to trading on inside information, unknown to the bookmaker until the actual
trade has taken place. The above suggests that the expected value of Pj(t) at any point
in time, E

Pj(t)

, should be equal to the initial value Pj(0).
Regarding the information possessed by the two presumed populations of bettors,
namely outsiders and insiders, and their betting behavior, we make the following
assumptions. First, nobody, not even an insider, knows in advance which horse will win
the race, in contrast to Hyun Song Shin (1991, 1992, 1993), who assumed that insiders
know which horse will win the race. Second, an insider knows only the true winning
probability of one horse, k, ˆPk, before this knowledge becomes public. However, the
insider does not know how 1 −ˆPk is distributed among the other horses. Given the
quoted opening price for horse k, φk(0), this true winning probability might involve a
proﬁt opportunity for the insider. A risk-neutral insider will wager on horse k only if
he or she expects a positive return. The expected return of the insider on a one-unit
bet is the expected value of either

−1 + ˆPk

φj(0)

or zero, whichever is greater, since
the insider bets only if −1 + ˆPk

φj(0) > 0 ⇔ˆPk > φj(0). This is similar to saying that
bookmakers actually offer insiders (call) options on the horses. Obviously it is in the
bookmakers’ interest to offer net out-of-the money options. However, when they err
by underestimating a particular horse’s true winning probability, they are liable to offer
a net in-the-money option on this particular horse, which the insider (who knows the
horse’s true winning probability) will be glad to snap up.
Outsiders have access only to public information regarding past performance and
current conditions. Therefore, we would expect outsiders to support the horses in
proportion to the winning probabilities implied by “public information,” Pj(0), which
areequaltotheexpectedvaluesof thetruewinningprobabilitiesattheclosingof betting,
E

Pj(T)

. However, in reality the winning probabilities perceived by the outsiders
should also account for their attitudes toward risk as well as for the existence of any
behavioral biases among them. Consequently, outsiders are assumed to support the
horses in proportion to their subjective winning probabilities, denoted by πj(t). A
favorite-longshot bias may arise if bettors are risk-loving (e.g., Quandt 1986) or due
to behavioral biases, such as those considered by Daniel Kahneman and Amos Tversky
(1979). There may of course also be herding, which would lead to plunge horses being

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pricing decisions and insider trading
319
overbet. The bookmakers are also assumed to know the horses’ winning probabilities
implied by“public information,”that is, E

Pj(T)

. Compared to outsiders,bookmakers
are particularly skillful in gathering and processing public information and are therefore
assumed to also know the marginal density function of each horse.2 In addition, we
assume that the bookmaker can accurately predict the expectations of outsiders, that
is, the outsiders’ subjective probabilities are known with certainty to the bookmaker.
Trading proceeds in a number of stages. At time zero the bookmaker declares the
opening prices (OPs), φj(0), based on the bookmaker’s perception of the true winning
probabilities at this time, Pj(0). At this ﬁrst stage, a proportion of the outsiders bet in
the market at the OP set by the bookmaker. Suppose now that a private signal revealed
to a group of insiders indicates that the true winning probability of k is actually higher
than the quoted OP, that is, ˆPk > φk(0). The insiders will then bet on this horse, say
at time t ∗. Note that such signals indicating mispricing might be revealed for more
than one horse. The bookmaker observes the insider betting pattern and therefore the
new value of the true winning probability and adjusts the prices accordingly. At the
other stages, the rest of the outsiders bet at the new updated prices. Note that insiders
are faced with a timing dilemma. To understand this, suppose that there are two such
groups of insiders, each wishing to plunge their own horse. Since a plunge reduces the
prices of other horses, each group has an incentive to wait for the other to plunge ﬁrst.
Insiders must utilize any special information they have during the betting, since it loses
all value once the race starts. Furthermore, since insider trading is both legal—only
jockeys are forbidden to bet—and takes place at ﬁxed prices, insiders have no incentive
to hide their trading behavior from outsiders. Moreover, since the insider information
concerning any given horse is likely known to more than one person, the longer insiders
wait, the greater the risk that the information will leak to a third party. The recipient of
the leak will then plunge the horse, and the group of insiders—except perhaps the one
responsible for the leak—may be left with odds at which betting is no longer worthwhile
(see also Schnytzer and Shilony 2002).
In the option pricing framework developed in this study to model the effect of
information asymmetries on prices, we did not account for competitive interactions
among insiders, since this would increase signiﬁcantly the complexity of the problem in
hand while offering limited additional insight. For simplicity, we assumed that insiders
will place their bet once they receive the private signal.3
Price updating effectively continues until the last stage, during which starting prices
(SPs) are determined as the equilibrium prices observed in the market at the end of
betting. Since in contrast to the British market there is no legal SP betting in the
Australian market, these prices may be assumed to embody all the available useful
information regarding the race’s outcome. Although price updating might actually take
place several times throughout the betting period, our empirical analysis considered
only three stages, the ﬁrst, an intermediate, and the last stage, at which opening prices
(OPs), middle prices (MPs) and starting prices (SPs), respectively, are set.
The chapter develops a model of bookmaker pricing that can be used to derive not
only the OP but also any intermediate prices. At each point in time the prices are

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320
horse race betting
modeled as the equilibrium of a perfectly competitive bookmaker market. Speciﬁcally,
the bookmaker is assumed to be risk-neutral, (i.e., an expected proﬁt maximizer) and
there is free entry in the market. Thus the long-run competitive equilibrium will be
established when all bookmakers earn zero expected proﬁts in the market correspond-
ing to each race. Moreover, assuming perfect competition allows for the simplifying
assumption of inelastic outsider demand. Note that if the bookmaker were a monop-
olist and demand were totally inelastic, maximizing proﬁts would lead to unbounded
prices (a formal proof is presented in the appendix to this chapter).
Insiders are assumed to have a collective wealth, Wi. When bookmakers price horses
according to the methodology developed in this chapter, they assume that insiders bet
to the full extent of Wi should the opportunity arise and that Wi is evenly distributed
among insider horses. Therefore, in a race of N horses, up to (1/N)Wi can be placed
by insiders on each horse.
We do not make any assumptions concerning the likelihood of inside traders vis-à-vis
either favorites or long shots. Finally, transaction costs are assumed to be negligible.
3 The Theoretical Model
.............................................................................................................................................................................
3.1 Development of the Mathematical Model
The problem of the bookmaker is that of determining the opening odds

1 + θj(0)

for
each one of the N horses in a race such that the expected proﬁt is equal to zero. Assume
for the moment that only outsiders exist in the market. Then, ignoring the time-value of
money, the expected proﬁt of the bookmaker at time zero (stage 1) is equal to the total
amount of money, Wn, bet by outsiders at stage 1 on the N horses minus the amount of
money that the bookmaker is expected to pay out to the winners. Assume also that wn,j
is the amount bet on horse j, where j = 1,2,…,N and E0

Pj(T)

is the expected value
of the true winning probability of horse j at the end of the betting period (time T).
Note that as explained in the previous section, the proportionate amount of money bet
by outsiders on each horse, wn,j/Wn, is known to the bookmaker. Regarding the true
winning probabilities, these might change throughout the betting period, since they
evolve according to the ﬂow of information, public and private, as this information is
revealed through the ﬂow of bets. However, in the absence of insiders and under the
assumption that the ﬂow of public information during the betting period is negligible
(see section above), then E0

Pj(T)

= Pj(0). The expected proﬁt of the bookmaker is
E0() = Wn −
N

j=1
Pj(0)wn,j

1 + θj(0)

.
(18.1)

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pricing decisions and insider trading
321
Setting φj(0) =
1
1+θj(0), where the notation φj(0) is used to denote the opening prices
(OPs), we obtain
E0() = Wn −
N

j =1
Pj(0)
φj(0)wn,j.
(18.2)
Given that
N
j=1
Pj(0) = 1, for the bookmaker to have a zero expected proﬁt it is sufﬁcient
that for each j the OP satisfy the following equation:
φj(0) =
wn,j
W (Wn).
(18.3)
Therefore, if only outsiders exist in the market and, as assumed earlier, the bookmaker
can accurately predict their expectations, for the latter to have zero expected proﬁt
on each horse it is sufﬁcient that opening prices are set equal to the expectation of
the bookmaker about the proportion of money bet on each horse, that is, φj(0) = πj,
where πj = wn,j

Wn is the winning probability of horse j as perceived by outsiders.
Considering that πj actually reﬂects outsiders’ beliefs as shaped by public information,
risk attitudes, and behavioral biases, under the assumption that the ﬂow of public
information is small, there is no reason for the opening prices to change during the
betting period.
Suppose now that insiders also exist in the market. Obviously the ﬁnal distribution
of bets will depend on the expectations of both outsiders and insiders. The bookmaker
can predict with accuracy the expectations of outsiders but not those of insiders, since
the latter are shaped according to the private information they receive; moreover, this
information is revealed to the bookmaker only after an inside trade has taken place.
Assume again that the bookmaker gives at time zero (opening) prices φj(0) for each
one of the horses and that the betting period is again T periods of time. It is assumed
that only part of the outsiders will bet at OP, ωOP
n
=

W OP
n

Wn

, while the other
part will bet at later stages after observing insider behavior. A risk-neutral insider will
wager on horse k only if the insider expects a positive return. The expected return of
the insider on a one-unit bet is the expected value of either

−1 + ˆPk

φj(0)

or zero,
whichever is greater, since the insider bets only if −1 + ˆPk

φj (0) > 0 ⇔ˆPk > φj(0).
Under the above assumptions, the bookmaker is always expected to lose from trading
with insiders. In particular, the bookmaker’s expected loss to an insider at time zero on
a one-unit bet (placed at time t ∗) is
E0(i) = −E0

max

−1 +
ˆPk
φj(0),0

.
(18.4)
Itholdsthat ˆPk = Pk(t ∗) ̸= Pk(0),wherePk(t ∗)isthetruewinningprobabilityof horsek
at the time the insiders place their bet (which is now revealed to the bookmaker).

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322
horse race betting
The expected proﬁt of the bookmaker is therefore
E0() = W OP
n
−
N

j=1
E0

Pj(T)

φj(0)
wOP
n,j −
N

j=1
wOP
i,j E0

max

−1 + Pj (t ∗)
φj (0) ,0

,
(18.5)
where wOP
i,j
is the amount of money bet by insiders at OP on horse j. Note that now
that insiders also exist in the market, the bookmaker cannot know what the true wining
probability will be at the end of the betting period. However, as explained in the
previous section, the bookmaker is assumed to know the expected value of the true
winning probability, E

Pj(t)

, at any time t.
The expression above is complicated by the fact that t ∗cannot be known a priori
to the bookmaker, and hence it should be treated as stochastic. In order to simplify
this we assumed that private information that may alter the true winning probability
of a given horse may arrive only once for each horse. Then we can safely state that
ˆPk = Pk(t ∗) = Pk(T), where Pk(T) is the value of the true winning probability at
the closing of betting since, as pointed out earlier, private information regarding a
certain horse may arrive in the marketplace only once. Of course one might argue
that the true winning probability of horse k may be lowered if at a later time new
(positive) information regarding a second horse r hits the market, implying ˆPr > Pr(0).
Obviously, this would always be true in a race of two horses only. However, in a race of
many horses, one could accept the supposition that this new information would reduce
the true winning probabilities of all other horses (for which no inside information has
hit the market) except for horse k.
Given that wOP
i,j
= (1/N)Wi, for the bookmaker to have zero expected proﬁt, the
following condition must be met:
1 −
N

j=1
wOP
n,j
W OP
n
E0

Pj(T)

φj(0)
= 1
N
Wi
W OP
n
N

j=1
E0

max

−1 + Pj(T)
φj(0)

,0

,
(18.6)
or
1 =
N

j=1
E0

Pj(T)

⎧
⎨
⎩
wOP
n,j
W OP
n
1
φj (0) + 1
N
Wi
W OP
n
E0

max

−1 + Pj(T)
φj(0)
 
,0
E0

Pj(T)

⎫
⎬
⎭.
(18.7)
Given that
N
j=1
E0

Pj(T)

= 1, for the above equation to hold, it is sufﬁcient that the
opening price of each horse j satisﬁes the following equation:
wOP
n,j
W OP
n
1
φj(0) + 1
N
Wi
W OP
n
E0

max

−1 + Pj(T)
φj(0)

,0
 
E0

Pj(T)

= 1,
(18.8)

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pricing decisions and insider trading
323
or, multiplying with the term
 W OP
n
Wn

and rearranging we obtain
W OP
n
Wn

−
W OP
n
Wn
 wOP
n,j
W OP
n
1
φj(0) = 1
N
 Wi
Wn
 E0

max

−1 + Pj(T)
φj(0)

,0
 
E0

Pj(T)

.
(18.9)
The left-hand side of the above equation is the expected bookmaker gain from trading
with outsiders while the right-hand side is the expected bookmaker loss to insiders.
The optimal price is the one that equalizes the gain from outsiders to the loss to
insiders. It can be found by solving the above equation through trial and error, given
the proportion of outsiders who bet at OP, ωOP
j
= W OP
n

Wn, outsider’s subjective
probabilities, πOP
j
= wOP
n,j

W OP
n
, the bookmaker’s expectation about the true winning
probability at the closing of betting, E0

Pj(T)

, the number of runners in a race, N,
and, of course, the degree of insider trading (as perceived by the bookmaker) deﬁned
as the ratio of total insider money to total outsider money,

Wi

Wn

.
Note that the left-hand side of this equation should be greater or equal to zero since
the right-hand side is always nonnegative. Therefore, if insiders exist in the market, in
order for the bookmaker to have zero expected proﬁt, prices should be set greater than
outsiders’ subjective probabilities, that is,
φj(0) ≥
wOP
n,j
W OP
n
= πOP
j
.
(18.10)
To summarize, our model suggests that since any private information is conveyed to
the bookmaker only after an informed trade takes place, the latter should include a pre-
mium in the OP to compensate for this risk. Moreover, this premium is related to the
cost of trading with insiders, which in turn is a function of the degree of insider trading
(Wi/Wn) and the potential value of private information that may be exploited by insid-
ers (as captured by the term E

max

1 −+ Pj(T)
φj(0) ,0
 
). Under these considerations, the
sum of OP would always be greater than one.
Suppose now that at a later point in time, time τ (stage 2), after the bookmaker
has observed insider trading, the bookmaker will set new prices (called MP). For those
horses on which insider trading has taken place, say m horses, prices will be set equal to
the horses’ new true winning probabilities (in the absence of any bookmaker margin).
The reason is that insiders pose no further risk to the bookmaker since they can only bet
at either OP or MP on a given horse but not both.4 For the rest of the horses (N −m),
the bookmaker will set prices as above. Therefore, at the second stage the total amount
of money available by insiders is Wi −m
N Wi ≤Wi. Thus, the bookmaker will quote MP
as if
1
N−m

Wi −m
N Wi

=

1

N

Wi would be wagered by insiders on each one of the
remaining N −m horses should the opportunity arise. Therefore we have
W MP
n
Wn

−
W MP
n
Wn
 wMP
n,j
W MP
n
1
φj(τ) = 1
N
Wi
Wn
 Eτ

max

−1 + Pj(T)
φj(τ)

,0
 
Eτ

Pj(T)

,
(18.11)

---

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324
horse race betting
where the term πMP
j
= wMP
n,j

W MP
n
captures outsiders’ new subjective probabilities
as these have been shaped after observing the insider trading pattern at stage 1 and
ωMP
j
= W MP
n,j

Wn is the proportion of outsiders that bets at this second stage.
Price updating effectively continues until the last stage at which starting prices (SPs)
are determined as the equilibrium prices observed in the market at the end of betting.
Under the assumption of zero bookmaker proﬁt, the sum of SP would be equal to
one. Then, following our model, in the presence of insiders the sum of OP should
always be greater in any race than the sum of SP. In reality, the sum of OP is always
greater in any race than the sum of SP, even in the apparent absence of insider trading.5
The reason is that opening prices tend to have a so-called cartel level of proﬁt built in
since they are recommended to individual bookmakers by the bookmakers’association.
Once betting begins competition among bookmakers also begins, and thus the sum of
prices will tend to decrease. This practically means that the estimates of insider trading
obtained when applying our model may overestimate its true extent if the premium
included in OP is largely due to this cartel proﬁt rather than to the risk that bookmakers
face in the presence of insiders. On the other hand, it may be that the expected proﬁt
margins built into OP are designed just to compensate the bookmakers for inside
trades.
3.2 The Option Analogy
The commitment made by bookmakers to sell at ﬁxed prices, the quoted odds, can
be analyzed as a call option. Speciﬁcally, the bookmaker gives an insider a call option
on horse j, that is, the right to bet at a ﬁxed price. Obviously the underlying asset
whose value changes stochastically is horse j’s true winning probability. Apparently,
only insiders are entitled to the option. The reason is that while an insider has perfect
information (both public and private) and therefore knows a horse’s true winning
probability, outsiders form their expectations, at least partially, according to the public
component of information, and based on that they assign subjective probabilities. The
insider will exercise the option to bet at the opening prices only if the insider expects a
positive return, that is, if the true probability at the time the bet is placed, t ∗, is greater
than the opening price.
One could assume that insiders would be better off exercising their option at the
last minute, that is, at the closing of betting. The reason is that since a plunge reduces
the prices of other horses each group of insiders has an incentive to wait for the other
groups to plunge ﬁrst. However, since the insider information concerning any given
horse is likely known to more than one person, the longer insiders wait, the greater
the risk that the information will leak to a third party. The recipient of the leak will
then plunge the horse and the group of insiders—except perhaps the one responsible
for the leak—may be left with odds at which betting is no longer worthwhile. This
timing dilemma is similar to the problem of the optimal exercise time faced by the
holder of an American option on a dividend-paying stock. In the betting market the

---

## Page 346

pricing decisions and insider trading
325
dividend equivalent is the potential value leakage as a result of competition among
insiders. However, for simplicity we ignored competitive interactions among insiders.
We assumed instead that insiders place their bet once they observe mispricing.
Assuming that the bookmaker is risk-neutral, today’s option price (time zero) can
be determined by discounting the expected value of the terminal option price by the
riskless rate of interest. Therefore, neglecting the time-value of money, the value of the
call option is
Cj(0) = COP
j
= E0

max

−1 + Pj(T)
φj(0) ,0

.
(18.12)
Similarly
Cj(τ) = CMP
j
= Eτ

max

−1 + Pj(T)
φj(τ) ,0

.
(18.13)
The value of the option can be derived by assuming a stochastic process for the true
winning probability and performing Monte Carlo simulations (see section 4).
3.3 The Favorite-Longshot Bias
In this section we show that the optimal prices set by the bookmaker using equation
(18.9) will exhibit the favorite-longshot bias.
Expected
returns
will
exhibit
the
favorite-longshot
bias
if
and
only
if
∂E(Rj)

∂

E0[Pj(T)]

> 0, where E(Rj) = −1 + E0

Pj(T)

φj. This is equivalent to
∂

E0

Pj(T)

φj

∂

E0

Pj(T)

> 0.
(18.14)
Denoting fj(0) =

E0

Pj(T)

φj

, equation (18.9) can be written as
W OP
n
Wn

E0

Pj(T)

−
W OP
n
Wn
 wOP
n,j
W OP
n

fj(0) = 1
N
 Wi
Wn

E0
$
max

−1 + fj(T)

,0
%
,
(18.15)
where fj(T) =

ET[Pj(T)]/φj

= Pj(T)/φj
DifferentiatingtheabovewithrespecttoE0

Pj(T)

andsetting ∂E0{max(−1+fj(T)),0}
∂E0[Pj(T)]
=
∂E0{max(−1+fj(T)),0}
∂fj(0)
∂fj(0)
∂E0[Pj(T)], we obtain
∂fj(0)
∂E0

Pj(T)
 =
 W OP
n
Wn

1 −fj(0)
∂

wOP
n,j

W OP
n

∂(E0[Pj(T)])

 W OP
n
Wn

wOP
n,j
W OP
n

+ 1
N

Wi
Wn
 ∂E0{max(−1+fj(T)),0}
∂fi(0)
.
(18.16)

---

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326
horse race betting
We focus on the denominator ﬁrst. The ﬁrst term is always positive. The second
term is positive too since the partial derivative ∂E0{max(−1+fj(T)),0}
∂fj(0)
is always posi-
tive. Note that a higher level of fj(0) =

E0

Pj(T)

φj

is equivalent to a lower quoted
price for the same level of expected true probability. Therefore the potential proﬁt
of insiders, as captured by the term E0
$
max

−1 + fj(T)

,0
%
, should increase since a
lower quoted price makes underpricing more likely. In the terminology of options
this is equivalent to saying that a lower strike price increases the value of a call
option.
We turn our attention now to the nominator. For the nominator to be positive it
is necessary that the term 1 −fj(0)
∂

wOP
n,j

W OP
n

∂(E0[Pj(T)]) is positive. This obviously depends
on the partial derivative of the outsiders’ subjective probability with respect to the
expected true winning probability. If the subjective winning probabilities of outsiders,
πj(t), are equal to the winning probabilities implied by “public information,” then this
partial derivative will be zero and the nominator will be positive. Suppose instead that
outsiders tend to overestimate the winning chances of long shots relative to those of
favorites, as is often argued in the literature, that is,
∂

E0

Pj(T)

wOP
n,j

W OP
n

∂

E0

Pj(T)

> 0 ⇔1 −
E0

Pj(T)


wOP
n,j

W OP
n

∂

wOP
n,j

W OP
n

∂

E0

Pj(T)
 > 0.
We know that
φj >
wOP
n,j
W OP
n
⇒1
φj
<
1

wOP
n,j

wOP
n
 ⇒E0

Pj(T)

φj
<
E0

Pj(T)


wOP
n,j

W OP
n

⇒E0

Pj(T)

φj
∂

wOP
n,j

W OP
n

∂

E0

Pj(T)
 <
E0

Pj(T)


wOP
n,j

W OP
n

∂

wOP
n,j

W OP
n

∂

E0

Pj(T)

⇒1 −E0

Pj(T)

φj
∂

wOP
n,j

W OP
n

∂

E0

Pj(T)
 > 1 −
E0

Pj(T)


wOP
n,j

W OP
n

∂

wOP
n,j

W OP
n

∂

E0

Pj(T)
 > 0
Therefore we have proved that when the bookmaker sets optimal prices following our
model, expected returns will exhibit the favorite-longshot provided that either outsiders
have no biases in their expectations and therefore their subjective probabilities reﬂect
the publicly available information or that they tend to overestimate the winning chances
of long shots relative to those of favorites.

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pricing decisions and insider trading
327
4 Empirical Model
.............................................................................................................................................................................
4.1 Option-Pricing Speciﬁcations of the Model
The challenge faced here is that the assumed speciﬁcation must be a realistic description
of probability dynamics. In particular we want to model the true winning probability
such that the following requirements are met: First, said probability is concentrated on
[0,1). A probability of a certain horse winning equal to one implies that the probabilities
of all other horses are zero. In practice this is never the case. For this reason we set as
an upper boundary for the true winning probabilities the value pmax < 1. In particular
pmax could be the highest single probability in our sample, which is found to be 0.7197.
Second, the sum of probabilities is equal to one at all times. Third, it may exhibit
positive and/or negative jumps throughout the betting period following the release
of new private information. Finally, in the long run it reverts to a mean equal to the
reciprocal of the number of runners in a race. This assumes that over a long period of
time all horses have equal chances of winning. Note that the behavior of this process in
the absence of mean reversion is problematic since in this case the boundaries become
absorbing.
Taking the above under consideration, the following stochastic process is assumed:
dPj(t) = h

μ −Pj(t)

dt + Pj(t)

Pmax −Pj(t)

Jdq,
(18.17)
where h is the speed of mean reversion, μ is the long-run mean (equal to 1/N), J
is the jump size, which is assumed to be normally distributed with mean zero and
standard deviation σJ, and dq describes a time-homogeneous Poisson jump process
such that dq = 1 with probability λdt and dq = 0 with probability (1 −λdt). Param-
eter λ is known as intensity or arrival rate and is the expected number of “events” or
“arrivals” that occur per unit time. The term Pj(t)

Pmax −Pj(t)

, which multiplies the
jump component Jdq, is employed in order to ensure that the probability will remain
inside the boundaries of zero and pmax. Furthermore, given that the jump size has a
mean of zero, it can be easily shown that the expected value of Pj(t) at any t > 0 is
given by
E

Pj(t)

= Pj(0)e−ht + μ

1 −e−ht
.
(18.18)
Note that when the speed of mean reversion is very small, as assumed herein, the
expected value of Pj(t), E

Pj(t)

, tends to the initial value Pj(0). This is important
since the theoretical model described previously in this chapter relied heavily on this
assumption.

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328
horse race betting
There is one ﬁnal concern with respect to the speciﬁcation for the true winning
probability, which, as mentioned earlier, refers to the fact that the sum of probabilities
must be equal to one at all times. Suppose that the probability of horse k follows the
above stochastic process while for all other horses j, j = 1,2,...,N, j ̸= k, it holds
that
dPj(t) = h

μ −Pj(t)

+ εj(t).
(18.19)
Then, taking the sum of all probabilities, setting it equal to one and observing that
N
j=1
h

μ −Pj(t)

dt = 0, it follows directly that
N

j=1
j̸=k
εj(t) + JkPk(t)(Pmax −Pk(t))dq = 0.
(18.20)
Therefore, although speciﬁcation (18.17) does not warrant that
N
j=1
Pj(t) = 1, we can
ﬁnd a condition under which this holds. Thus the above speciﬁcation is indeed a
realistic description of probability dynamics. We now need to estimate the parameters
that appear in the stochastic process followed by the true winning probability. For the
purpose of this estimation we will ignore the mean-reverting component, assuming
instead that the speed of mean reversion is very close to zero. Thus we only have to
estimate the parameters of the jump process and, in particular, the standard deviation
σJ of the jump size and the intensity λ of the Poisson process. The intensity parameter
tells us how often the true winning probability experiences a sudden jump while the
parameter of jump volatility measures the size of these jumps. We calculate these
parameters by computing the second and fourth (raw) moments. These are speciﬁed
as follows:
μ2 = E

Y 2
= E

J 2
E

dq2
= σ 2
j λ	t
(18.21)
μ4 = E

Y 4
= E

J 4
E

dq4
= 3σ 4
J λ	t,
(18.22)
where Y =
	P
P (1 −P).
Those two moments completely identify the jump components. Moreover, they can be
derived from the bookmakers’ odds as following: as the dataset includes prices at three
points in time (OP, MP, and SP), prices are available roughly every 15 minutes. The
15-minute moments may thus be calculated for each race
2M : m2 =
1
s −1 (u1 −u2)2
(18.23)
4M : m4 =
1
s −1 (u1 −u2)4
(18.24)

---

## Page 350

pricing decisions and insider trading
329
where s = 2 and u1,u2can be calculated as follows:
u1 =
φMP −φOP
φOP · (1 −φOP)
(18.25)
u2 =
φSP −φMP
φMP · (1 −φMP).
(18.26)
Obviously the one-minute moments can be calculated from the ﬁfteen-minute
moments by dividing by ﬁfteen. Using equations (18.21) and (18.22) for 	t = 1 minute
and the estimated values for the one-minute moments, we determined the jump
components λ and σJ for all horses in each race:
λ = 3μ2
2
μ4
σj =
& μ4
3μ2
.
Finally, we calculate the average values of σj and λ for our sample, which are then
used in the options calculations. Note that these are“one-minute” values. For example,
λ = 0.1 implies that we have a jump every 10 minutes. The results are presented below.
4.2 A Measure of Insider Trading
We focus now on the task of estimating the degree of insider trading, that is, the
parameter

Wi

Wn

. To this end, we assume that in practice bookmakers set their
prices according to the methodology described above. Thus using the actual prices
we can infer the degree of insider trading by using expression (18.6) to directly solve

Wi

Wn

. However, the theoretical model was built under the assumptions of zero
expected proﬁt and zero transaction costs. This may yield estimates of insider trading
that are biased upward. Starting from expression (18.6)
1 −
N

j=1
wOP
n,j
W OP
n
E0

Pj(T)

φj(0)
= 1
N
Wi
W OP
n
N

j=1
COP
j
.
(18.27)
By multiplying with W OP
n
Wn , the part of outsider trading that occurs at OP,
Wi
Wn
1
N
N

j=1
COP
j
= W OP
n
Wn
⎛
⎝1 −
N

j=1
W OP
n,j
W OP
n
E0

Pj(T)

φj(0)
⎞
⎠
(18.28)
or that
q
N

j=1
COP
j
= N W OP
n
Wn
DOP,
(18.29)

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330
horse race betting
where DOP =

1 −
N
j=1
πOP
j
E0[Pj(T)]
φj(0)

for each race. The superscript OP indicates that
these values refer to the ﬁrst stage at which the opening prices are set. This is the
basic equation for our empirical analysis. Obviously this expression refers only to OP.
However,as we said,we assumed that trading takes place in two stages. At stage 1 (t1 = 0)
a proportion of the outsiders bet in the market at the OP set by the bookmaker. At any
subsequent point in time, t1 + 	t ≤T, all insiders may bet should the opportunity
arise. The bookmaker observes the insider trading pattern and at time t2, t1 < t2 ≤T,
updates prices. At stage 2 the rest of the outsiders bet at the new set of updated prices,
denoted by MP. Again, at any subsequent point in time, t2 + 	t ≤T, all insiders may
bet should the opportunity arise. The bookmaker observes the insider trading pattern
and at time T sets new updated prices denoted by SP (starting prices).
Similarly, for the second stage at which MP is set we have
q
N

j=1
CMP
j
= N W MP
n
Wn
DMP,
(18.30)
where DMP =
⎛
⎝1 −
N

j=1
πMP
j
Eτ

Pj(T)

φj(τ)
⎞
⎠.
We can use equations (18.29) and (18.30) to calculate the proportion of outsiders that
bet at OP and MP
ωOP = W OP
n
Wn
=
DMP N
j=1
COP
j
DMP
N
j=1
COP
j
+ DOP
N
j=1
CMP
j
.
(18.31)
Then we can use equations (18.29) and (18.31) to calculate q. In order to do so we still
have to explain how to calculate the option values at both OP and MP, COP
j
and CMP
j
,
as well as the quantities DOP and DMP for each race.
We begin with betting at OP. The option values COP
j
can be estimated via Monte
Carlo simulation. The required inputs to perform the simulations are Pj(0), OPj, T,
and the speciﬁcations of the stochastic process followed by the true winning probability.
OPj is the observed opening price quoted by the bookmaker. T is assumed to be equal to
30 minutes. With respect to the speciﬁcations of the stochastic process followed by the
true winning probability, we need to know the speed of mean reversion, h, the long-run
mean, μ, which is set equal to 1/N, the standard deviation of the jump size, σJ, given
that J ∼N

0,σ 2
J

and the intensity λ of the Poisson process. A way to derive those
parameters has been shown in the previous section of this chapter. The speed of mean
reversion is assumed to be very small since we are dealing with a betting period of no

---

## Page 352

pricing decisions and insider trading
331
more than 30 minutes and is therefore set at 0.001. The true winning probability, Pj(t),
is derived via a conditional logit regression on a dummy win, ensuring that the sum of
probabilities in each race equals 1. The subjective probabilities πOP
j
are calculated by
simply normalizing OP as suggested by Jack Dowie (1976), though this yields estimates
with a favorite-longshot bias. The true winning probability is simulated in 1,000 steps
using the stochastic process (18.17). When the simulated true winning probability after
1,000 steps is larger than the true winning probability in time t = 0, the option value
is this difference; otherwise the option value is zero. Each horse is subject to 1,000
repetitions. The option value for the horse is the averaged value over all repetitions. A
similar procedure is followed to calculate CMP
j
, using as inputs Pj(τ), MPj, and T −τ,
where τ is assumed to be equal to 15 minutes. We used the same speciﬁcations for the
stochastic process as above.
We still need to calculate DOP and DMP for each race. The expected true winning
probabilities at the end of the betting period, E0

Pj(T)

, are assumed to be equal to the
true winning probabilities at time 0, that is, E0

Pj(T)

= Pj(0). This is derived from
equation (18.18) if we assume that the speed of mean reversion is very small. This way
we assumed that mean reversion has almost no effect on the true winning probabilities
in the very short betting period of 30 minutes while any deviations from the initial
value are due to the effect of jumps that come as surprises.
Next, we used equation (18.31) to calculate ωOP = W OP
n
Wn . The extent of insider trading
for each race is then q = NωOPDOP
N
j=1
COP
j
The probability of insider trading is simply
a =
q
1 + q .
As we said, our model was built from the viewpoint of the bookmaker, and the approach
we have followed so far effectively supposes that bookmakers know the probability of
insider trading in advance. Or, more reasonably, such a measure is of the bookmakers’
expectations regarding insider trading. However, we have access to ex post plunging
information, which the bookmaker cannot know until after insider activity has taken
place. We will use this (ex post) plunging information in order to get closer to the true
probability of insider trading for a given horse that got plunged.
In order to calculate the probability of insider trading per horse, we used both an
unweighted and a weighted average of q. The weight was derived as the absolute size
of the plunge, called PW: max(MP −OP, 0) + max(SP−MP, 0). Using the unweighted
and weighted average, the probability of insider trading for each horse in a given race
in the sample was calculated. Note that when we weighted absolute plunges sizes, we
were weighting on those horses that insiders were observed to have bet on more heavily
in accordance with plunge size. Using these weights, the weighted average probability
of insider trading for each of the races in the sample was calculated. The simple average
of these values is the probability of insider trading in the dataset.

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332
horse race betting
5 Results
.............................................................................................................................................................................
We used the above model to derive a measure of the extent of insider trading. Our
measure was applied to a dataset of the 1998 Australian Horse Racing season, covering
4,017 races with 45,296 runners.6 The dataset includes for each horse prices at three
moments (OP, MP, and SP). The time period during which betting takes place is set
at 30 minutes, meaning that prices are available roughly every 15 minutes. Given that
there were some cases in which the sum of OP, MP, or SP in a race was less than one,
these races are dropped from the sample. This left us with 3,995 races out of the initial
sample of 4,017 races.
The true winning probabilities at OP and MP,necessary for the measure, were derived
by running a conditional logit regression, the results of which are displayed in table 18.1.
Table 18.2 displays descriptive statistics for OP, MP, SP; the subjective winning prob-
abilities at OP and MP; the true winning probabilities following from table 18.1; and
the sum of OP, MP, and SP per race.
The table shows clearly that the average sum of prices decreases between OP and SP.
At the opening of betting this margin was 43 percent, but by the start of the race the
margin had decreased to 24 percent. The decrease in the margin indicates competition
among bookmakers, forcing them to decrease prices and leading to lower proﬁts. Since
the OPs are above the competitive level, this could deter insiders from trading at these
prices, leading to a lower degree of insider trading.
The option values were generated via Monte Carlo simulation as explained in the
previous section. The average 1-minute values for λ and σ in the dataset are 0.37 and
0.11, respectively. On average, there seems to be a jump every 3 minutes or 10 times
per a 30-minute betting period, indicating quite some inﬂow of private information
into the prices. Table 18.3 shows the values of the non-zero options generated at OP
and MP.
Table 18.1 Conditional Logit Regression
Win
Win
OP
6.713∗∗∗
(0.133)
MP
7.155∗∗∗
(0.141)
N
45266
45266
Log Likelihood
−8259.18
−8238.81
Note: Standard errors in parentheses.
∗∗∗signiﬁcant at 1%.

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pricing decisions and insider trading
333
Table 18.2 Descriptive Statistics
Variable
Mean
Min
Max
Standard Deviation
OP
0.1255
0.0019
0.8889
0.1017
MP
0.1107
0.0013
0.8670
0.0946
SP
0.1092
0.0010
0.8462
0.0972
πj(OP)
0.0883
0.0014
0.7197
0.0731
πj(MP)
0.0883
0.0011
0.7165
0.0768
Pj(OP)
0.0883
0.0026
0.9657
0.0970
Pj(MP)
0.0883
0.0020
0.9723
0.0984
N
j=1
OP
1.4339
1.0225
2.0631
0.1117
N
j=1
MP
1.2660
1.0003
1.8508
0.1008
N
j=1
SP
1.2487
1.0122
1.7646
0.0921
There were 5,184 horses for which a zero option was generated at OP and 6,806
horses for which the option value was zero at MP. Moreover, we can see from table
18.3 that the options generated at MP have a higher value, indicating more proﬁtable
trading opportunities for insiders. This should not come as a surprise, as we already
saw in table 18.2 that the MPs are lower, leading to a lower strike price for the insiders
and a higher proﬁt.
One last thing is required to calculate the degree of insider trading, namely ωOP,
the group of outsiders who bet at opening prices. Using the data from tables 18.2 and
18.3, the average ωOP in the dataset was calculated to be 0.41. On average 41 percent
of outsider trading occurs at OP and 59 percent at MP, though there are races in
which almost no outsider betting is found to occur at OP. The ratio of insider betting
to outsider betting, which is expected by the zero-proﬁt bookmaker, was found to
have a mean of roughly 25 or an average probability of insider trading of around
95 percent. The density plot is shown in 18.1. This seems very high, but there are a
few considerations to take into account. First, the insider in our model was assumed to
know only the true winning probability of one horse k and not the winning probabilities
Table 18.3 Option Statistics
Variable
N
Mean
Max.
Standard Deviation
COP
j
40,082
0.00454
0.20610
0.01385
CMP
j
38,460
0.00723
0.25498
0.02087

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334
horse race betting
of any other horses. When compared to the insider by Shin (1991, 1992, 1993), our
insider does not know which horse will win but simply has a better understanding of the
true winning probabilities compared to the probabilities as quoted by the bookmaker.
Second, the deﬁnition of insider trading is the amount of money being bet by insiders
compared to outsiders. The fact that 95 percent of the total money is bet by insiders
does not mean that they place more bets, but it could mean that they wager more money
per bet. The bulk of the bets placed could still be made by outsiders, but the amount
that insiders bet compared to outsiders is just much higher; that is, for every Australian
dollar bet by outsiders, 25 is bet by insiders. Third, the assumption underlying the
measure is that the bookmaker set his expected proﬁt at zero, as would be the case
under perfect competition. This is, of course, a very strict assumption to make and may
not suit the reality all that well. A solution would be to assume that the bookmaker sets
prices that guarantee a certain level of proﬁt. This level could be assumed to be equal to
the proﬁt the bookmaker would make in a market with no insiders. However, the prices
that the bookmaker would set in this market are unobservable prices by deﬁnition.
By looking at equation (18.32), keeping everything else constant and assuming the
bookmaker sets prices to have a positive expected proﬁt, it becomes obvious that we
are estimating the degree of insider trading with an upward bias.
Finally, the measure that was generated is the bookmaker’s expectation regarding
insider trading. To have a zero expected proﬁt, the bookmaker expects the probability
of insider trading to be 95 percent. However, as mentioned in section 4, we used
ex post plunging information to get closer to the true probability of insider trading
in the dataset. The weight that we used is based on the absolute size of the plunge:
PW = max(MP−OP, 0) + max(SP−MP, 0). We used PW to weight the extent of insider
0.3
0.2
Density
0.1
0
70
80
Expected Probability of Insider Trading (in %)
90
100
figure 18.1 Expected probability of insider trading

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pricing decisions and insider trading
335
0.025
0.02
0.15
0.01
Density
0.005
0
0
20
40
Ex-Post Probability of Insider Trading (in %)
60
80
100
figure 18.2 Ex post probability of insider trading
trading, q, per race. By deﬁning a plunge as an upward movement of the price, we found
that there have been 13,852 plunges in the dataset, mainly occurring between MP and
SP. The 13,852 horses account for 30 percent of the total observations in the dataset. An
additional beneﬁt is that PW weights horses that have experienced a more severe plunge
higher. However, a downside is that the estimate will be too high if part of the plunging
is actually due to herding. The mean of the weighted extent of insider trading qpw for
the dataset is 2.20, and the average probability of insider trading, apw, is 59 percent.
Figure 18.2 displays the distribution of the ex post probability of insider trading.
We can see that there are around 611 races in which no plunges occurred and hence no
insidertradingisobserved. Wheninsidertradingdoestakeplace,theaverageprobability
is around 60 percent, though there is plenty of dispersion around the mean.
One ﬁnal remark should be made with respect to the ex post probability of insider
trading. It should be noted that the value depends on the bookmaker’s expectation
of the degree of insiders compared to outsiders. If we allow for a higher-than-zero
expected proﬁt, the bookmaker’s expectation will be lower and we would ﬁnd values
of insider trading closer to the 20–30 percent range found by Schnytzer, Lamers, and
Makropoulou (2010).
6 Conclusions
.............................................................................................................................................................................
In this chapter, we modeled a ﬁxed-odds horse betting market from a bookmaker’s
point of view under uncertainty. We relied on a model by Makropoulou and Markellos

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336
horse race betting
(2011) and Schnytzer, Lamers, and Makropoulou (2010) that conceptualizes ﬁxed-odds
betting markets as option markets. Starting from a proﬁt function we showed that a
bookmaker offers an implicit call option to insiders when setting prices. The insid-
ers in this chapter are assumed to know only the true winning probability of their
horses, not the identity of the winning horse. Moreover, insiders bet only if their
expected proﬁt is positive. In the case in which both outsiders and insiders exist
in the market, the bookmaker will set prices in such a way that the expected loss
from dealing with insiders equals the expected gain from dealing with outsiders.
When the bookmaker sets prices in this way, the latter will exhibit a favorite-longshot
bias.
By allowing for betting in multiple time periods and making an assumption on
how the insider money will arrive, the zero-proﬁt condition of Schnytzer, Lamers, and
Makropoulou (2010) has to hold only for the race and not for each individual horse.
From this model it becomes possible to measure the expectations of the bookmaker
regarding the ratio of insider money to outsider money. Using Monte Carlo simulations,
we generated the implicit option values as quoted by the bookmaker and found that
a zero-expected-proﬁt bookmaker expects 95 percent of the money bet to be placed
by insiders. However, these estimates are biased in the sense that we do not allow the
bookmaker to make a positive proﬁt. By keeping the expected proﬁt equal to zero, we
overestimated the expected degree of insider trading. When we used ex post plunging
information, we concluded that the probability of insider trading in our dataset lies
around 59 percent. Or to put it differently, for every Australian dollar bet by outsiders,
the average amount bet by insiders is 2.20 dollars.
Appendix
.............................................................................................................................................................................
Proof
Suppose ﬁrst that only outsiders exist in the market and that their demand is inelastic,
that is, ∂Wn
∂OPj = 0. A monopolistic bookmaker will set prices that maximize his expected
proﬁt:
max E() = Wn −
N

j=1
E

Pj(T)
 wj
Wn
Wn
1
OPj
∂E()
∂OPj
= 0 ⇒−E

Pj(T)
 wj
Wn
Wn
−1
OP2
j
= 0
Since inﬁnite prices do not make any sense, this leads to the conclusion that out-
siders’ demand should be elastic, that is, ∂Wn
∂OPj < 0. In this case we have the following

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pricing decisions and insider trading
337
solution:
∂E()
∂OPj
= 0 ⇒∂Wn
∂OPj
−E

Pj(T)
 wj
Wn
Wn
−1
OP2
j
−E

Pj(T)
 wj
Wn
1
OPj
∂Wn
∂OPj
= 0.
Suppose now that insiders also exist in the market:
max E() = Wn
⎛
⎝
N

j=1
OPj
⎞
⎠−
N

j=1
E

Pj(T)
 wj
Wn
Wn
1
OPj
−Wi max
j
Cj
∂E()
∂OPj
= 0 ⇒
∂Wn
∂OPj
−E

Pj(T)
 wj
Wn
Wn
−1
OP2
j
−E

Pj(T)
 wj
Wn
1
OPj
∂Wn
∂OPj
−∂Wi
∂OPj
max
j
Cj −Wi
∂Ci
∂OPj
= 0.
In the above equation all terms except for the ﬁrst one are positive. Speciﬁcally, ∂Wi
∂OPj
is negative given that insider demand drops as the price increases, and ∂Ci
∂OPj is negative
since the option price decreases as the strike price increases (or equivalently as the level
of moneyness decreases).
Notes
1. The computational resources (Stevin Supercomputer Infrastructure) and services used in
this work were provided by Ghent University, the Hercules Foundation, and the Flemish
Government—Department EWI.
2. As we will see in section 4, knowing the marginal density function is equivalent to knowing
the volatility of the jump size and the Poisson arrival rate.
3. One way to capture potential value erosion of the option due to other insiders would be
to incorporate a dividend yield. According to the theory of options, it is never optimal
to exercise an American option before maturity in the absence of dividends. This means
that, in our context, insiders would always bet at the last minute. It is the presence of other
insiders (dividends) that makes it optimal to bet before maturity.
4. If they bet at OP prices will exhibit a plunge, and therefore betting at MP would be
worthless. This is true under the assumption that information regarding a certain horse
can be revealed only once.
5. Races in which no plunges are visible in the data (odds at no point fell for any horse
during the betting) are races in which inside trades were not observed. Of course, it could
be that an insider placed a discreet bet with a single bookmaker and that this bet cannot
be discerned in the average odds that rule in the market and are published. The greater the

---

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338
horse race betting
extent of this phenomenon, the more our estimates of insider trading will underestimate
its true extent.
6. The data were obtained from the CD-Rom Australasian Racing Encyclopedia ’98, presented
by John Russell.
References
Dowie, Jack. 1976. On the efﬁciency and equity of betting markets. Economica 43(170):
139–150.
Kahneman, Daniel, and Amos Tversky. 1979. Prospect theory: An analysis of decision under
risk. Econometrica 47(2):263–292.
Makropoulou, Vasiliki, and Raphael N. Markellos. 2011. Optimal price setting in ﬁxed-
odds betting markets under information uncertainty. Scottish Journal of Political Economy
58(4):519–536.
Schnytzer, Adi, Martien Lamers, and Vasiliki Makropoulou. 2010. Measuring the extent of
inside trading in a horse betting market. Journal of Gambling and Business Economics
4(2):21–41.
Schnytzer, Adi, and Yuval Shilony. 2002. On the timing of inside trades in a betting market.
European Journal of Finance 8(2):176–186.
Shin, Hyun Song. 1991. Optimal betting odds against insider traders. Economic Journal
101(408):1179–1185.
——. 1992. Prices of state contingent claims with insider traders, and the favourite-longshot
bias. Economic Journal 102(411):426–435.
——. 1993. Measuring the incidence of insider trading in a market for state-contingent claims.
Economic Journal 103(42):1141–1153.
Quandt, Richard E. 1986. Betting and equilibrium. Quarterly Journal of Economics 101(1):
201–207.

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## Page 360

s e c t i o n iv
........................................................................................................
BETTING STRATEGY
........................................................................................................

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chapter 19
........................................................................................................
BETTING ON SIMULTANEOUS
EVENTS AND ACCUMULATOR
GAMBLES
........................................................................................................
andrew grant
1 Introduction
.............................................................................................................................................................................
As bettors become more sophisticated, there is an increasing focus on bankroll risk
management or how much to bet on certain opportunities. Bettors often face situa-
tions where multiple games are played simultaneously, and therefore the problem of
allocating capital across different games or events must be considered, much the same as
an investor allocating capital to different stocks in a portfolio. In this chapter, I explore
the use of accumulator bets (parlays) as part of a portfolio betting strategy. Accumula-
tors are a security offered by bookmakers (as opposed to casino games) that pay out on
the joint outcome of multiple games. The optimal use of accumulators allows the bettor
to replicate payoffs from sequential betting (with proportional strategies) by betting
simultaneously (Grant, Johnstone, and Kwon 2008).
Using ﬁxed-stake (e.g., £10 per outcome) betting strategies, betting simultaneously
will not pose a problem as long as there are fewer stakes to be made than the bankroll
permits. A proportional-stake betting system, as used by many sophisticated bettors,
requires the bettor to wager a ﬁxed proportion (e.g., 5%) of their bankroll at each
betting opportunity. The most widely discussed proportional staking strategy with
respect to ﬁxed odds betting is the log-utility or Kelly (1956) strategy and its fractional
variants(Maclean,Ziemba,andBlazenko,1992),whichapproximateotherpowerutility
functions.
Proportional systems, as the name implies, require the bettor to wager some fraction,
f , of their total wealth, W , at each point in time. In particular the Kelly (1956) criterion

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betting strategy
requires the bettor to risk the fraction, f , at each opportunity to maximize the logarith-
mic utility function, U(W ) = ln(W ). Bettors employing fractional variants of the Kelly
criterion will wager some fraction λf , 0 ≤λ ≤1, of the “full” (λ = 1) Kelly fraction,
which increases the security of the bankroll at the cost of reducing the bankroll growth.
Fractional Kelly strategies represent the use of the power utility function U(W ) = 1
θ W θ
for θ < 0 and will see the bettor wager less than the full Kelly stake. Under the power
utility function θ →0 is the special case of log utility. The following work discusses the
full-Kelly criterion only but can be easily applied to fractional Kelly strategies.
In this chapter I review the literature on betting on simultaneous games with partic-
ular focus on the Kelly (1956) criterion. In section 2 I discuss the general problem of
ﬁnding the optimal amount to bet by considering the simultaneous tossing of identical,
independent, biased coins with payoffs at even odds. I ﬁnd characteristic functions for
the tossing of up to 7 simultaneous coins and review some approximations to the opti-
mal bet size. In section 3 I ﬁnd analytical solutions to the optimal betting strategy for the
special case of 2 games with symmetric payouts (the two games have the same payouts
but not necessarily even odds). Section 3 discusses numerical techniques for ﬁnding the
optimal amount to bet when there are a general number of games available and payoffs
possible. In section 4 I provide a brief discussion of the relative merits of using accumu-
lators over single-game bets and present an empirical comparison between Kelly betting
strategies involving no accumulators, maximal level accumulators, and the Optimal M
strategy of , Johnstone, and Kwon (2008). Section 6 discusses practical matters related
to betting on simultaneous games and avenues for future research opportunities.
Readers interested in ﬁxed-staking strategies may like to focus on the number of
bets required to employ various approaches to betting. I conclude with a discussion of
potential future research directions for simultaneous staking strategies.
2 Betting on the Simultaneous
Tossing of Biased Coins
.............................................................................................................................................................................
Consider the case of a single favorable coin, which pays out even odds. Refer to the gross
payout per dollar bet as α ($2 in this case per $1 bet) and the net payout as β ($1 per
$1 bet). Let the bettor hold probability p > 0.5 of heads occurring (and hence q = 1−p)
of tails. According to the Kelly criterion, the optimal bet is that which maximizes the
growth rate, G, of the bettor’s bankroll
G = p ln(1 + f ) + q ln(1 −f ).
(19.1)
The Kelly bettor hence wages a fraction f ∗= p −q = 2p −1 on the outcome heads. For
example, if p = 0.60, then the Kelly bettor would wager f ∗= 20% of his or her bankroll
on the outcome heads. Clearly if ﬁve identical independent favorable coins are tossed

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betting on simultaneous events and accumulator gambles
343
simultaneously, and the bettor wagers 20 percent of bankroll on each toss, he or she
faces the possibility of ruin if all coins happen to land on tails. Thus the proportional
bettor needs to consider the fact that the coins are tossed simultaneously and adjust the
bet size accordingly. This is best illustrated with the simultaneous tossing of two coins
(see also Thorp 2000; Medo, Pis’mak, and Zhang 2008).
Suppose that there are i = 1,2,3...,M independent and identical coins, to be tossed
simultaneously. Assume that the payouts on offer are all even money (α = $2) and,
because the coins are identical, that the bettor holds an identical probability pi = p for
each of the coins. Thus the optimal bet size will be f ∗
i = f ∗, simplifying the process
to a one-variable problem. For M simultaneous coin tosses there is a probability of
(1 −p)M > 0 that all coins land on tails. It therefore follows that the optimal bet size
takes the restriction f ∗< 1/M. In other words, the simultaneous bettor should never
risk more than half his wealth on any particular coin in a two-coin scenario, even if the
probability of heads is greater than p = 0.75.
In the special case of pi = p and α = 2 for every game, Medo, Pis’mak, and Zhang
(2008) provide us with a simple method for ﬁnding the optimal wager for the Kelly
bettor. Suppose there are w winning tosses and M −w losing tosses. The bettor’s return
will be (2w −M)f in this case (and will hence increase by a factor of 1 + (2w −M)f )).
For example, if M = 3 and w = 2, the bettor’s bankroll will increase by a factor of
(1 + f ), which would be economically equivalent to two coins landing on heads and
one on tails.
The growth rate of the Kelly bettor’s bank roll in the coin-tossing game is given by
G =
M
w=0 P(w;M,p)ln[1 + (2w −M)f ],
(19.2)
where P(w;M,p) =
M
w

pw(1 −p)M−w is the binomial probability distribution func-
tion. We ﬁnd the optimal investment fraction by using the ﬁrst-order condition ∂G
∂f = 0.
Then, rewriting 2w −M = [f (2w −M) + 1 −1]/f and using the normalization of
P(w; M, p), we obtain the resultant equation to ﬁnd the optimal fraction for M
independent coins
M
w=0
p(w;M,p)
1 + (2w −M)f = 1
(19.3)
In this form the case M = 1 reduces to (1 −p)/(1 −f ) + p/(1 + f ) = 1, and so
f ∗= (2p −1)
When M = 2, the optimal betting strategy may be found by using the generating
function (19.3)
2
0

(1 −p)2
1 −2f
+
2
1

p(1 −p)
1
+
2
2

p2
1 + 2f = 1.
The ﬁrst term provides the payoff when both coins land tails with probability (1 −p)2,
and the bettor’s bankroll is increased by a factor of (1 −2f ). The second term provides
the payoff when one coin lands heads and the other tails with probability 2p (1 −p)
with the coefﬁcient of two indicating order indifference. The bettor’s bankroll would

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betting strategy
increase by a factor of (1+f −f ) = 1. The ﬁnal term on the left-hand side is the payoff
when both coins land heads (with probability p2), which increases the bettor’s bankroll
by (1 + 2f ).
(1 −p)2(1 + 2f ) + 2p(1 −p)(1 −2f )(1 + 2f ) + p2(1 −2f )
(1 −2f )(1 + 2f )
= 1,
which, after some relatively simple algebra, reduces to
f = 0 or f (−8p2 + 8p −4) + 4p −2 = 0.
Ignoring the trivial solution we rearrange to obtain
f ∗=
2p −1
4p2 −4p + 2 =
2p −1
(2p −1)2 + 1
(19.4)
It is worth examining this solution more closely. The numerator of the expression is
simply the optimal fraction for M = 1 coin or the single-game Kelly fraction. The
expression in the denominator is a parabola, which serves as a reduction factor for the
bet from the nonsimultaneous case. The denominator takes a minimum value of 1 at
p = 0.5. For p > 0.5 (the case of interest) the denominator increases (at an increasing
rate) and approaches 2 as p →1, meaning that the bet size is maxed out at f ∗= 1/2, as
required. As the edge gets larger, the impact of the restriction on the bet size becomes
more binding; the optimal bet for each coin ﬂip when p = 0.55 is f ∗= 0.1/1.01 = 0.099,
whereas the optimal bet when p = 0.8 is f ∗= 0.6/1.36 = 0.441.
It is possible (but considerably more complicated) to construct an analytical solution
for the simultaneous tossing of M = 3 identical coins. Again the generating function
(19.3) is used
3
0

(1 −p)3
1 −3f
+
3
1

p(1 −p)2
1 −f
+
3
2

p2(1 −p)
1 + f
+
3
3

p3
1 + 3f = 1.
Note that there are three ways of obtaining two heads and one tail (which increases
the bankroll by a factor of (1 + f ) and three ways of obtaining two tails and one head.
Expanding out this equation yields
(1 −P)3(1 −f )(1 + f )(1 + 3f ) + 3p(1 −p)2(1 −3f )(1 + f )(1 + 3f )
+ 3p2(1 −p)(1 −3f )(1 −f )(1 + 3f ) + 3p3(1 −3f )(1 + f )(1 −f )
= (1 −3f )(1 −f )(1 + f )(1 + 3f ),
which we can simplify to
(1 −p)3(1 −3f −f 2 −3f 3) + 3p(1 −p)2(1 + f −9f 2 −9f 3)
+ 3p2(1 −p)(1 −f −9f 2 + 9f 3) + 3p3(1 −3f −f 2 + 3f 3)
= 1 −10f 2 + 9f 4

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betting on simultaneous events and accumulator gambles
345
After some simpliﬁcation, and ignoring a trivial solution f = 0, we are left with a
characteristic cubic function
9f 3 + (6(2p −1)3 −9(2p −1))f 2 + (−6(2p −1)2 −9)f + 3(2p −1) = 0.
(19.5)
The coefﬁcients of f in this equation are reduced to the form involving the original
“edge” on the Kelly bet, (2p −1), or constants. Examining these coefﬁcients will allow
us to glean some information about the optimal solution. From this we can clearly see
that the coefﬁcients of f 2 and f will be negative while the constant will be positive when
0.5 < p < 1. We can ﬁnd an analytical solution to this function using the cubic formula,
but we gain little insight into the problem. It is very easily solved using numerical
methods in this characteristic format.
When ﬁnding the characteristic equations for M simultaneous coin tosses it
may useful to consider an adjustment to the generating function (19.3) to reduce
the burden in simpliﬁcation. Letting X = (2w −M)f
and using the identity
1/(1 + X) = 1 −X/(1 −X), we can rewrite (19.3) as
M
w=0
M
w

pw(1 −p)M−w(2w −M)
1 + (2w −M)f
= 0.
(19.6)
The new generating function (19.6) is signiﬁcantly simpler to work with because of the
lack of constant on the right-hand side. When w = M/2 (the number of heads and tails
is equal) the number of terms in the expression is also reduced by 1.
Using this new compact form, and following a similar process as in the case M = 3,
we can ﬁnd the characteristic equation for the M = 4 simultaneous coin case
(−24(2p −1)4 + 48(2p −1)2 + 40)f 3 + (24(2p −1)3 −40(2p −1))f 2
+ (−12(2p −1)2 −28)f + 4(2p −1) = 0
(19.7)
Figure 19.1 presents the optimal single coin betting fractions for M = 1,2,3,4 simul-
taneous coins as found by using the expressions in (19.1), (19.4), (19.6), and (19.7).
When the bettor has only a small edge, the optimal betting fractions are not reduced
substantially from the single-coin case. As the edge becomes large it can be observed
quite clearly that the optimal bet approaches f ∗= 1/M.
Figure 19.2 shows the total amount bet Mf ∗across all coins by bettor probability
for M = 1, 2, 3, 4 coins. The bettor is constrained by the restriction Mf ∗< 1 for
simultaneous betting. The restriction becomes binding at smaller probability edges as
the number of coins increases.
Figure 19.3 presents the expected bankroll growth rate (or expected log-utility) G
for M = 1, 2, 3, 4 coins. The bettor’s wealth is diversiﬁed across multiple coins as
M increases, and there is a commensurate improvement in their expected bankroll

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betting strategy
1
0.9
M = 1
M = 2
M = 3
M = 4
0.8
0.7
0.6
0.5
0.4
Optimal Single Coin Bet f*
0.3
0.2
0.1
0
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Probability
figure 19.1 Optimal individual coin bets for M = 1, 2, 3, 4 coins by bettor probability
M = 1
M = 2
M = 3
M = 4
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Probability
Total fraction bet Mf *
figure 19.2 Total amount bet Mf ∗for M = 1, 2, 3, 4 simultaneous coin tosses by bettor
probability
growth rate. Thus it is advisable to bet optimally on M > 1 simultaneous coins than a
single coin alone. There are diminishing marginal returns to diversifying one’s bet by
increasing the number of coins.
It is illustrative to ﬁnd the characteristic functions for increasing numbers of coins,
derived from the generator (19.6). Note that for M > 4 numerical methods must be

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M = 1
M = 2
M = 3
M = 4
0.8
0.7
0.6
0.5
0.4
Expected Utility (Bankroll Growth Rate) G
0.3
0.2
0.1
0
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Probability
figure 19.3 Expected Utility or bankroll growth rate for M = 1, 2, 3, 4 simultaneous coin tosses
by bettor probability
used to ﬁnd the optimal fractions, f ∗. The case M = 5 has the characteristic function
−225f 5 + (120(2p −1)5 −300(2p −1)3 + 225(2p −1)f 4 + (−120(2p −1)4
+ 260(2p −1)2 + 110)f 3 + (60(2p −1)3 −110(2p −1)f 2 + (−20(2p −1)2 −5)f
+ 5(2p −1) = 0
(19.8)
The characteristic function for M = 6 is
(−720(2p −1)6 + 2160(2p −1)4 −2160(2p −1)2 −1584)f 5 + (720(2p −1)5
−1920(2p −1)3 + 1584(2p −1)f 4 + (−360(2p −1)4 + 840(2p −1)2
+ 240(2p −1))f 3 + (120(2p −1)3 −240(2p −1))f 2 + (−30(2p −1)2f
+ 6(2p −1) = 0
(19.9)
The characteristic function for the M = 7 coin case is
11025f 7 + (5040(2p −1)7 −17640(2p −1)5 + 22050(2p −1)3 −11025(2p −1)f 6
+ (−5040(2p −1)6 + 15960(2p −1)4 −17178(2p −1)2 −6433)f 5 + (2520(2p −1)5
−7140(2p −1)3 + 6433(2p −1 ))f 4 + (−840(2p −1)4 + 2100(2p −1)2 + 455)f 3
+ (210(2p −1)3 −455(2p −1 ))f 2 + (−42(2p −1)2 −7)f + 7(2p −1) = 0
(19.10)

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betting strategy
What we can see from this is that there is a common pattern among the coefﬁcients of f .
When the number of coins, M, is even the polynomial is of degree (M −1), and when
the number of coins is odd the polynomial is of degree M. In either case, note that
the coefﬁcient of f M = M
w=0(2w −M), which will be negative for M = 5, 9, 13, ...,
positive for M = 3, 7, 11,..., and zero for M even. The degree of the polynomial is
reduced by one for even M because if M/2 coins land on heads, the bettor’s return will
be zero.
It is apparent that in the characteristic format the constant term (i.e., not involving f )
is M(2p−1) Each of the coefﬁcients of f then follows a pattern of descending functions
of even powers of (2p −1) if the exponent of f is odd or odd powers of (2p −1) if f
is even. For example, the coefﬁcient of f involves terms in (2p −1)2 and (2p −1)0, the
coefﬁcient of f 2 involves powers of (2p −1)3 and (2p −1), and so on. Therefore, if =
1/2, and hence the bettor does not have an edge, the optimal bet size will be zero.
Moreover, the leading term in each of the coefﬁcient is, beginning from the constant
term, increasing by a factor of −M for each additional power of f . For example, in
the case M = 7, the leading term in the coefﬁcient of f is (7 × −6) = −42, the leading
term in the coefﬁcient of f 2 is (7 × −6 × −5) = 210, and so on, all the way up to the
f 6 term where the coefﬁcient is 7! = 5040. Hence even powers in f will have a positive
leading coefﬁcient while odd powers in f will have negative leading coefﬁcients. The
non-leading terms in the coefﬁcients of f can be found mechanically through the
comparison of powers with the direct expansion.
Medo, Pis’mak, and Zhang (2008) discussed methods for ﬁnding approximate solu-
tions to the simultaneous coin-tossing problem. They found approximate solutions for
an “unsaturated” portfolio, where the constraint of betting less than the total bankroll
over all coins does not bind, (Mf ∗<< 1), and the“saturated”portfolio, where the total
fraction constraint is binding (1 −Mf ∗<< 1). The approximate solution, (exact for
M = 1, 2), for the unsaturated portfolio is
f ∗=
2p −1
M(2p −1)2 + 4p(1 −p),
(19.11)
and the approximate solution for the saturated case is
f ∗= 1
M
+
1 −2p(1 −p)M
2p −1
,
.
(19.12)
The ﬁrst approximation (19.11) should be used in the range p ∈
 1
2,pc

while the second
(19.12) should be used in the range p ∈(pc,1]. The critical value of the probability, pc
is at the point where the two approximations intersect. These approximations work
well in practice for most values of p. Either there is a small reduction from the single
game betting fraction or the bettor’s optimal strategy is close to f ∗= 1/M. The worst
performance is typically around p = pc. Figure 19.4 presents a comparison of the actual
solution and its approximation for the M = 3 coin case.

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0.35
0.25
0.15
0.05
0
0.5
0.55
0.6
0.65
0.7
0.75
Probability
Optimal Betting Fraction
0.8
0.85
0.9
Actual Solution
Joint Approximation
0.95
0.3
0.2
0.1
figure 19.4 Optimal betting fraction and approximate solution by probability for M = 3
simultaneous coin tosses
3 Simultaneous Betting on Two Games with
Symmetric Generalized Payouts
.............................................................................................................................................................................
Up to this point I have considered only the special case of betting on identical biased
independent coins, which meant that the payoff was of the “double or nothing” type
at even odds and the bettor’s subjective probability (or the coins’ known mechanical
probabilities) was identical in every case. In the more realistic case of betting with
non-identical probabilities and more generalized payoffs, the problem of ﬁnding the
optimal amount to bet changes in nature.
Edward Thorp (2000) presented the solution to the two-game, two-outcome case
for which the Kelly bettor does not require identical probabilities (p1 is not necessarily
equal to p2), but the payoff is restricted to even odds (α = $2). Here we follow the
methodology but extend the problem to ﬁnd the optimal amount to bet on two simul-
taneous two-outcome games, with non-identical probabilities and symmetric payouts
(α1 = α2 = α ̸= 2).
The Kelly criterion for the two-simultaneous, two-outcome game maximizes, with
respect to the Kelly fractions f1,f2, the expected log-utility
U(f1,f2) = p1p2 ln(b + αf1 + αf2) + p1q2 ln(b + αf1) + q1p2 ln(b + αf 2) + q1q2ln(b),
(19.13)
where b = 1 −f1 −f2 is the fraction not bet and α is the (assumed) common bookies
payout for the two outcomes.
Figure 19.5 shows the contours of U(f1,f2) for two cases (α > 2 and 1 < α < 2)
in the permissible domain: fi ≥0,f1 + f2 ≤1. Speciﬁcally, the cases are α = [2.3,1.8],
p1 = [0.5217,0.6667];p2 = [0.6087,0.7778].

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betting strategy
1
0.8
0.6
0.4
0.2
0
0.2
0.4
0.6
0.8
1
Kelly Fraction f1
0
0.2
0.4
0.6
0.8
1
Kelly Fraction f1
α = 2.3
α = 1.8
Kelly Fraction f2
0
1
0.8
0.6
0.4
0.2
Kelly Fraction f2
0
figure 19.5 Growth function from equation (19.13) for two simultaneous betting opportuni-
ties. Left panel, α > 2; Right panel, 1 < a < 2.
A single clearly deﬁned maximum is seen in both situations. The analysis that follows
seeks to ﬁnd this maximum analytically.
The master equation. Standard differential methods show that the optimal Kelly
fractions are related to the “master” equation
k1
a1 + b1f +
k2
a2 + b2f +
k3
a3 + b3f = 0,
(19.14)
where the coefﬁcients are given by
a1 = 1 + βc;
b1 = β(1 + d);
k1 = βp1p2
a2 = 1 −c;
b2 = β −d;
k2 = (β −1)p1q2
q3 = 1 −c;
b3 = −(1 + d);
k3 = −q1q2.
The parameter β = α −1 (the odds against) and the constants c and d are deﬁned by
c = q1p2 −p1q2
βp1q2 + q1p2
and
d = p1q2 + βq1p2
βq1p2 + q1p2
.
Once f
is determined from (19.14) the two optimal Kelly fractions are given
respectively by
f1 = f
and
f2 = c + df .
The task before us therefore is to ﬁnd solutions for fi in the range [0, 1] as functions of
the parameters pi and β.

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The master quadratic. Observe that the master equation is actually equivalent to the
quadratic
Af 2 + Bf + C = 0,
(19.15)
where
A = k1b2b3 + k2b1b3 + k3b1b2
B = k1(a2b3 + a3b2) + k2(a1b3 + a3b1) + k3(a1b2 + a2b1)
C = k1a2a3 + k2a1a3 + k3a1a2
⎫
⎬
⎭.
(19.16)
The discriminant 	 = B2 −4AC of the quadratic (19.15) can be written in the form
	 = X2 + Y 2 + Z 2 −2(XY + YZ + ZX),
where
X = k1(a2b3 −a3b2);
Y = k2(a3b1 −a1b3);
Z = k3(a1b2 −a2b1).
Let v denote the vector (X, Y, Z)’, then 	 = v’Qv where Q is the matrix
Q =
⎡
⎣
1
−1
−1
−1
1
−1
−1
−1
1
⎤
⎦.
Since Q has eigenvalues (−1, 2, 2) the quadratic form 	 = v’Qv is indeﬁnite, which
means that the discriminant 	 may be positive, negative, or zero. In practice, however,
for the range of parameters involved, 	 is always positive.
The coefﬁcients A, B, C. The coefﬁcients A, B, C deﬁned by (19.16) can be reduced
to functions of the parameters p1,p2, and β. After some rather tedious algebra, and
canceling the common factor
(β + 1)2p1q2
(βp1q2 + q1p2)2 ,
we obtain
A = −β(β −1)D,
(19.17)
B = β(β −1)p1q2(D + p1p2) −(β −1)q1p2(D + q1q2) −βD(p1p2 + q1q2), (19.18)
C = p2q2

(β + 1)p1 −1

,
(19.19)
with
D = p1q2 + q1p2 = p1 + p2 −2p1p2.
(19.20)
Two things immediately follow from these expressions. The ﬁrst is that A is positive,
negative, or zero according to β being respectively less than, greater than, and equal to

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betting strategy
one. The second is that since the subjective odds and bookies payout must in practice
satisfy the condition
αpi = (β + 1)pi > 1; (i = 1,2),
C is always positive. Determining the sign of B is considerably more troublesome.
Since the product of the roots of (19.16) is C

A, we can conclude that the
two roots (assuming them to be real) have opposite signs if β < 1 and have the
same sign if β >1. Of course if β = 1 we have the special case of even odds. In
this situation A = 0 and hence the quadratic equation reduces to a linear equation
with the single root f = −C

B. For this case we ﬁnd that the corresponding Kelly
fractions are
f1 = p2q2(p1 −q2)
D(1 −D)
,
f2 = p1q1(p2 −q2)
D(1 −D)
,
(19.21)
which are both positive, as pi >qi since pi >0.5, and D > 0 since pi <1. The expression
further reduces to the special coin-tossing example when p1 = p2, in which case
f =
2p −1
(2p −1)2 + 1
as obtained earlier.
Summary. Let us write the two roots of the master quadratic (19.16) as
f ± = −B ± 	
2A
;
	 =

B2 −4AC.
Then we are able to show the following:
Case α > 2 (β > 1).
Here A < 0,C > 0 and 	 > |B|. Note that B may be positive or negative. The roots f ±
have opposite signs with f −> 0 and f + < 0.
So the only feasible root is
f −= 	 + B
2|A| ,
and thus the optimal betting strategy f1,f2 is
f1 = 	 + B
2|A| , f2 = c + df1 = q1p2 −p1q2
βp1q2 + q1p2
+ (p1q2 + βq1p2)f1
βq1p2 + q1p2
Case α < 2(β < 1).
(19.22)

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Here A > 0, C > 0, B < 0 and 	 > |B|. Both roots f ± are positive with f −< f +. For
all practical values of parameters involved in the Kelly betting strategy, 0 <f −< 1 and
f + > 1. In every case we need only take the single root f = f −of the master quadratic,
and then the optimal betting strategy f1,f2 is
f1 = 	 + B
2A
, f2 = c + df1 = q1p2 −p1q2
βp1q2 + q1p2
+ (p1q2 + βq1p2)f1
βp1q2 + q1p2
.
(19.23)
4 Numerical Methods for Finding
the Optimal Strategy
.............................................................................................................................................................................
Finding the optimal bet size with a generalized problem is quite involved. The solution
to the general problem for a two-game case with nonsymmetric payouts becomes
intractable, as does any nonidentical coin-tossing problem for three or more games.
First we will introduce some notation for the generalized simultaneous betting case.
Denote by pi,j the bettor’s subjective probability of outcome j in game i, where
1 ≤i ≤n and 1 ≤j ≤m. Let ai,j denote the corresponding bookmaker’s or market
payout, and let fi,j be the fraction of the bettor’s wealth wagered on the game/outcome
pair (i,j). We further denote by bi the fraction of wealth not wagered on game i, so that
bi = 1−m
j=1fi,j, and by b the total fraction not bet on all simultaneous games, so that
b = 1 −m
i=1
m
j=1fi,j.
Let S = {j1,j2,...,jn} denote a sequence of outcomes for games {1,2,...,n} Over all
possible outcomes the set S has dimension dim(S) = mn. Assuming that the games
are independent, the (subjective) probability of obtaining this sequence of outcomes is
given by
p(S) = p1,j1 p2,j2 ···pn,jn .
(19.24)
Obviously we require that m
j=1pj = 1 for all i ∈{1,2,...,n}. We may then write the
corresponding bettor’s return as
R(S) = b +
n
i=1αi,jifi,ji,
(19.25)
where b = 1 −m
i=1
m
j=1fi,j is the total fraction not wagered over all games and
outcomes. The objective function a Kelly bettor maximizes is given by
U = E{logR(S)} =

S
p(S)logR(S).
(19.26)
Note that while each return R(S) involves a sum over the n simultaneous games, the
objective function U involves a sum over the mn possible game outcomes in set S,
where m is ﬁxed across all games in S. This outer sum may include up to 3n terms when
there are n simultaneous soccer games and the bettor can wager on home win, draw, or

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betting strategy
away win (1 × 2 betting). To ensure non-negativity in the fractions and to incorporate
the bankroll constraint, the optimization must be performed subject to the constraints
0 ≤fi,j ≤1 and b > 0.
In the general setting it is more effective to use numerical rather than analytical
methods to ﬁnd the optimal bet size for more than two simultaneous games with
generalized probabilities and payouts.
The contour diagrams of ﬁgure 19.2 present visualizations of the function to be
maximized in the two-game case. Leo Breiman (1961) showed that the Kelly growth
function has a global optimum from the properties of concavity of the logarithmic
function: positive ﬁrst partial derivatives and negative second partial derivatives pro-
vided the bettor has an edge in each game. This optimum may not be unique in the
case of multiple-outcome simultaneous games (that is, there may be more than one set
of f ’s that produce the maximum growth), but all the global optima will share the same
value (Whitrow 2007). The maximum will be at an interior point because the bettor
will never want to risk all his or her capital (b>0).
The numerical solution to the problem can be solved directly for a relatively small
number of games (practically, less than 10) using iterative hill-climbing algorithms,
such as the conjugate-gradient or active-set algorithms, which are used in the empirical
analysis of Andrew Grant and Peter Buchen (2012). Robin Insley, Lucia Mok, and
Tim Swartz (2004) proposed a derivative-based method for ﬁnding the optimal Kelly
betting strategy based on a modiﬁed version of the Gauss-Seidel algorithm. Because
the solution surface is typically ﬂat in the neighborhood of the optimum (as seen in
ﬁgure 19.5) the methods based on derivatives or iterative procedures may oscillate
around the maximum value if the successive step sizes are not sufﬁciently small in
magnitude.
The number of terms in the objective function (and derivative) increases exponen-
tially with the number of games. Iterative numerical methods, such as the active-set
algorithm (which is used by Matlab’s fmincon routine), require successive calculations
of these functions with a very large number of terms, which can make the computation
very time-consuming. Because the solution surface is ﬂat, it is practically useful to set
the tolerance on the function maximum to be relatively low; optimization routines
will often spend large amounts of time increasing the bettor’s capital growth by an
inﬁnitesimal amount. It is imperative to consider that many betting websites have a
minimum stake size, and as such increasing the accuracy of the betting fractions is
likely unnecessary. Moreover, the precision of the optimal solution is likely to exceed
that of the bettor’s probabilities in the neighborhood of the maximum.
As the size of set of possible game outcomes S becomes large, either due to multiple-
outcome bets or an increased number of games, it is efﬁcient to use the Monte Carlo
techniques of Chris Whitrow (2007) to ﬁnd the optimal betting strategy. Because the
solution is nonunique and the solution surface is quite ﬂat, the Monte Carlo approach
is able to ﬁnd an approximate solution in the near neighborhood of the actual numer-
ical solution quite efﬁciently by simulating game outcomes to estimate the objective
function.

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5 Optimal Betting When the Bookmaker
Accepts Accumulator Gambles
.............................................................................................................................................................................
Up to this point it has been assumed that the bettor’s universe of possible stakes is
limited to the outcomes of single games only. In practice it is possible to bet on the
joint outcome of multiple games by using accumulator bets (also known as parlays).
This allows the bettor to multiply his or her gross winnings in the case of a joint event
occurring.
The bookmaker will typically offer these types of bets for uncorrelated events only.
For example, if there were two football matches, with the two home teams paying
α1 = $1.50 and α2 = $1.80, respectively, the bettor could place a wager that would
pay off conditioned on both home teams winning, with a gross payout of α1 × α2 =
1.50 × 1.80 = $2.70. The number of joint bets in an accumulator is usually referred to
as the number of “legs”or“ways”or simply as an“n-fold”or“n-tuple”(e.g., a three-way
accumulator or a quadruple).
Tim Kuypers (2000) mentioned that this particular strategy is quite popular in the
United Kingdom for soccer betting because historically bettors could not bet on the
outcome of a single football match but were restricted to betting on the joint outcome of
at least three simultaneous games. This law has since been rescinded, but accumulators
remain a popular instrument in betting markets: this may be in part a preference for
skewness (Golec and Tamarkin 1998) or a means to prolong the consumption utility
of the bet.
In the modern era of online bookmakers, accumulators are often used as incentive
for new bettors to join websites or as part of special promotions. For example, the
U.K.-based bookmaker Sportingbet offered a promotion in 2011—a bettor opening an
account and depositing at least £10 was offered up to £100 of free bets consisting of
matched bets of up to £10 on single game bets and £30 each of matched bets on doubles,
triples, and quadruples or higher. Irish bookmaker Paddy Power held a promotion
whereby bettors were offered a refund for losing four-plus-leg football accumulators
if all bets were winning at halftime. Bet365 provided bonuses to a bettor’s payout
on successful football accumulator bets—winning three-way accumulators received a
bonus 5 percent return, with increasing bonus returns (up to 100%) to accumulators
with a higher number of legs.
It is interesting to note that many bookmakers use accumulators as a loss leader to
generate revenue either through website advertising or, more likely, through increased
market share of turnover. Accumulators are relatively proﬁtable for the bookmakers,
on average. This is because the bookmaker’s transaction costs, as measured by the
implicit overround, are multiplied for accumulators (see Ali 1979; Kuypers 2000). As
a simple example, suppose that the bookmaker offers equal payouts on heads (H) and
tails (T) of αH = αT = $1.90, respectively, on a fair coin-tossing game. Observe that

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betting strategy
the overround, ε1, for a single game bet is
ε1 = 1

αH+1

αT = 1

1.90 + 1

1.90 −1 = 5.26%.
(19.27)
Now,
if the bookmaker accepts bets on the set of two-way accumulators
{(HH),(HT),(TH),(TT)} which each occur with probability 0.25, the bookmaker
will offer payouts of αHH = αHT = αTH = αTT = 1.90 × 1.90 = $3.61. The set of
doubles thus has overround ε2
ε2 =
1
αHH
+
1
αHT
+
1
αTH
+
1
αTT
= 4
 1
3.61

−1 = 10.80% = (1 + ε1)2 −1 (19.28)
In general, the bookmaker’s overround will grow exponentially with the number of
legs in the accumulator. It is therefore less costly for bookmakers to offer free bets in
the form of accumulators and is potentially beneﬁcial if it encourages bettors to use
accumulators in future betting. Bookmakers do, however, face an increased level of
difﬁculty in balancing their books or hedging risks when they accept these potentially
unique, high-liability bets.1
5.1 Notation for Accumulators
Before we analyze the optimal use of accumulators in general, we introduce the
following notation (adapted from Buchen and Grant 2012).
For each 1 ≤k ≤n, deﬁne the set of k-leg accumulators by
Mk =
$
i1,j1

,

i2,j2

,...,

ik,jk
%
,
(19.29)
where each

is,js

denotes a speciﬁc (unique) game/outcome pair. This means that
is = it only if s = t, so that accumulators are made across games but not within games.
The collection of all accumulators is denoted by the set-product M = -n
k=1 Mk.
5.2 Optimal Betting with Accumulators
How might a Kelly bettor go about utilizing accumulators in a simultaneous betting
strategy? Suppose there are n simultaneous games available to the bettor. An obvious
strategy is to use bets of maximal level only, so the bettor would use three-way accumu-
lators only for three simultaneous games. Alternatively, the bettor can use accumulator
bets of all k-levels up to and including n, a strategy ﬁrst discussed in Grant, Johnstone,
and Kwon (2008). Thus the bettor would use triples, doubles, and single-game bets to
wager on three simultaneous games. Thus the bettor would use triples, doubles, and
single-game bets to bet on three simultaneous games.

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357
5.3 Using Maximal Level Accumulators
If the bettor uses n-way accumulator bets only, then each bet is mutually exclusive (only
one bet may pay off), and hence this strategy will work under the original Kelly (1956)
framework. This strategy was discussed in Grant and Buchen (2012) and is as follows:
Let pj be the bettor’s subjective probability of outcome j in the set Mn of maximal
accumulators, and let aj be the corresponding bookmaker payout. Order the outcomes
so that
p1α1 ≥p2α2 ≥· · · ≥pmαm.
(19.30)
Then let k ∈1,2,...,m be the maximum integer with properties
σk =
k
i=1
1
αj
< 1 and pkαk > 1 −πk
1 −σk
,
(19.31)
where πk = k
i=1 pk. Then the optimal Kelly betting fractions fj are given explicitly by
the formula
fj = max[pj −1
αj
1 −πk
1 −σk

,0].
(19.32)
In particular, when the outcomes are sorted as in (19.30), it is optimal to bet only on
the ﬁrst k outcomes.
Let’s return to the example of two coins, each with payouts of αH = αT = $1.90.
Supposethatabettorhassubjectiveprobabilityof headsontheﬁrstcoinbep(1,H) = 0.55
and heads on the second coin be p(2,H) = 0.64. Each of the corresponding accumulators
will have a joint payout of αj = $3.61.
Following that strategy we order the payouts by expectation so that we have
p(1,H) × p(2,H) × αHH = 0.55 × 0.64 × 3.61 = 1.2707
p(1,T) × p(2,H) × αTH = 0.45 × 0.64 × 3.61 = 1.0397
p(1,H) × p(2,T) × αHT = 0.55 × 0.36 × 3.61 = 0.7149
p(1,T) × p(2,T) × αTT = 0.45 × 0.36 × 3.61 = 0.5848
Then ﬁnd the payout reciprocals,
1
αj =
1
3.61 = 0.277, so we can ﬁnd that σ =
(0.277,0.554,0.831,1.108) and so the bettor will never bet on more than three outcomes
from the ﬁrst condition. From the second condition, 1−πk
1−σk = (0.8963,0.8072,0.9587,0),
and thus only the ﬁrst two outcomes (HHand TH) provide positive betting fractions

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betting strategy
due to being greater than their respective expectations. The optimal maximal
accumulator strategy is, from (19.32),
fHH = 0.1037, fTH = 0.0644, fHT=0, fTT = 0.
The total amount bet is therefore fHH + fTH = 0.1037 + 0.0644 = 0.1681, and hence
b = 1 −0.1681 = 0.8319. This bet provides expected utility (bankroll growth rate) of
E (U) = G = 0.55 × 0.64 ln(0.8319 + 0.1037(3.61)) + 0.45 × 0.36 ln(0.8319
+ 0.0644(3.61)) + 0.55 × 0.36ln(0.8319)
+ 0.45 × 0.36 ln(0.8319) = 0.0177.
(19.33)
5.4 Using All Levels of Accumulators—The Optimal
M Strategy
Grant, Johnstone, and Kwon (2008) developed the optimal M strategy for simultaneous
games (see their paper for a detailed proof; this chapter provides a detailed illustration).
In the optimal M strategy the Kelly bettor uses all levels of accumulator up to and
including the maximal level n to maximize utility. The optimal amount to bet on each
accumulator is simply derived from the product of the union and complements of each
of the individual game betting fractions, as calculated from (19.32).
Let’s return to the example of two coins, each with payouts of αH = αT = $1.90.
Supposethatabettorhassubjectiveprobabilityof headsontheﬁrstcoinbep(1,H) = 0.55
and heads on the second coin be p(2,H) = 0.64. The optimal bet on the ﬁrst coin
individually would be
f(1,H) = p(1,H) −1 −p(1,H)
α(1,H) −1 = 0.55 −0.45
0.9 = 0.55 −0.50 = 0.05,
and the corresponding optimal bet for the second coin would be f(2,H) = 0.64 −
0.36
0.9 = 0.24. The corresponding amounts withheld from betting on the coins are
b1 = 0.95 and b2 = 0.76. The optimal M strategy involves the placement of a two-
leg accumulator bet of {HH}on f{(1,H)(2,H)} = f(1,H) ×f(2,H) = 0.05×0.24 = 0.012 and
two separate single-game bets of f{(1,H)} = f1,H × b2 = 0.05 × 0.76 = 0.038 on H on
the ﬁrst coin and f{(2,H)} = f(2,H) × b1 = 0.24 × 0.95 = 0.228 on H on the second coin.
Note that the amount remaining in the bank, b, for this strategy is
b = 1 −f{(1,H)(2,H)} −f{(1,H)} −f{(2,H)} = 1 −0.012 −0.038 −0.228 = 0.722,
which is, in fact, b1 × b2 = 0.95 × 0.76 = 0.722
It is interesting to see that, had the games been played sequentially, the bettor’s
expected utility from the construction of the optimal M strategy corresponds exactly

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betting on simultaneous events and accumulator gambles
359
to the bettor’s utility. Let’s consider the two-game example again. The expected utility
from betting sequentially may be written as
E

U

f1,f2

= p1p2 ln

b1b2 + α1f1b2 + α2f2b1 + α1α2f1f2

+ p1q2 ln

b1b2 + α1f1b2

+ q1p2 ln

b1b2 + α2f2b1

+ q1q2 ln(b1b2),
(19.34)
where f1 and f2 are the individual game betting fractions. For the two-coin example,
the expected utility would be
E

U

f1,f2

= 0.55 × 0.64 ln(0.722 + 1.90(0.05 × 0.76) + 1.90 × (0.24 × 0.95)
+3.61 × (0.05 × 0.24)) + 0.55 × 0.36 ln(0.722 + 1.90(0.05 × 0.76))
+ 0.45 × 0.64 ln(0.722 + 1.90(0.95 × 0.24)) + 0.45 × 0.36 ln(0.722)
= 0.02749
(19.35)
We can compare this solution to the expected utility of betting on two games with
symmetric payouts using the analytical solution in (19.23). By calculations, we have
A = 0.04374,B = −0.22109,C = 0.01037,D = 0.486,c = 0.19305 and d = 0.98070.
Solving the quadratic gives the solution f1 = 0.04734 and f2 = c + df1 = 0.23947. This
gives expected utility (bankroll growth rate) of U = 0.02743, which is slightly lower
than the value obtained from the optimal strategy with accumulators (but higher than
the value from using maximal accumulators only).
Figures 19.6 to 19.9 present simple comparisons of the wealth distribution that a
bettor would realize from the examples just considered. Figure 19.6 shows the bettor’s
wealth distribution had the two coins been tossed sequentially. Figure 19.7 shows the
wealth distribution for the bettor that uses the optimal M strategy. The bettor’s wealth
Initial wealth
W = 100
{Heads}
W = 100(0.95+
0.005(1.90)) = 104.50
{Tails}
W = 100(0.95)
= 95.00
{Heads, Heads}
W = 104.5(0.76+
0.24(1.90)) = 127.07
{Tails, Heads}
W = 95(0.76+
0.24(1.90)) = 115.52
{Tails, Tails}
W = 95(0.76)
= 72.20
{Heads, Tails}
W = 104.5(0.76)
= 79.42
figure 19.6 Outcomes of betting optimally on the tossing of two biased coins, sequential
betting; p1 = 0.55, p2 = 0.64, α1 = α2 = 1.90

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betting strategy
Initial wealth
W = 100
{Heads, Heads}
W = 100(0.722+0.05×0.76(1.90)+0.95×0.24(1.90)+0.05×0.24(3.61))
= 127.07
{Heads, Tails}
W = 100(0.722+0.05×0.76(1.90))
= 79.42
{Tails, Heads}
W = 100(0.722+0.95×0.24(1.90))
= 115.52
{Tails, Tails}
W = 100(0.722)
= 72.20
figure 19.7 Outcomes from the optimal use of accumulators to bet on two simultaneous games;
p1 = 0.55, p2 = 0.64, α1 = α2 = 1.90
Initial wealth
W = 100
{Heads, Heads}
W = 100(0.7131+0.0473(1.90)+0.2395(1.90))
= 125.81
{Heads, Tails}
100(0.7131+0.0473(1.90)+0.2395(1.90))
= 80.31
{Tails, Heads}
W = 100(0.7131+0.2395(1.90))
= 116.82
{Tails, Tails}
W = 100(0.7131)
= 71.31
figure 19.8 Outcomes from the optimal betting strategy without accumulators; p1 = 0.55,
p2 = 0.64, α1 = α2 = 1.90
in each of the four states is the same if they bet optimally using sequential bets or
bet simultaneously using the optimal M strategy. Figures 19.8 and 19.9 present the
analogues for the simultaneous betting strategy without accumulators and using only
two-way accumulators.
5.5 Comparing Typical Distributions from Simultaneous
Kelly Betting Strategies
The three approaches to simultaneous Kelly betting produce quite different expected
return distributions for the bettor. Expanding the example to actual betting markets

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betting on simultaneous events and accumulator gambles
361
Initial wealth
W = 100
{Heads, Heads}
W = 100(0.8319+0.1037(3.61))
= 120.63
{Heads, Tails}
W = 100(0.8319)
= 83.19
{Tails, Heads}
W = 100(0.8319+0.0644(3.61))
= 106.44
{Tails, Tails}
W = 100(0.8319)
= 83.19
figure 19.9 Using two-way accumulators only to bet optimally simultaneous coin tosses; p1 =
0.55, p2 = 0.64, α1 = α2 = 1.90
and odds will help explore the differences. Suppose the bettor has the opportunity to
bet on ﬁve simultaneous English Premier League games, as shown in table 19.1.
Each cell in table 19.1 contains the bookmaker’s payouts, the bettor’s assumed subjec-
tive probability, and the optimal individual game bet for, respectively, the home team,
Table 19.1 Bookmaker 1X2 Payouts, Bettor Subjective Probabilities, and Individual
Game Betting Fractions for Five Simultaneous English Premier League Matches
Home Team
Away Team
Home Payoff
Draw Payoff
Away Payoff
Bankroll Growth
Rate, Gi
Prob. Home
Prob. Draw
Prob. Away
Fraction not bet,
f ∗
i,1
f ∗
i,2
f ∗
i,3
bi
Chelsea
Bolton
1.29
5.50
11.00
G1 = 0.001815
0.80
0.12
0.08
0.1103
0
0
b1 = 0.889655
Newcastle
Wolves
1.57
4.00
6.00
G2 = 0.008847
0.70
0.20
0.10
0.1737
0
0
b2 = 0.826316
QPR
Fulham
2.63
3.25
2.75
G3 = 0.002137
0.35
0.25
0.40
0
0
0.0571
b3 = 0.942857
West Brom
Sunderland
2.40
3.25
3.00
G4 = 0.0155688
0.45
0.35
0.20
0.1477
0.1267
0
b4 = 0.725582
Wigan
Aston Villa
2.75
3.25
2.63
G5 = 0.058984
0.25
0.20
0.55
0
0
0.2739
b5 = 0.726074
Note: Matches were played on Feb. 25, 2012. Bookmaker prices are from Bet 365.

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betting strategy
Table 19.2 Optimal Non-Accumulator Betting Fractions for the Five-
Game Betting Opportunity Presented in Table 19.1
Match
Home
Draw
Away
Chelsea v Bolton
0.088692
0
0
Newcastle v Wolves
0.144736
0
0
QPR v Fulham
0
0
0.047596
West Brom v Sunderland
0.12401
0.107394
0
Wigan v Aston Villa
0
0
0.261187
Note: Sum of betting fractions: 0.7736; expected logarithmic utility: 0.08411; total
number of bets made: 6.
draw, and away team. The optimal fractions for each game (individually) are shown in
the third row of each cell. The probabilities are such that the bettor would prefer to bet
on a single outcome in four of the ﬁve games and bet on both West Brom and the draw
in the fourth game. The ﬁfth column shows the expected utility Gi (bankroll growth
rate) and the fraction of wealth withheld bi for each individual game i. The sum of the
growth rate across the ﬁve games is 5
i=1 Gi = 0.0088033, which would be the bettor’s
expected utility if the games were played sequentially rather than simultaneously.
A bettor who does not use accumulators will ﬁnd the numerical solution using either
theMonteCarlomethodorthedirectoptimizationmethod. Inthiscase,usingthedirect
optimization through Matlab’s “active-set” algorithm, the optimal non-accumulator
strategy (M1 strategy) is as in table 19.2.
In each case the betting fractions are slightly reduced from the individual game
case, as expected. The overall expected utility from the ﬁve-game betting opportunity
is E(U1) = 0.08411, and the total amount wagered is 77.36 percent of the bettor’s
bankroll. The bettor makes a total of 6 bets in the strategy without accumulators.
Figure 19.10 presents the distribution of potential gross returns that the bettor could
realize from following the optimal strategy without accumulators.
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
0
0.5
1
1.5
2
Gross Return
Probability
figure 19.10 Distribution of bettor’s gross return from employing the optimal non-
accumulator betting strategy as shown in table 19.2.

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betting on simultaneous events and accumulator gambles
363
The bettor who uses n-way accumulators (in this case ﬁve-way accumulators) only,
would place 54 total bets on the 35 = 243 mutually exclusive outcomes. These fractions
were computed using the method from the original Kelly (1956) paper. The bets with
the highest expectation were those on sets (Chelsea, Newcastle, Fulham, Draw, Aston
Villa) and (Chelsea, Newcastle, Fulham, West Brom, Aston Villa), to which the bettor
allocated2.26percentand2.8percentof thebankroll,respectively. Thenon-zerobetting
fractions are shown in the table 19.3.
The total amount wagered across the 54 bets was 18.53 percent of the bankroll,
and the expected utility was E(Un) = 0.050838. This is substantially lower than the
expected utility from single-game only strategy (and in fact lower than simply betting
optimally on Aston Villa alone). This is partially due to the multiplicative nature of the
transaction costs, as previously discussed. The distribution of return outcomes from
employing the ﬁve-way only strategy was capped from below because of the relatively
low total amount bet, as seen in ﬁgure 19.11.
The optimal strategy using all levels of accumulators (the optimal M strategy) is
shown in table 19.4. The strategy consists of a total of 47 bets: 2 ﬁve-ways, 9 four-ways,
16 triples, 14 doubles, and 6 singles. The total amount bet is 63.48 percent of the bettor’s
bankroll; 42 percent of the bankroll is invested in the single-game bets and 28 percent of
the bankroll is in the two-way accumulators. The expensive, higher level accumulators
make up only 5.81 percent of the total wager. This strategy produces expected utility of
E(U) = 0.088033, which is the same as betting sequentially on the ﬁve games as shown
earlier.
Comparing the outcomes between the optimal M strategy and the non-accumulator
strategy provides us with some interesting insights, as demonstrated by the distribution
of gross return differential shown in ﬁgures 19.12 and 19.13.
The mean of the distribution of differentials is 0.022, and the median is −0.1825,
so the distribution is positively skewed. The optimal strategy without accumulators
outperforms the optimal M strategy 60.8 percent of the time, but in these cases, the
average outperformance is 3.24 percent. In the cases where the optimal M strategy
outperforms, the average outperformance is 5.51 percent. Much of this is made up of
the extreme right of the distribution, where either one of the 2 ﬁve-way accumulators
(and all the corresponding lower level accumulators) or 4 of the 5 preferred bettor
outcomes pay off. A small proportion of the outperformance of the optimal M strategy
also comes from the bettor’s worst-case scenario, where either 1 or 0 of the single-game
bets pays off (because the bettor does not risk as much of the bankroll, as explained
earlier.)
The intermediate cases, where most of the bets were made ( two-ways and three-
ways accounted for 30 of the 47 total bets under the optimal M strategy) provide the
scenarios where the single-game only strategy tends to outperform. Bettors spend a
large proportion of their bankroll on expensive accumulators that do not pay off and,
subsequently, would have been better off without them.

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betting strategy
Table 19.3 Non-Zero Betting Fractions from Maximal Kelly Betting on the Five-
Game Betting Opportunity Presented in Table 19.1
Game 1
Game 2
Game 3
Game 4
Game 5
Probability
Payoff
Expectation
Fraction
Chelsea
Newcastle
Fulham
Draw
Aston Villa
0.0431
$ 47.61
2.052768
0.0225887
Chelsea
Newcastle
Fulham
West Brom
Aston Villa
0.0554
$ 35.16
1.949002
0.0284643
Bolton
Newcastle
Fulham
Draw
Aston Villa
0.0043
$ 405.94
1.750423
0.0019810
Chelsea
Newcastle
QPR
Draw
Aston Villa
0.0377
$ 45.53
1.717794
0.0173482
Bolton
Newcastle
Fulham
West Brom
Aston Villa
0.0055
$ 299.77
1.66194
0.0024573
Chelsea
Newcastle
QPR
West Brom
Aston Villa
0.0485
$ 33.62
1.63096
0.0216876
Chelsea
Newcastle
Draw
Draw
Aston Villa
0.0270
$ 56.26
1.516249
0.0111431
Chelsea
Draw
Fulham
Draw
Aston Villa
0.0123
$ 121.29
1.494281
0.0050352
Bolton
Newcastle
QPR
Draw
Aston Villa
0.0038
$ 388.23
1.464785
0.0015016
Chelsea
Newcastle
Draw
West Brom
Aston Villa
0.0347
$ 41.55
1.439604
0.0138095
Chelsea
Draw
Fulham
West Brom
Aston Villa
0.0158
$ 89.57
1.418746
0.0062560
Bolton
Newcastle
QPR
West Brom
Aston Villa
0.0049
$ 286.69
1.390741
0.0018646
Draw
Newcastle
Fulham
Draw
Aston Villa
0.0065
$ 202.97
1.312817
0.0022633
Bolton
Newcastle
Draw
Draw
Aston Villa
0.0027
$ 479.75
1.292926
0.0009184
Bolton
Draw
Fulham
Draw
Aston Villa
0.0012
$ 1,034.25
1.274193
0.0004084
Chelsea
Draw
QPR
Draw
Aston Villa
0.0108
$ 116.00
1.250441
0.0034732
Draw
Newcastle
Fulham
West Brom
Aston Villa
0.0083
$ 149.89
1.246455
0.0026834
Bolton
Newcastle
Draw
West Brom
Aston Villa
0.0035
$ 354.28
1.227569
0.0010858
Bolton
Draw
Fulham
West Brom
Aston Villa
0.0016
$ 763.75
1.209783
0.0004812
Chelsea
Draw
QPR
West Brom
Aston Villa
0.0139
$ 85.66
1.187232
0.0040867
Chelsea
Wolves
Fulham
Draw
Aston Villa
0.0062
$ 181.93
1.120711
0.0015694
Chelsea
Draw
Draw
Draw
Aston Villa
0.0077
$ 143.34
1.10373
0.0018904
Draw
Newcastle
QPR
Draw
Aston Villa
0.0057
$ 194.11
1.098589
0.0013786
Chelsea
Newcastle
Fulham
Sunderland
Aston Villa
0.0246
$ 43.94
1.082779
0.0059048
Bolton
Draw
QPR
Draw
Aston Villa
0.0011
$ 989.12
1.066268
0.0002460
Chelsea
Wolves
Fulham
West Brom
Aston Villa
0.0079
$ 134.35
1.064059
0.0018126
Chelsea
Draw
Draw
West Brom
Aston Villa
0.0099
$ 105.85
1.047937
0.0021762
Draw
Newcastle
QPR
West Brom
Aston Villa
0.0073
$ 143.35
1.043056
0.0015881
Bolton
Draw
QPR
West Brom
Aston Villa
0.0014
$ 730.42
1.012369
0.0002702
Chelsea
Newcastle
Fulham
Draw
Wigan
0.0196
$ 49.78
0.97565
0.0033193
Draw
Newcastle
Draw
Draw
Aston Villa
0.0040
$ 239.87
0.969694
0.0006680
Draw
Draw
Fulham
Draw
Aston Villa
0.0018
$ 517.12
0.955645
0.0002835
Bolton
Wolves
Fulham
Draw
Aston Villa
0.0006
$ 1,551.37
0.955645
0.0000946
Bolton
Draw
Draw
Draw
Aston Villa
0.0008
$ 1,222.29
0.941165
0.0001083
Chelsea
Wolves
QPR
Draw
Aston Villa
0.0054
$ 173.99
0.937831
0.0007480
Chelsea
Newcastle
Fulham
West Brom
Wigan
0.0252
$ 36.76
0.926332
0.0033608
Bolton
Newcastle
Fulham
Sunderland
Aston Villa
0.0025
$ 374.72
0.9233
0.0003229
Chelsea
Newcastle
Fulham
Draw
Draw
0.0157
$ 58.83
0.922433
0.0020963
Draw
Newcastle
Draw
West Brom
Aston Villa
0.0052
$ 177.14
0.920677
0.0006924
Draw
Draw
Fulham
West Brom
Aston Villa
0.0024
$ 381.88
0.907337
0.0002874
Bolton
Wolves
Fulham
West Brom
Aston Villa
0.0008
$ 1,145.63
0.907337
0.0000959
Chelsea
Newcastle
QPR
Sunderland
Aston Villa
0.0216
$ 42.03
0.906089
0.0026871
Bolton
Draw
Draw
West Brom
Aston Villa
0.0010
$ 902.62
0.89359
0.0001115
Chelsea
Wolves
QPR
West Brom
Aston Villa
0.0069
$ 128.49
0.890424
0.0007683
Chelsea
Newcastle
Fulham
West Brom
Draw
0.0202
$ 43.44
0.875805
0.0020133
(Continued)

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365
Table 19.3 (Continued)
Game 1
Game 2
Game 3
Game 4
Game 5
Probability
Payoff
Expectation
Fraction
Bolton
Newcastle
Fulham
Draw
Wigan
0.0020
$ 424.46
0.83195
0.0001032
Chelsea
Wolves
Draw
Draw
Aston Villa
0.0039
$ 215.01
0.827798
0.0001858
Chelsea
Newcastle
QPR
Draw
Wigan
0.0172
$ 47.61
0.816442
0.0006239
Chelsea
Newcastle
Draw
Sunderland
Aston Villa
0.0154
$ 51.93
0.79978
0.0002602
Draw
Draw
QPR
Draw
Aston Villa
0.0016
$ 494.56
0.799701
0.0000273
Bolton
Wolves
QPR
Draw
Aston Villa
0.0005
$ 1,483.68
0.799701
0.0000091
Bolton
Newcastle
Fulham
West Brom
Wigan
0.0025
$ 313.45
0.789895
0.0000119
Chelsea
Draw
Fulham
Sunderland
Aston Villa
0.0070
$ 111.96
0.788192
0.0000184
Bolton
Newcastle
Fulham
Draw
Draw
0.0016
$ 501.64
0.786571
0.0000009
Note: Only ﬁve-way accumulators were used. Sum of betting fractions: 0.1853; expected logarithmic utility: 0.05838;
total number of bets made: 54.
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
Probability
0
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
Gross Return
figure 19.11 Distribution of gross returns from using the ﬁve-way accumulators only strategy
as shown in table 19.3
6 Practical Aspects of Betting on
Simultaneous Games
.............................................................................................................................................................................
The illustrative ﬁve-game example demonstrated quite clearly a number of the potential
difﬁcultiesof implementingsophisticatedKellybettingstrategiesacrossarelativelylarge
number of games.
First, some of the betting fractions produced were very small (such as the amount
bet on the ﬁve-way accumulators in the optimal M strategy or the amount bet on
non-preferred diversifying outcomes in the ﬁve-way only strategy), and bookmakers

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Table 19.4 Non-Zero betting fractions from Optimal M Betting Strategy on
Five-Game Betting Opportunity Presented in Table 19.1
Game 1
Game 2
Game 3
Game 4
Game 5
Probability
Payoff
Fraction
Chelsea
Newcastle
Fulham
West Brom
Aston Villa
0.0554
$ 35.16
0.000044
Chelsea
Newcastle
Fulham
Draw
Aston Villa
0.0431
$ 47.61
0.000038
Chelsea
Newcastle
Fulham
West Brom
0.1008
$ 13.37
0.000117
Chelsea
Newcastle
Fulham
Draw
0.0784
$ 18.10
0.000101
Chelsea
Newcastle
Fulham
Aston Villa
0.1232
$ 14.65
0.000218
Chelsea
Newcastle
West Brom
Aston Villa
0.1386
$ 12.78
0.000731
Chelsea
Newcastle
Draw
Aston Villa
0.1078
$ 17.31
0.000627
Chelsea
Fulham
West Brom
Aston Villa
0.0792
$ 22.39
0.000211
Chelsea
Fulham
Draw
Aston Villa
0.0385
$ 35.84
0.000181
Newcastle
Fulham
West Brom
Aston Villa
0.0693
$ 27.25
0.000357
Newcastle
Fulham
Draw
Aston Villa
0.0539
$ 36.90
0.000307
Chelsea
Newcastle
Fulham
0.224
$ 5.57
0.00058
Chelsea
Newcastle
West Brom
0.252
$ 4.86
0.00194
Chelsea
Newcastle
Draw
0.196
$ 6.58
0.00166
Chelsea
Newcastle
Aston Villa
0.308
$ 5.33
0.00359
Chelsea
Fulham
West Brom
0.144
$ 8.51
0.00056
Chelsea
Fulham
Draw
0.112
$ 11.53
0.00048
Chelsea
Fulham
Aston Villa
0.176
$ 9.33
0.00104
Chelsea
West Brom
Aston Villa
0.198
$ 8.14
0.00348
Chelsea
Draw
Aston Villa
0.154
$ 11.03
0.00298
Newcastle
Fulham
West Brom
0.126
$ 10.36
0.00095
Newcastle
Fulham
Draw
0.098
$ 14.03
0.00081
Newcastle
Fulham
Aston Villa
0.154
$ 11.36
0.00175
Newcastle
West Brom
Aston Villa
0.173
$ 9.91
0.00589
Newcastle
Draw
Aston Villa
0.135
$ 13.42
0.00506
Fulham
West Brom
Aston Villa
0.099
$ 17.36
0.00170
Fulham
Draw
Aston Villa
0.077
$ 23.51
0.00146
Chelsea
Newcastle
0.560
$ 2.03
0.00952
Chelsea
Fulham
0.320
$ 3.55
0.00274
Chelsea
West Brom
0.360
$ 3.10
0.00922
Chelsea
Draw
0.280
$ 4.19
0.00791
Chelsea
Aston Villa
0.440
$ 3.39
0.01709
Newcastle
Fulham
0.280
$ 4.32
0.00465
Newcastle
West Brom
0.315
$ 3.77
0.01562
Newcastle
Draw
0.245
$ 5.10
0.01341
Newcastle
Aston Villa
0.385
$ 4.13
0.02896
Fulham
West Brom
0.180
$ 6.60
0.00450
Fulham
Draw
0.140
$ 8.94
0.00387
Fulham
Aston Villa
0.220
$ 7.23
0.00835
West Brom
Aston Villa
0.248
$ 6.31
0.02804
Draw
Aston Villa
0.193
$ 8.55
0.02406
Chelsea
0.80
$ 1.29
0.04529
Newcastle
0.70
$ 1.57
0.07675
Fulham
0.40
$ 2.75
0.02213
West Brom
0.45
$ 2.40
0.07432
Draw
0.35
$ 3.25
0.06379
Aston Villa
0.55
$ 2.63
0.13776
Note: Five-way, four-way, three-way, and two-way accumulators plus single game bets were used. Sum of betting
fractions: 0.6348; expected logarithmic utility: 0.088038; total number of bets made: 47.

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betting on simultaneous events and accumulator gambles
367
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
Probability
0
0
0.5
1
1.5
Gross Return
2
2.5
figure 19.12 Distribution of gross returns from employing the optimal M strategy as shown in
table 19.4.
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
0.01
0
–0.2
–0.1
Probability
0
0.1
Gross Return Differential (Optimal M - Non-Accumulator)
0.2
0.3
figure 19.13 Distribution of gross return differential between optimal M and non-accumulator
betting strategies
typically accept only bets of a minimum size. The impact of non-divisibility of a bettor’s
capital on betting strategies is an area that requires further exploration. Consideration
should be given also to the number of bets that are required to implement a strategy,
whichisdiscussedinGrantandBuchen(2012). Foraﬁxed-stakegambler,productsexist
in many betting markets that place equal-sized bets on, say, a three-way accumulator
and the three corresponding two-way accumulators for a total of four equal-sized bets (a
Trixie). These products are known as“full cover” bets and are referred to by nicknames
related to the maximum-sized accumulator.2 These full cover bets do not include single-
game bets. An interesting project would be to see the relative improvement of the
single-game only strategy when augmented with full cover products to minimize the

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betting strategy
drawback of having to place a large number of bets to implement the optimal M
strategy.
Second, we have assumed that prices are ﬁxed for the bettor or that only a single
bookmaker is available for the different strategies. Bettors are restricted to the use of
a single bookmaker when employing accumulators but not with single-game outcome
bets. Hence the advantage of the optimal M strategy might be reduced for a savvy
bettor by shopping around for the best odds across a set of bookmakers. Grant and
Buchen (2012) compared the impact of a bettor using the optimal M strategy with
a single bookmaker and the non-accumulator strategy using the best odds across a
set of bookmakers. They found, using simulated results of English Premier League
matches, that a bettor who shops around and bets optimally without accumulators can
outperform a bettor who takes the average market odds (proxying for the odds offered
by a single large bookmaker), provided that the bettor’s probability edge is sufﬁcient.
A potential downside with shopping around increases the Kelly bettor’s stake size, and
thus there is an associated increase in risk.
Third, the strategies discussed herein (from both the bettor’s and the bookmaker’s
perspective) consider only simultaneous bets on the outcomes of independent games.
Bookmakers very occasionally offer correlated accumulator bets (such as betting on
point spreads and over-under totals in the same National Football League game), but
these are mainly for promotional purposes or on a limited number of outcomes. Bet365
offers the Scorecast product, which pays on the combination of a limited number of
correlated outcomes. For example, Tottenham to win 2–0 pays $6.50 and Jermain
Defoe as ﬁrst goal scorer pays $4.50; the Scorecast “combination” of these two events
pays $15.00.
It would be interesting to explore the implications of a bettor’s belief that game
outcomes were correlated to a different degree from that of the bookmaker. Thorp
(2000) discussed betting on simultaneous blackjack hands at the same table, which have
a correlation of approximately 0.5 (Grifﬁn 1999) but do not allow accumulators. As
one might expect, if outcomes exhibit positive correlation, Kelly bettors should reduce
their overall wager relative to the identical case without correlation. It is difﬁcult to
estimate correlations across multiple outcomes for non-casino games,and the provision
of markets would likely require more sophisticated modeling from the bookmaker’s
perspective than presently exists. Rainbow derivatives, which are usually call options
or put options on the best or worst of a set of assets, provide a useful starting analogy
from ﬁnance.
Finally, it would be useful to explore the use of simultaneous betting strategies
from the bookmaker’s perspective. Bookmakers ﬁnd themselves exposed to poten-
tially disastrous outcomes from bettors placing small wagers on large accumulators. It
would be interesting to analyze whether the additional proﬁts generated from offer-
ing accumulator bets exceed the costs of potentially large payouts. Given the strong
marketing of accumulator bets, it appears that the occasional large bookmaker payout
is more than made up for by the large number of small, unsuccessful bets made by
punters.

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369
Notes
1. The Financial Times (Thompson 2012) reported that the U.K. bookmaker Ladbrokes
blamed a series of victories in December for heavily backed Premier League teams, com-
bined in accumulator bets, for a 12.3 percent decline in annual proﬁts. Ladbrokes had
ironically advertised on their website the big win of a punter earlier that year (Kemp 2011).
2. These are known (in betting parlance)as Trixies (4 total bets, three-way accumulator max-
imum), Yankees (11 total bets, four-way maximum), Canadians (26 total bets, ﬁve-way
maximum), Heinz (57 total bets, six-way maximum), Super Heinz (120 total bets, seven-
way maximum), and Goliaths (247 total bets, eight-way accumulator maximum). Separate
products exist for a bettor to add the ﬁxed-stake bet on the single outcome to the full
cover bets (a patent, for example, is the same as the Trixie but with three single-game bets
included).
References
Ali, Mukhtar M. 1979. Some evidence on the efﬁciency of a speculative market. Econometrica
47(2):387–392.
Breiman, L. 1961. Optimal gambling systems for favorable games. Proceedings of the fourth
Berkeley Symposium of Probability and Statistics 1:65–78.
Golec, Joseph, and Maurry Tamarkin. 1998. Bettors love skewness, not risk, at the horse track.
Journal of Political Economy 106(1):205–225.
Grant, Andrew, and Peter W. Buchen. 2012.A comparison of simultaneous Kelly betting
strategies. Journal of Gambling Business and Economics 6(2):1–28.
Grant, Andrew, David Johnstone, and Oh Kang Kwon. 2008. Optimal betting strategies for
simultaneous games. Decision Analysis 5(1):10–18.
Grifﬁn, Peter A. 1999. The theory of blackjack: The compleat card counter’s guide to the casino
game of 21. 6th ed. Las Vegas, Nev.: Huntington.
Insley, Robin, Lucia Mok, and Tim Swartz. 2004. Issues related to sports gambling. Australian
& New Zealand Journal of Statistics 46(2):219–232.
Kelly, John L. (Jr) 1956. A new interpretation of information rate. Bell Systems Technical
Journal 35(4):917–926. http://en.wikipedia.org/wiki/John_Larry_Kelly,_Jr.
Kuypers, Tim. 2000. Information and efﬁciency: An empirical study of a ﬁxed odds betting
market. Applied Economics 32(11):1353–1363.
Maclean, Leonard C. William T. Ziemba, and George Blazenko 1992. Growth versus security
in dynamic investment analysis. Management Science 38(11):1562–1585.
Medo, Matus, Yury M. Pis’mak, and Yi-Cheng Zhang. 2008. Diversiﬁcation and limited
information in the Kelly game. Physica A 387:6151–6158.
Thompson, Christopher. 2012. Online proﬁts down at Ladbrokes. Financial Times, Feb 17;
http://www.ft.com/cms/s/0/af12bb14-58ab-11e1-9f28-00144feabdc0.html#axzz2SXCUu9Sj.
Thorp, Edward O. 2000. The Kelly criterion in blackjack sports betting, and the stock market.
In Finding the edge: Mathematical analysis of casino games, edited by Olaf Vancura, Judy A.
Cornelius, and William R. Eadington. Reno, Nev.: Institute for the Study of Gambling and
Commercial Gaming, 163–213.
Whitrow, Chris. 2007. Algorithms for optimal allocation of bets on many simultaneous events.
Journal of the Royal Statistical Society, Series C (Applied Statistics) 56(5):607–623.

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chapter 20
........................................................................................................
A PRIMER ON THE MATHEMATICS
OF GAMBLING
........................................................................................................
robert c. hannum
Introduction
.............................................................................................................................................................................
The mathematics underlying gambling can explain why, over time , one player wins
while another loses. In the context of commercial gaming, the “player” who wins is
typically the house—the operators of the casino, racetrack, card room, or lottery.
Simply put, commercial gaming enterprises make money because of the mathematics
behind the games. As many experienced gamblers have learned—for better or worse—
and some knowledgeable insiders have voiced, “There is no such thing as luck; it is all
mathematics.” This chapter presents the fundamental mathematics of gambling and
shows how the math behind the games generates revenues and drives the economics of
gambling.
Win Rate Metrics
.............................................................................................................................................................................
In the gambling business a variety of terms are used to refer to the rate at which a player
wins (or loses) money. These include
• house advantage,
• house edge,
• theoretical win percentage,
• expected win percentage,
• win percentage,
• hold percentage.

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Some of these win rate metrics refer to the same concept, but others are distinctly
different measures of win rate. The house advantage is (under the usual formulation)
the long-term percentage of money wagered that is retained by the house. The house
edge, theoretical win percentage, and expected win percentage are just different names
for the house advantage. Win percentage refers to the actual percentage of money
won during a ﬁnite gambling session or series of bets. In the short term the actual
win percentage will differ from the theoretical win percentage; the magnitude of this
deviation can be predicted from statistical theory. The win percentage is equal to the
observed win divided by the handle, the total amount wagered. Because of the law
of large numbers, the actual win percentage should get closer to the theoretical win
percentage as the number of trials gets larger: As n →∞, Win% →HA.
In the casino business handle can be difﬁcult to measure for table games (this may
well change when smart table/chip technology becomes cost-effective), and game per-
formance is often measured by hold percentage. Hold percentage is equal to win divided
by drop. Drop is the total amount of the currency and chips in the table’s drop box—a
locked box afﬁxed to the underside of the table—plus the value of credit instruments
issued or redeemed at the table.
For slot machines, where each bet is recorded, actual hold percentage and actual win
percentage are in principle equivalent, and the house advantage for a slot is sometimes
referred to as the theoretical hold percentage. For table games, however, hold percentage
is sometimes confused with house advantage and/or win percentage. To illustrate how
different these metrics are, consider that in Nevada in 2010 the hold percentage for
roulette was about 17 percent, whereas the house advantage is about 5 percent. Similar
large differences between hold percentage and house advantage exist for other games.
Nevada’s hold percentages in 2010 for blackjack, baccarat, three-card poker, Caribbean
stud, and let it ride were 11 percent, 11 percent, 28 percent, 26 percent, and 23 percent,
respectively, compared to house advantages of roughly 1 percent for blackjack and
baccarat and 3–5 percent for the latter three games. It would be a mistake to think that
the house wins more than 10 percent of all monies wagered at any of these games.
In summary, house advantage, house edge, theoretical win percentage, and expected
win percentage are different names for the same metric. Hold percentage is win divided
by drop; (actual) win percentage is win divided by handle. Win percentage approaches
the house advantage as the number of plays increases.
House Advantage—A Caveat
The house advantage can be subject to varying formulations and interpretations. In the
table game let it ride, for example, the casino advantage can be expressed as 3.51 percent
of the base bet or 2.86 percent of the average bet. Those familiar with the game know
that the player begins with three equal base bets but may withdraw one or two of
these initial units. The ﬁnal amount put at risk, then, can be one (84.6% of the time
assuming proper strategy), two (8.5%), or three units (6.9%), making the average bet

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betting strategy
size 1.224 units. In the long run the casino will win 3.51 percent of the hands, which
equates to 2.86 percent of the money wagered. So it is correct to say that the house
edge is 3.51 percent per hand; it is also correct that it is 2.86 percent per unit wagered.
Regardless, the bottom line is that with three $1 base bets, the casino can expect to earn
3.5c per hand (1.224 × 0.0286 = 0.035). The question of whether to express the house
advantage relative to a base bet or average bet also arises in the casino games Caribbean
stud poker (5.22% vs. 2.56%), three-card poker (3.37% vs. 2.01%), casino war (2.88%
vs. 2.68%), and red dog (2.80% vs. 2.37%).
Another situation that admits varying formulations of the house advantage is a bet
that can result in a tie. For such bets the house edge can be stated either including
or excluding ties. Examples include baccarat’s player bet (1.24% if ties are included vs.
1.37% if ties are excluded), banker bet (1.06% vs. 1.17%), and the don’t pass bet (1.36%
vs. 1.40%) in craps. Again, regardless of which view is taken, proper interpretation leads
to the same expected revenue in dollars and cents.
The Basic Mathematics of Gambling
.............................................................................................................................................................................
The language of gambling math revolves around such terms as probability, odds, expec-
tation, house advantage, and volatility. This section presents an overview of these
terms.
Probability and Odds
Probability is a number between zero and one that represents the relative likelihood
that an event will occur. The closer the probability is to one, the more likely the event
is to occur—an event with a probability of one is certain to occur; the closer to zero,
the less likely it is to occur—if the probability is zero, it is impossible for the event to
occur. A probability of one-half, or 50 percent, means that the event in question is just
as likely to occur as not occur. Probability can be viewed as the long-run ratio of {# of
times an outcome occurs}to {# of times experiment is conducted}. The odds against an
event represent the long-run ratio of {# of times an outcome does not occur}to {# of
times an outcome occurs}. For example, the probability of rolling a seven with a pair
of honest dice is 1/6 and the odds against are 5 to 1. If one card is randomly selected
from a standard deck of 52 playing cards, the probability that it is a diamond is 1/4 and
the odds against it being a diamond are 3 to 1; the probability that it is an ace is 1/13
and the odds against it being an ace are 12 to 1.
The odds against an event represent the payoff that would make a bet on that event
fair. A bet on black in single-zero roulette has a probability of winning equal to 18/37,
so the payoff necessary to make it a fair bet is 19 to 18 (the actual payoff is 18 to 18);

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373
for the same game a bet on a single number has a probability of winning equal to 1/37,
so to break even in the long run a player winning this bet would need to be paid 36 to
1 (the actual payoff is 35 to 1).
Laws of Probability
The three major laws of probability are the Complement Law, the Addition Law, and
the Multiplication Law.
Complement Law: The probability of an event not occurring is equal to one minus
the probability of that event occurring.
Addition Law: The probability of at least one of two events occurring equals the sum
of their individual probabilities, minus the probability they both occur.
Multiplication Law (independent events): For independent events, the probability of
all of them occurring equals the product of their individual probabilities. (Events are
independent if the occurrence of one has no effect on the probability of the occurrence
of the others.)
Multiplication Law (dependent events): For nonindependent events, the probability
of all of them occurring equals the product of their conditional probabilities, where the
conditional probability of one event is affected by the event(s) that came before it.
Examples illustrating the use of these basic probability laws are given below.
Complement Law: When selecting a card at random from a standard deck of playing
cards, the probability it is a spade is 13/52 or .25. The probability it is not a spade is
(1 –.25) = .75.
Addition Law: When a single card is randomly selected from a deck, the probability
it is an ace or a spade is (4/52 + 13/52 −1/52) = 16/52 or .308. When rolling a pair
of dice, the probability of getting a total of 7 or 11 is (6/36 + 2/36) = 8/36, and the
probability of rolling a 2, 3, or 12 is (1/36 + 2/36 + 1/36) = 4/36.
Multiplication Law (independent events): If you ﬂip a coin two times, whether you ﬂip
heads or tails on the ﬁrst ﬂip has no inﬂuence on whether you will ﬂip heads or tails on
the second ﬂip. The two ﬂips of the coin are independent events. Thus the probability
of two heads in two tosses is (1/2) × (1/2) = 1/4. Similarly, the probability of getting
ﬁve heads in ﬁve tosses of a fair coin is (1/2)5 = 1/32 or about .031. The probability
of getting ﬁve consecutive 12’s in ﬁve tosses of a pair of dice is (1/36)5 = .000000017
or about 1 in 60,466,176. The probability of 10 consecutive red numbers in 10 spins of
a roulette wheel is (18/38)10 = .0005687 or about 1 in 1,758. The calculations in these
examples are valid because the events involved are independent trials. The outcome on
any given trial has no effect on the outcome of any other trial.
Multiplication Law (dependent events):
If three cards are randomly selected
(without replacement) from a standard deck, the probability all three are aces is
(4/52)(3/51)(2/50) or .000181 (1 in 5,525). Notice that the trials here are not
independent since the outcome of the ﬁrst draw will affect the outcome on the second,
and the outcome of the second will affect the outcome on the third.

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betting strategy
The latter examples highlight a key difference between games like roulette and craps
and the game of blackjack. Roulette and craps involve independent trials, whereas
blackjack involves dependent trials. In roulette and craps the probabilities remain the
same from trial to trial (it matters not if there are 10 consecutive red numbers; the
probability of red is still 18/38 on the 11th trial). In blackjack the trials are dependent
since the composition of the cards remaining to be played depends on which cards
have already been played. It is this feature, dependent trials, which causes the advantage
in blackjack to ﬂow back and forth between the house and the player and why “card-
counting” can be effective in blackjack.
Mathematical Expectation
The amount of money a player can expect to win or lose in the long run on a given
wager at a given bet size—if the same bet is made over and over again—is called the
wager expectation or expected value (EV ). When the EV for a bet is negative, the player
will lose money over time on this bet.
The general formula for the expectation, or EV, of a bet, is
EV =

(Wini × pi),
(20.1)
where Wini is the net win associated with outcome i and pi is the probability of Wini.
The EV for a bet represents the amount of money the bettor will win or lose on average
(in the long run) from making the speciﬁed bet.
For example, a $5 bet on the color red in double-zero roulette (38 total numbers, of
which 18 are red, 18 are black, and 2—the 0 and 00—are green) has a probability of
winning equal to 18/38, a probability of losing equal to 20/38, and pays even money if
won. The wager expectation is
EV = (+5)(18/38) + (−5)(20/38) = −0.263.
On the average the player will lose just over $0.26 for each $5 bet on red.
House Advantage
As Nicholas Pileggi phrased it in his novel Casino (1995), “A casino is a mathematics
palace set up to separate players from their money. Every bet made in a casino has been
calibrated within a fraction of its life to maximize proﬁt while still giving the players
the illusion that they have a chance.” The fundamental reason that casino games make
money is the house advantage, a mathematical edge built into virtually every bet in the
casino. This house edge, coupled with the famous mathematical result called the law of
large numbers, virtually guarantees that the casino will win in the long run.

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The house advantage (HA) is the negative of the expected value of the bet, expressed
as a percentage of the amount bet
HA = −EV
Bet × 100%.
(20.2)
Note that if the EV calculation in (20.1) is performed for a one-unit amount, the
negative of the resulting value is the house edge, expressed as a decimal. For example,
for a one-unit bet on a single number (payoff equal to 35 to 1) in double-zero roulette
EV = (+35)(1/38) + (−1)(37/38) = −0.053.
Thus the house advantage is 5.3 percent.
The house advantage, or house edge, represents the long-run percentage of the
wagered money that will be retained by the house. In economics terms, the house
advantage is the price to the player for playing the game. Although the house edge
can be computed easily for some games—for example, roulette and craps—for others
it requires more sophisticated mathematical analysis and/or computer simulations.
Table 20.1 shows typical prices for some popular casino games.
Because this positive house edge exists for virtually all bets in a casino, in these
commercial gambling halls players are faced with an uphill and, in the long run, losing
battle. There are some exceptions, however. The odds bet in craps has zero house
edge (although this bet cannot be made without making another negative expectation
wager); a select few video poker machines return greater than 100 percent if played
with optimal strategy, and skilled blackjack card counters, poker players, and sports
bettors can make money playing their games. But these are small groups—very few
Table 20.1 Typical Prices for Popular Casino Games
Game
House Advantage
Roulette (double-zero)
5.3%
Craps (pass/come)
1.4%
Craps (pass/come with double odds)
0.6%
Blackjack∗(6 decks)
0.5%
Blackjack—average player
2.0%
Baccarat (no tie bets)
1.2%
Caribbean Stud∗
5.2%
Let It Ride∗
3.5%
Three-Card Poker∗
3.4%
Pai Gow Poker (ante/play)∗
2.5%
Slots
5% – 10%
Video Poker∗
0.5% – 3%
Keno (average)
27.0%
∗optimal strategy

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betting strategy
have what it takes to win money in the long run at any of these games. Occasionally the
casino will offer a promotion that gives the astute player a positive expectation. These
promotions are often mistakes—sometimes casinos fail to check the math—and are
terminated once the casino realizes the player has the edge. But by and large the player
will lose money in the long run, and the house edge is a measure of how fast the money
will be lost.
Gambling Economics
.............................................................................................................................................................................
In the gambling business the standard revenue-price-quantity economics relationship,
R = p × q, becomes
Expected Win = HA × handle.
(20.3)
The left side of expression (20.3) is “Expected Win” rather than “Win” because of the
statistical nature of the gambling business. While the house advantage (HA) will be
realized in the long run, the actual win is subject to statistical ﬂuctuations, and in
the short term the win percentage may differ from the house advantage. The size of
these ﬂuctuations can be predicted using statistical theory. The subject of volatility is
discussed in more detail below.
Game Pricing
Unlike most other consumer purchases where the price of a product is ﬁxed, the price
of a gambling game depends on the speciﬁc rules of the game, the payoffs for winning
wagers, the amount of time the player plays, and possibly the skill of the player. In
large part, then, pricing in the gaming business is made by conscious or unintentional
decisions on setting the house advantage (informally,“setting the odds”) for the games.
This can be done through rule variations that are more or less favorable to the player,
by altering payoffs, or by offering a different type of game product.
Rule Variations
Rule variations can affect the house advantage in all games. Two of the more notable
in which casinos vary the rules most often are blackjack and craps. In some blackjack
games, the dealer must hit a soft seventeen (a soft hand is one that includes an ace
that is being counted as 11), which increases the house advantage 0.2 percent over
a comparable game where the dealer stands on soft seventeen. Other examples of
rule variations in blackjack that are house-favorable include multiple decks, no soft

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doubling, no re-splitting of pairs, and naturals paying 6 to 5 (usually 3 to 2). Player-
favorable blackjack rule variations include double down after splitting pairs, late and
early surrender, and re-splitting aces.
In craps the amount of “free odds”that can be taken by a player will change the price
of the game product. A player who bets the pass line and takes single odds (i.e., the
amount of the odds bet is equal to the amount of the pass line bet) is at a 0.85 percent
disadvantage but only at 0.61 percent with double odds and 0.47 percent with triple
odds. This means that for every $100 combined bet on the pass line with single odds
(i.e., $50 pass line plus $50 odds) the player, on average, will pay a price of about $0.85,
while a $100 combined bet on the pass line with triple odds ($25 pass line plus $75
odds) will cost about $0.47. A casino allowing triple odds offers a better priced craps
game than one that permits only single odds. Some casinos have offered as high as 100X
odds—a player taking full 100X odds will face only a 0.02 percent house advantage on
the combined pass line (or come) plus odds wagers.
Altering Payoffs
Another way to set prices on games is to alter the payoffs. The ﬁeld bet in craps, for
example, typically offers even money on the 3, 4, 9, 10, and 11, and a 2 to 1 payoff for
the 2 and 12. The house advantage for this payoff structure is 5.56 percent. If either the
2 or the 12 (but not both) were to pay triple, the house advantage would be reduced
to 2.78 percent. If both the 2 and the 12 pay 3 to 1, the ﬁeld bet is “free”—the house
advantage is equal to zero.
In baccarat, the usual casino commission on winning banker bets is 5 percent. Some
casinos attempt to attract and keep players by lowering this commission to 4 percent
or even 3 percent (setting the commission at only 2% would give the player the advan-
tage). Such a reduction is equivalent to raising the payoff on this bet from 95 to 96
or 97 percent, with the effect of reducing the house advantage from the usual 1.06 to
0.60 percent (with the 4% fee) or 0.14 percent (3% fee).
Keno and video poker are other examples where payoffs can be easily manipulated to
raise or lower the price of the game. Payoffs for various keno wagers vary widely across
casinos. A full-pay Jacks-or-Better video poker machine pays 9 for 1 and 6 for 1 for a full
house and ﬂush, respectively (hence the moniker “9/6” in reference to this game), but
machines paying only 8 for 1 and 5 for 1 for these hands (“8/5”machines) are common.
The former returns 99.54 percent with perfect play while the maximum payback on the
latter is 97.29 percent. Some casinos have offered a version of Jacks-or-Better with a 7 for
1 payoff on ﬂushes, giving the player a greater than 100 percent return with perfect play.
Offering a Different Game Product
Introducing new games, or variations on standard games, is a way to diversify both
the product mix and the range of prices offered. Games like Double Exposure and
Spanish 21 are just twists on blackjack, and three-card poker, let it ride, and Caribbean
stud are variations on poker. These differing game products offer players a wide variety

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of prices to pay for their gaming experience. Single-zero roulette costs the player about
$0.27 for every $10 wagered compared to the double-zero wheel with a price of $0.53
per $10 bet.
Other Factors Affecting Game Prices
For games with a skill component, the effective house advantage depends on the skill
level of the player. In a typical six-deck blackjack game, for example, the average player
gives about a 1.5 percent edge to the house while a perfect basic strategy player is at
a 0.5 percent disadvantage. Game speed (number of decisions per hour) affects the
cost per hour to the player, though it does not alter the base price per unit wagered.
In roulette, for example, a $20-per-spin player betting at a double-zero table making
40 spins per hour can expect to pay about $42 per hour ($20 × 40 × .0526). At a table
completing 60 spins each hour the same player would spend an average of $63 per hour.
Similarly, at a base price of 1.15 percent, a $1,000-per-hand baccarat player will pay, on
average, about $920 per hour if playing 80 hands per hour, but it will cost this same
player $1,380 per hour if dealt 120 hands per hour.
Pricing Gaffes
Commercial gaming establishments occasionally offer novel wagers, side bets, increased
payoffs, or rule variations in an effort to entice players and increase business. These
promotions are intended to lower the house advantage and the effective price of the
game for the player. While this might be sound reasoning from a marketing standpoint,
it can have negative consequences for the gaming business enterprise if care is not taken
to ensure that the math behind the promotion is sound.
An Illinois riverboat casino reportedly lost $200,000 in one day with a “2 to 1
Tuesdays” promotion that paid players 2 to 1 on blackjack naturals (the usual pay-
off is 3 to 2). Without other compensating rule changes, a 2-to-1 payoff on naturals
in a typical blackjack game can increase the players’ expectation enough to give them
a 1.5 to 2 percent advantage over the house. Other casinos also fell victim to this faux
pas, and one casino in California went so far as to pay out 3 to 1 on naturals during a
“happy hour” offered three times a day, two days a week, for over two weeks, giving the
player a healthy 6 percent edge.
A casino in Mississippi ran a promotion in which it offered 80 to 1 payoffs instead
of the usual 60 to 1 for bets on (a total of) 4 and 17 in sic bo, a game in which players
bet on the outcome of the roll of three dice. The effect of this change on the player’s
expectation is easy to determine. Since the probability of rolling a total of 4 (or 17) with
three dice is 1/72(1/6×1/6×1/6×3), the expected values of this bet under the usual
and the promotional payoffs are, respectively,
EV = (+60)(1/72) + (−1)(71/72) = −0.153

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and
EV = (+80)(1/72) + (−1)(71/72) = +0.125.
The increase in payout changed the advantage from 15.3 percent in favor of the house
to 12.5 percent in favor of the player. With this advantage, a player betting $100 per
hand at 50 hands per hour can expect to win $625 per hour; a $500 per hand bettor
would win an average of $3,125 per hour.
In still other examples of pricing blunders in the gambling business:
• A major Las Vegas casino suffered a $230,000 loss in three-and-a-half days on a
“50/50 Split”blackjack side bet that allowed the player to stand on an initial holding
of 12–16 and begin a new hand for equal stakes against the same dealer up card.
Although the game marketers claimed the variation was to the advantage of the
casino, it turned out that those players who exercised the 50/50 Split only against
a dealer’s 2–6 enjoyed a 2 percent advantage.
• A small Las Vegas casino lost an estimated $17,000 in eight hours when it offered
a blackjack rule variation called the “Free Ride” in which players were given a free
right-to-surrender token every time they received a natural—proper use of the
token led to a player edge of 1.3 percent.
• Another casino reduced the commission on winning baccarat banker bets from 5
to 2 percent, resulting in a 0.32 percent player advantage.
The pricing mistakes above serve to highlight how important it is to be vigilant when
altering payoffs or varying rules to offer a more or less attractive game. Payoffs that
are too large or rules that are too player-favorable could give the players an advan-
tage and cost the house dearly. On the other hand, if payoffs are too low or rules too
house-friendly, sales volume may suffer because players will not want to play. A proper
mathematical analysis is needed on all proposed side bets, payoff changes, rules vari-
ations, and marketing promotions to ensure that the economics of the game is both
attractive to players and acceptable to the house.
Price and Product Demand
In most businesses, if an operator lowers the price of goods or services the volume
of sales will increase, provided that the operator’s competitors also do not lower their
prices. A commercial gaming establishment may consider lowering the price (house
advantage) to the player to increase the volume of play. In some cases the motivation for
this may be to keep the tables full—the gaming operators may see idle tables and come
to the conclusion that they would be better off ﬁlling the empty tables at worse odds
since they are already paying for the dealers and other game supervisors. Ultimately the
gaming establishment needs to consider the impacts of lowering the price on operating
proﬁts. Unfortunately this is not a simple question—whether the reduced price will

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result in sufﬁciently increased volume of play is often unknown. That is, it is difﬁcult
for gaming establishments to accurately estimate price elasticities of demand.
Player Value
The most valuable assets to a commercial gaming establishment are its players—the
player base is the economic engine that drives revenues. An important problem for
management is to determine the value of each player. Assessing a player’s value to the
gambling establishment allows it to develop typical player proﬁles and decide game
mixes that appeal to its players. Player value is also necessary for effective marketing
programs such as complimentaries, rebates on theoretical loss, discounts on actual loss,
and dead chip programs that attempt to attract and retain players.
Player value is simply how much the gambling establishment can expect to win from
that player. It is often called earning potential, player worth, or theoretical win. Player
value can be computed using the house advantage (HA), bet size, duration of play, and
pace of the game as follows:
Player Value = Average Bet × Hours Played × Decisions per Hour × HA.
For example, suppose a roulette player bets $25 per spin for four hours at 50 spins per
hour. Using a house advantage of 5.3 percent (double-zero roulette), this player would
be expected to lose, and would be rated at a player value of, $265(25 × 4 × 50 × .053).
If this player were betting $100 per spin for 12 hours, the player value rating would be
$3,180.
Complimentaries, or simply “comps,” can include anything from free drinks to pay-
ment of every conceivable expense, including room, food, and beverage (RFB) and
airfare. A typical comp policy is to award a player with comps equal to a set percentage
of the player’s earning potential. Rebates and discounts are similar to comps but offer
a monetary return rather than a meal or a hotel room in exchange for a certain level
of play.
Risk and Volatility
.............................................................................................................................................................................
The risk associated with a gamble is due to the uncertainty of the outcome. Although
the house advantage can be used to predict the amount that will be won (or lost) in
the long run, in the short term the actual win will deviate from the expected win. How
much variation from the theoretical win can be expected? What might be considered a
normal ﬂuctuation and what is considered unusual? The magnitude of the difference
between actual and theoretical wins for a given number of wagers can be predicted using
statistical theory. The basis for such a volatility analysis is the standard deviation. This

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statistical measure of variation is, roughly speaking, the average deviation of all possible
outcomes from the expected. Together with the central limit theorem—one of the most
important results in statistics—the standard deviation can provide conﬁdence limits
on the amount a player should win or lose over a series of wagers. The mathematical
formulation of the standard deviation (SD) of a bet is
SD =
&
[(Wini −EV )2 × pi]
(20.4)
where Wini is the net win associated with outcome i, EV is the expected value of the
bet given by (20.1), and pi is the probability of Wini.
As an example, consider a $5 bet on a single number in double-zero roulette. With a
payoff of 35 to 1 the base expected value and standard deviation of this bet are
EV = (+175)(1/38) + (−5)(37/38) = −0.263;
SD =

(175 −(−0.263))2(1/38) + (−5 −(−0.263))2(37/38) = 28.813.
The single-number bet has the greatest volatility in roulette. Analogous calculations for
a $5 bet on red, for example, yield a bet standard deviation of 4.993 (the bet EV is the
same –0.263 as the single-number bet).
Conﬁdence Limits
While expressions (20.1) and (20.4) can be used to calculate the base EV and SD of a
bet, it is the expected value and standard deviation of a series of n bets that are needed
to obtain conﬁdence limits for the amount won over a series of wagers. For a series of n
identical, independent bets of one unit each, the expected value and standard deviation
of the total number of units won are given by
EV (units won) = n × EV ;
(20.5)
SD(units won) = √n × SD,
(20.6)
where EV and SD are the bet expected value and bet standard deviation given by (20.1)
and (20.4), respectively.
Assuming n is large, the central limit theorem guarantees that the distribution of the
observed units won in the n trials will be approximately normal with mean and standard
deviation equal to (20.5) and (20.6), respectively. Thus standard normal distribution
theory can be invoked to obtain upper and lower limits for the actual number of units
won for any desired level of conﬁdence. The following example illustrates how this is
done.

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betting strategy
Consider a series of 1,000 one-unit bets on a single number—payoff equal to 35 to
1—in double-zero roulette. The bet expected value and bet standard deviation from
(20.1) and (20.4) are –0.05263 and 5.76262, respectively. From (20.5) and (20.6), then,
the expected value and standard deviation of the number of units won in a series of
1,000 bets are
EV (units won) = 1,000 × −0.05263 = −52.63;
(20.7)
SD(units won) =
√
1,000 × 5.76262 = 182.23.
(20.8)
Using (20.7), (20.8), and the appropriate standard normal probability value (z) for the
desired level of conﬁdence, limits for the number of units won in the series of 1,000
bets can be derived. The z value can be obtained from a table of standard normal
probabilities or a software package, such as MS Excel. For example, the z value for
95 percent conﬁdence is 1.96, so the 95 percent conﬁdence limits for the number of
units won are
−52.63 ± 1.96(182.23) = −409.8 and 304.5.
(20.9)
The interpretation of (20.9) is that in a series of 1,000 independent single-number
(double-zero) roulette bets of one unit each, 95percent of the time the player win will
be between −409.8 and +304.5 units.
It is easy to convert limits for the number of units won to limits for the amount
of money won or the win percentage. If the bets in the above roulette example were
$5 each, the 95 percent limits for the amount of money won in the series would be
−$2,049 and +$1,523 (obtained by merely multiplying the limits in (20.9) by $5), and
the 95 percent limits for the win percentage would be −41.0 percent and 30.5 percent
(dividing the limits in (20.9) by 1,000).
Appropriately modifying the z value will produce limits for other desired levels of
conﬁdence. For example, using z = 2.58 for the above series of $5 single-number
roulette bets produces 99 percent conﬁdence limits for number of units won, amount
of money won, and win percentage: −522.8 and 417.5, −$2,614 and $2,088, and
−52.3 percent and 41.8 percent, respectively.
Note that the conﬁdence limits for the win percentage will converge to the house
advantage as the number of bets increases. This is the result of the law of large
numbers—as the number of trials gets larger the actual win percentage should get
closer to the theoretical win percentage.
Volatility Benchmarks
An easy rule of thumb set of benchmarks for volatility can be fashioned around the
percentages of times an outcome will be more than a various number of standard
deviations (SDs) from the expected outcome.

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Volatility Benchmarks
• Outcomes will be more than 2 SDs from the expected about 5 percent of the time.
• Outcomes will be more than 3 SDs from the expected about 0.3 percent of the
time.
• Outcomes will be more than 4 SDs from the expected about 0.006 percent of the
time.
• Outcomes will be more than 5 SDs from the expected about 0.00006 percent of the
time.
For the number of units won in the series of 1,000 one-unit bets on a single number in
double-zero roulette considered above, the volatility benchmarks translate to
• About 5 percent of the time the player will either win more than 312 units or lose
more than 417 units.
• About 0.3 percent of the time the player will either win more than 494 units or lose
more than 599 units.
• About 0.006 percent of the time the player will either win more than 676 units or
lose more than 782 units.
• About 0.00006 percent of the time the player will either win more than 859 units
or lose more than 964 units.
One-Sided Limits and Benchmarks
The conﬁdence limits and volatility benchmarks described above are two-sided, pro-
viding probabilities that an observed win will deviate from the expected win by more
or less than a certain amount in either direction. If one is concerned with a deviation in
only one direction, one-sided limits and benchmarks are appropriate. This would be
the case, for example, when a player in a commercial gaming establishment wins what
appears to be an unusually large amount and management is interested in the odds of
such a large win, assuming an honest game.
For the roulette example considered above—a series of 1,000 bets of $5 each on
a single number in double-zero roulette—one can say that 95 percent of the time
the player win should be no more than 248.0 units or $1,240. These values are the
95th percentiles of their respective distributions, obtained by using z = 1.65, the 95th
percentile of the standard normal distribution. (Note that from the two-sided, 95%
conﬁdence limits one can say there is a 97.5% chance that the player win will be no
more than 304.5 units or $1,523.)
Volatility benchmarks are easily modiﬁed to one-sided
• Outcomes will be more than 2 SDs above the expected about 2.5 percent of the
time.

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betting strategy
• Outcomes will be more than 3 SDs above the expected about 0.15 percent of the
time.
• Outcomes will be more than 4 SDs above the expected about 0.003 percent of the
time.
• Outcomes will be more than 5 SDs above the expected about 0.00003 percent of
the time.
One-sided benchmarks for outcomes more than a certain number of standard devia-
tions below the expected are analogous to those above, replacing the word“above”with
“below.”
Likelihood of an Observed Win
Although conﬁdence limits and benchmarks provide useful tools for analyzing risk and
volatility, it often is helpful to compute the likelihood of a particular observed win. This
can be accomplished by calculating the z score associated with the observed win and
then ﬁnding the relevant probability referring to a standard normal probability table
(Z table). The observed z score is calculated as follows:
z = Observed Win −Expected Win
SD(Win)
.
(20.10)
TheExpectedWin andSD(Win)in(20.10)aretheexpectedvalueandstandarddeviation
of the series win, measured in the same units as the Observed Win (units, dollars, or
percent). For example, suppose after a series of 1,000 bets of $5 each on a single number
in double-zero roulette a player has won $3,000. What are the chances of this happening
(assuming an honest game)? From (20.7) and (20.8), the expected value and standard
deviation of the number of units won are −52.63 and 182.23, respectively, or −$263.16
and $911.15. Thus, the z score associated with the observed $3,000 win is
z = $3,000 −(−$263.16)
$911.15
= 3.58.
This means that the player’s $3,000 win was 3.58 standard deviations more than what
was expected. A lookup in a standard normal probability table shows the likelihood of
such a win or greater to be .00017 or about 1 in 5,851. Had this player won $5,000, the
odds against such a win or greater would be about 1 in 262 million (probability equal
to .0000000038).
Note that had the player in the above example been making bets on red rather than a
single number, a $3,000 win or more would have been practically impossible (z = 20.67)
due to the much smaller volatility associated with a bet on red—the SD = 4.993 for a
$5 bet on red versus SD = 28.813 for a $5 bet on a single number.

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A Final Example
Consider a series of 1,000 pass line wagers in craps. It can be shown from (20.1) and
(20.4) that the expected value and standard deviation of a single pass line bet are
EV = −0.014 and SD = 1.000, respectively. For a series of 1,000 pass line wagers, then,
from (20.5) and (20.6)
EV (units won) = 1,000 × −0.014 = −14.0;
SD(units won) =
√
1,000 × 1.000 = 31.6.
The expected value results mean that the house advantage for a pass line bet is 1.4 per-
cent and after 1,000 bets on average the player will be behind by 14 units. Applying
the two-sided volatility benchmarks, there is roughly a 95 percent chance that the
player’s actual win will be between 49 units ahead and 77 units behind and about
a 0.15 percent chance that the player win will be between 81 units ahead and 109
units behind. If each of the 1,000 bets was $50, the player would be expected to
lose $700, with two and three standard deviations benchmark limits of –$3,860 and
+$2,460 and –$5,440 and $4,040, respectively. That is, approximately 5 percent of
the time the player will either win more than $2,460 or lose more than $3,860, and
about 99.85 percent of the time the player will either win more than $4,040 or lose
more than $5,440. If, for example, the player actually won $10,000, management
might want to scrutinize this player and game more closely, as such a win would rep-
resent an event with one-sided odds of 157.6 billion to 1 (z = 6.77), assuming an
honest game.
Additional Sources
Ethier (2010) provides the most comprehensive coverage of the mathematics of gam-
bling; a more practical, somewhat less mathematical treatment can be found in
Hannum and Cabot (2005). Other general references on the mathematics of gam-
bling include Epstein (2009), Grifﬁn (1991), Packel (1981), and Thorp (1984).
David (1998) gives an excellent historical perspective on the subject. Two volumes
produced by the University of Nevada at Reno’s Institute for the Study of Gam-
bling and Commercial Gaming, Ethier and Eadington, eds. (2007) and Vancura,
Cornelius, and Eadington, eds. (2000), contain scholarly research articles on the
subject. Kilby, Fox, and Lucas (2005) cover casino operations management issues
related to the mathematics of gambling; Cabot and Hannum (2002) explore the
relationship between gaming regulation and mathematics. Two classic and excel-
lent books on probability theory more generally are Feller (1968) and Weaver
(1982).

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Summary
.............................................................................................................................................................................
Mathematics lies at the heart of the gambling business. It helps us understand how
a commercial gaming establishment generates a proﬁt and why players usually lose,
in the long run. A familiarity with probability is necessary in order to understand
the principles of gambling mathematics, principles that include such gambling theory
fundamentals as mathematical expectation, house advantage, and volatility. From these
topics ﬂow a plethora of related economics issues, such as game pricing, player value,
and risk assessment and management. From the assurance of revenues due to the game
advantage to the earning potential of players and the risk inherent in making a bet,
mathematics is the key to the economics of gambling.
References
Cabot, Anthony N., and Robert C. Hannum. 2002. Gaming regulation and mathematics: A
marriage of necessity. John Marshall Law Review 35:333–358.
David, F. N. 1998. Games, gods, and gambling: A history of probability and statistical ideas.
Mineola, N.Y.: Dover Publications.
Epstein, Richard A. 2009. The theory of gambling and statistical logic. 2nd ed. Burlington,
Mass.: Elsevier.
Ethier, Stewart N. 2010. The doctrine of chances: Probabilistic aspects of gambling. Berlin:
Springer-Verlag.
Ethier, Stewart N., and William R. Eadington, eds. 2007. Optimal play: Mathematical studies of
games and gambling. Reno: Institute for the Study of Gambling and Commercial Gaming,
University of Nevada.
Feller, William. 1968. An introduction to probability theory and its applications. 3rd ed. New
York: Wiley.
Grifﬁn, Peter. 1991. Extra stuff: Gambling ramblings. Las Vegas, Nev.: Huntington Press.
Hannum, Robert C., and Anthony N. Cabot. 2005. Practical casino math. 2nd ed. Reno:
Institute for the Study of Gambling and Commercial Gaming, University of Nevada.
Kilby, Jim, Jim Fox, and Anthony F. Lucas. 2005. Casino operations management. 2nd ed. New
York: Wiley.
Packel, Edward. 1981. The mathematics of games and gambling. Washington, D.C.:
Mathematical Association of America.
Thorp, Edward O. 1984. The mathematics of gambling. Hollywood, Calif.: Gambling Times.
Vancura, Olaf, Judy A. Cornelius, and William R. Eadington, eds. 2000. Finding the edge:
Mathematical analysis of casino games. Reno: Institute for the Study of Gambling and
Commercial Gaming, University of Nevada.
Weaver, Warren. 1982. Lady luck: The theory of probability. New York: Dover Publications.

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chapter 21
........................................................................................................
THE SCIENCE AND ECONOMICS
OF POKER
........................................................................................................
robert c. hannum
Introduction
.............................................................................................................................................................................
Although poker has roots in card games played in Europe and the Middle East as
far back as the ﬁfteenth century, the modern game of poker originated in the early
nineteenth century in the gambling saloons of New Orleans. It has long been the
most popular card game among Americans and recently has reached unprecedented
popularity due to a variety of factors, including television and Internet exposure. Poker
is somewhat unique among gambling activities due to the fact that it is not house
banked and because of the considerable elements of skill required and not present
in other casino-style and lottery-type games. Those interested in the history of card
games generally may wish to consult Parlett (1991). For more on the history of poker
in particular see McManus (2009) and Parlett (2005).
Unlike such games as roulette or blackjack, poker is a player-versus-player game—
the house does not wager against its players. Instead of making money through the
house edge present in house-banked casino games, poker typically generates revenues
for the card room operating the game through a mechanism called the rake, a scaled
commission fee taken by the card room operators. Generally the rake is 5 to 10 percent
of the pot in each poker hand, up to a predetermined maximum amount, but there are
also other non-percentage ways for a card room to collect a rake, such as charging an
hourly fee or collecting a ﬂat amount for every hand.
Since there is a large element of skill in poker—most experienced players would
attest to this, and there is also a growing body of scientiﬁc evidence that supports this
notion—and players are competing against each other and not the house, poker can
be a positive expectation game for players who are skilled. Good poker players can
win money over time, and the game attracts professional and semiprofessional players.

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For most casino games—roulette, craps, baccarat, and keno—it is not mathematically
possible to win in the long run. Blackjack and some video poker machines offer the
opportunity for a slight player edge—one to two percent—and a few players can make
money at these games with perfect play (and counting cards in the case of blackjack).
It is not easy, however, and the earnings are small. Skill does play a part in these games,
but luck is a large factor. In card room poker, skill is a much greater factor, and the
better players will win out over the weaker players in the long run. Few people earn a
living or make money consistently playing casino games, but the majority of those who
do are poker players.
Because players in a poker game compete against each other and not the house,
money won or lost is merely transferred from one player to another. The basic prin-
ciples of gambling math still apply, however, and are at the core of the science and
economics of poker, albeit intertwined with other signiﬁcant elements of skill neces-
sary for success. The sections that follow examine the various facets of the science and
economics behind poker.
Types of Poker
.............................................................................................................................................................................
Poker is a vying game played with standard playing cards where players bet as to who
holds the best card combination by progressively raising the stakes until either there is
a showdown, when the best hand wins all the stakes (“the pot”), or all but one player
has given up betting and dropped out of play. In the latter case, the last person to raise
the bet wins the pot without a showdown.
The game of poker can be played almost anywhere and in many different forms.
Poker is really a generic name for a collection of literally hundreds of games, varying
widely with respect to speciﬁc rules of play and betting structure. The variations include
high games (the highest hand wins), low games (lowest hand wins), high-low split, ﬁxed
limit, spread limit, pot limit, no limit, stud, draw, games in which the hands are closed
and others in which some of the players’ cards are exposed. Jokers, wild cards, and
special rules can be used to produce even more variations. The most popular version
of poker today is Texas hold ’em, by far the most common type of poker found in card
rooms and the variation played most often in tournaments, including the main event
that determines the poker world champion at theWorld Series of Poker. Other common
variants played in card rooms include seven-card stud, Omaha, lowball, and Razz.
Mathematics of Poker
.............................................................................................................................................................................
The science and economics aspects of poker are, in large part, grounded in the math-
ematics behind the game. Although there are numerous skills necessary for excellence

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389
in poker play, understanding and using the mathematics is crucial for success in poker.
Knowledge of the relevant mathematical probabilities and odds will not necessarily
make a poker player more effective, but a total disregard for them will make a player
bad. The following sections show how poker hand probabilities are calculated and used,
with a focus on various odds in Texas hold ’em, the most popular form of poker today.
Combinatorics
Informally, combinatorics is the branch of mathematics concerned with counting
methods. The two main techniques used in combinatorics are permutations and com-
binations. A permutation of a set of objects is an arrangement of those objects into a
particular order. The other technique, combinations, refers to the number of ways that
a set of objects can be selected from a group without regard to the order in which the
members of the set are arranged. Both permutations and combinations are useful for
computing probabilities in poker.
Permutations: The number of permutations of a set of n distinct objects is given by
n! = n × (n −1) × (n −2) × κ × 2 × 1
(21.1)
for integer n > 1. The left side of expression (21.1) is read “n factorial.”
For example, there are six permutations of the set {A,B,C}, namely (A,B,C), (A,C,B),
(B,A,C), (B,C,A), (C,A,B), and (C,B,A).
Combinations: The number of combinations of n objects taken x at a time (each
object can appear only once, and order is not relevant) is given by
 n
x

=
n!
x!(n −x)!,
(21.2)
where n! = n × (n −1) × (n −2) × κ × 2 × 1, for integer n >1, and by deﬁnition
0! = 1. The left-side of expression (21.2) is usually read “n choose x.”
As an example of combinations, the number of different ﬁve-card poker hands that
can be dealt from a standard deck of 52 playing cards can be found using expression
(21.2) with n = 52 and x = 5, that is,“52 choose 5,” which evaluates to 2,598,960. Since
four of these are royal ﬂushes, the probability of being dealt a royal ﬂush is 4 divided
by 2,598,960, or 1 in 649,740.
Poker Hand Rankings and Probabilities
Most variants of poker are based on a ﬁve-card hand-ranking system, from the strongest
(least likely) to the weakest (most likely). The ranking of the types of hands in a standard
52-card deck is as follows:
1. Straight ﬂush—any ﬁve-card sequence in the same suit.
2. Four of a kind—all four cards of the same value.

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betting strategy
3. Full house—any three cards of the same value combined with a pair.
4. Flush—any ﬁve cards of the same suit that are not in sequence.
5. Straight—any ﬁve cards in sequence but not in the same suit.
6. Three of a kind—any three cards of the same value.
7. Two pair—any two separate pairs.
8. One pair—any two cards of the same value.
9. High card—a hand with none of the above combinations (valued by its highest
card).
In standard poker suits are not ranked. If two hands are identical apart from the suits,
they are considered to be equal. If there are two highest equal hands in a showdown,
the pot is split between them.
Poker hand rankings are determined by their likelihood of occurrence when ﬁve
cards are dealt at random from a shufﬂed deck of 52 cards. The highest-ranking hand
is the least likely; the second highest-ranking hand is the second least likely, and so
on. The probabilities of the various ﬁve-card poker hands can be determined using
combinations, permutations, and the usual probability laws.
First note since there are
52
5

= 2,598,960 possible ﬁve-card hands that can be dealt
from a single deck of 52 cards, the probability associated with a particular type of poker
hand can be computed by counting the possible number of such hands and divid-
ing by 2,598,960. Table 21.1 shows the ﬁve-card poker hand rankings and associated
probabilities of occurring in a ﬁve-card hand dealt from a deck of 52 cards.
Further Probability Considerations
The basic ﬁve-card poker hand probabilities presented in table 21.1 serve as a reference
point, but further knowledge of the probabilities and odds associated with the play of
the hands is required for excellence in playing poker. To illustrate, consider the most
popular form of poker today, Texas hold ’em.
Texas Hold ’em
Typically Texas hold ’em is played with 8 to 10 players, though it is not unusual to have
fewer than 8. Before any cards are dealt in a hold ’em hand, two players post “blind”
bets—a “small blind” by the player to the dealer’s immediate left and a “big blind” by
the next player to the left of the small blind. These blinds are forced bets made before
the players see their cards and are used to start the pot and stimulate action. The small
blind is usually equal to one-half the amount of the big blind. Since the deal rotates
around the table (in a casino where the dealer is not a player, a button used to signify the
nominal dealer rotates after each hand), all players participate equally in the posting of
any forced blind bets.

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Table 21.1 Poker Hand Rankings and Probabilities
Hand
Number of Ways
Number
Probability
≈1 in
1. Royal ﬂush
⎛
⎝4
1
⎞
⎠
4
0.00000154
649,740
2. Straight ﬂush∗
⎛
⎝9
1
⎞
⎠
⎛
⎝4
1
⎞
⎠
36
0.00001385
72,193
3. Four of a kind
13 ·
⎛
⎝48
1
⎞
⎠
624
0.00024010
4,165
4. Full house
13 ·
⎛
⎝4
3
⎞
⎠× 12 ·
⎛
⎝4
2
⎞
⎠
3,744
0.00144058
694
5. Flush
4 ·
⎡
⎣
⎛
⎝13
5
⎞
⎠−10
⎤
⎦
5,108
0.00196540
509
6. Straight
10 ×

20·16·12·8·4
5!

−40
10,200
0.00392465
255
7. Three of a kind
13 ×
⎡
⎣
⎛
⎝4
3
⎞
⎠· 48·44
2!
⎤
⎦
54,912
0.02112845
47
8. Two pairs
13 · 12 ×
⎧
⎨
⎩
⎡
⎣
⎛
⎝4
2
⎞
⎠·
⎛
⎝4
2
⎞
⎠÷ 2!
⎤
⎦× 44
⎫
⎬
⎭
123,552
0.04753902
21
9. One pair
13 ×
⎛
⎝4
2
⎞
⎠× 48·44·40
3!
1,098,240
0.42256903
2.4
10. High card
⎡
⎣
⎛
⎝13
5
⎞
⎠−10
⎤
⎦
⎡
⎢⎣
⎛
⎝4
1
⎞
⎠
5
−4
⎤
⎥⎦
1,302,540
0.50117739
2.0
Total
⎛
⎝52
5
⎞
⎠
2,598,960
1.00000000
∗Excluding royal ﬂushes.
After the blinds are posted, each player is dealt two cards face down, followed by a
round of betting. After this ﬁrst round of betting, three community cards (the ﬂop)
are exposed, followed by a second round of betting. After the second betting round, a
fourth community card (the turn) is exposed, followed by another round of betting,

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betting strategy
and then the ﬁfth and ﬁnal community card (the river) is exposed, followed by a ﬁnal
round of betting.
Each betting round except for the ﬁrst begins with the ﬁrst active player to the left of
the dealer (or in a game dealt by a house dealer, the ﬁrst active player to the left of the
button used to indicate dealer position). Because the ﬁrst two players to the left of the
dealer (or button) have already acted by putting in blind bets, the player one to the left
of the big blind is the ﬁrst with any choices on the ﬁrst betting round. In general, when it
is a player’s turn to act, that player may choose to (a) bet—if there has been no previous
bet made in the round, (b) call—match the current outstanding bet, (c) raise—match
the current outstanding bet and simultaneously make an additional bet, (d) check—
if there is no current outstanding bet, or (e) fold—withdraw from the hand, leaving
all previously wagered money in the pot. Subject to the usual maximum of three (or
sometimes four) raises per round, betting rotates clockwise until each player who has
not folded has put the same amount of money into the pot for the current round or
until one player remains. In the latter case, this player is the winner and is awarded the
pot without having to reveal the cards.
If more than one player remains in the hand after the ﬁnal round of betting, there is
a showdown and the player with the best ﬁve-card poker hand—formed by using any
combination of the ﬁve community cards and the player’s own two hole cards—wins
the pot. If a tie occurs, the pot is split.
Hold ’em Probabilities
Suppose in a Texas hold ’em game you held the ace and seven of diamonds and the
ﬂop contained the two of diamonds, the jack of diamonds, and the ﬁve of spades. At
this point you have four to a diamond ﬂush and would make an ace-high ﬂush (and
likely win the hand) if a diamond fell on the turn or the river (or both). What is the
probability you will make your ﬂush?
Theeasiestwaytocomputetheprobabilityyouwillmakeyourﬂushistoﬁrstcompute
the probability you don’t make the ﬂush and then subtract this value from one. Since
you have seen ﬁve cards—your two hole cards and the three ﬂop cards—there are 47
remaining unseen cards, of which 9 are diamonds and 38 are non-diamonds. Thus the
probability you will not make your ﬂush with the turn card is 38/47, and the probability
you will not make the ﬂush with the river card, given that you missed the ﬂush with the
turn card, is 37/46. Using the multiplication law (dependent events), the probability
you will not make your ﬂush is, then, (38/47)(37/46) = .650. Thus the probability you
will make your ﬂush (on either the turn or the river or both) is 1 – .650 = .350. Put
another way, the odds against making your ﬂush are 1.86 to 1.
Note that in the above ﬂush draw example, the probability that the ﬂush is made with
one card to come depends on whether we look at making the ﬂush on the turn card or,
having not made the ﬂush on the turn, the river card. The probability of making the
ﬂush on the turn is 9/47 = .191, for odds against of about 4.2 to 1; if you don’t make

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Table 21.2 Texas Hold ’Em Probabilities and Odds
Two Cards to Come
One Card to Come∗
Outs
Drawing to (Example)
Probability
Odds Against
Probability
Odds Against
21
69.9%
.43 to 1
45.7%
1.19 to 1
20
67.5%
.48 to 1
43.5%
1.30 to 1
19
65.0%
.54 to 1
41.3%
1.42 to 1
18
62.4%
.60 to 1
39.1%
1.56 to 1
17
59.8%
.67 to 1
37.0%
1.71 to 1
16
57.0%
.75 to 1
34.8%
1.88 to 1
15
Open straight ﬂush draw
54.1%
.85 to 1
32.6%
2.07 to 1
14
51.2%
.95 to 1
30.4%
2.29 to 1
13
48.1%
1.08 to 1
28.3%
2.54 to 1
12
45.0%
1.22 to 1
26.1%
2.83 to 1
11
41.7%
1.40 to 1
23.9%
3.18 to 1
10
38.4%
1.60 to 1
21.7%
3.60 to 1
9
Four ﬂush (ﬂush)
35.0%
1.86 to 1
19.6%
4.11 to 1
8
Open straight draw (straight)
31.5%
2.18 to 1
17.4%
4.75 to 1
7
27.8%
2.59 to 1
15.2%
5.57 to 1
6
24.1%
3.14 to 1
13.0%
6.67 to 1
5
20.4%
3.91 to 1
10.9%
8.20 to 1
4
Gutshot straight (straight)
16.5%
5.07 to 1
8.7%
10.50 to 1
3
12.5%
7.01 to 1
6.5%
14.33 to 1
2
Pocket pair (three of a kind)
8.4%
10.88 to 1
4.3%
22.00 to 1
1
Three of a kind (four of a
kind)
4.3%
22.50 to 1
2.2%
45.00 to 1
∗River (ﬁfth community card) to come.
your ﬂush on the turn, the probability you make it on the river is 9/46 = .196, for odds
against of 4.1 to 1.
The ﬂush draw described above is an example of a post-ﬂop hold ’em situation in
which a player has nine outs—cards that will make the desired hand (in this case a
ﬂush). A similar situation but drawing to an inside straight offers the player only four
outs, while an outside straight draw offer eight outs (ignoring the possibility of making
other hands, such as a pair, three of a kind, etc.). Table 21.2 shows probabilities and odds
for making hands with two cards to come and one card to come for speciﬁed numbers
of outs, with the one-card-to-come probabilities and odds computed assuming that the
one card is the ﬁnal river card.
Expected Value
To fully utilize the mathematics of gambling in poker play, the odds and/or probabilities
in table 21.2 (or analogous values for other poker games) would need to be balanced

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againsttheamountof moneythatwouldbewonorlost. Thiscomparisonof thewinning
odds and the pot odds is at the heart of mathematical expectation, or, expected value.
Proper poker play requires the ability to correctly evaluate the expected value of the
various alternative decisions (bet, fold, call, raise, re-raise, etc.). The expected value of
a decision is a function of both the probability of the possible outcomes of the action
and the values of these outcomes. In poker, the value of an outcome is the amount of
money won or lost.
The expected value (EV ) of a wager can be computed by multiplying the possible
payoffs by their probabilities and then summing the resulting terms. Mathematically
EV =

(Wini × pi)
(21.3)
where Wini is the net win associated with outcome i and pi is the probability of Wini.
The EV for a bet represents the amount of money the bettor will win or lose on average,
or in the long run, from making the speciﬁed bet.
As a simple example, suppose you pay $1 to play a game where a single card is drawn
at random from a standard deck of playing cards and if the selected card is a spade you
will win even money. That is, you will be given $1 in addition to the $1 you paid to play
the game. It should be clear that this is not a smart bet, as you will win only once every
four times, and therefore you will be, on average, down two dollars for every four times
you play this game. Your expected value for this wager is negative $0.50.
EV = (+$1)(1/4) + (−$1)(3/4) = −$0.50.
That the EV is negative means you will lose $0.50 on average each time you make this
wager. If, on the other hand, the net payoff in this game of spades is $4.00, the EV
would be $0.25—you will win $0.25 per time you make this bet on average—and the
wager is now favorable.
The EV is a function of both the probability of winning and the amount you will
win. Even if the probability of winning is small—if the payoff is large enough—the EV
will be positive, making the bet favorable. The section below describes how expected
value is used in poker.
EV and Poker
If we consider only wagers where the outcome is either a single winning value with
probability p or a loss equal to the amount bet with probability (1 −p), then (21.3)
simpliﬁes to
EV = (Net Win)p −(Bet)(1 −p) = (Net Win + Bet)p −Bet.
(21.4)
Expression (21.4) essentially says that the EV in this situation is equal to the expected
return of the bet, where the return is the amount paid back to the player for (rather
than in addition to) the cost of playing (i.e., the amount bet), minus the cost of playing.

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When contemplating the efﬁcacy of a making a bet in poker, it can be viewed it in the
above outlined framework—that is, the bet can result in either the player winning
the pot if he makes his hand or the player losing the amount bet. If p is the probability
the player makes his hand, then (21.4) becomes
EV = (Pot + Bet)p −(Bet) = (Pot)p −Bet(1 −p).
(21.5)
From (21.5), the EV of the contemplated bet is positive when
Pot
Bet > 1 −p
p
.
The left side of (21.6) is the ratio of the size of the pot to the amount of the bet needed—
the pot odds; the right side is the ratio of the probability of losing to the probability of
winning—the odds against winning. In other words, the EV is positive when the pot
odds are greater than the odds against winning.
To illustrate, consider the following generic example. Suppose you need to call a $10
bet to stay in the hand, and the current size of the pot is $30. Further suppose that the
probability you will win if you call the bet is .20. Then, Pot = $30, Bet = $10, p = .20,
and (1 −p) = .80. The odds against winning, (1 −p)/p, are 4 to 1, and the pot odds,
Pot/Bet, are 3 to 1. Because the odds against winning are greater than the pot odds the
EV is negative (EV = −$2), and from a purely mathematical perspective you will lose
money in the long run by calling this bet. One in ﬁve times (p = .20) you make this bet
you’ll win $30, and the other four out of ﬁve times you’ll lose $10, for a total loss of $10,
an average of $2 per bet. Other considerations aside, you should fold in this situation.
On the other hand, if in the same situation the current size of the pot is $50.00, the pot
odds (5 to 1) would be greater than the odds against winning, and EV analysis would
recommend making the bet.
The comparison between what the pot offers and the chances of winning or losing
lies at the heart of the mathematics of poker. Although the outcome of any given hand
is uncertain, and a bet with positive expectation could lose while one with a negative
expectation could win, when faced with a decision to bet, fold, or raise, a player who
consistently chooses the action with the largest EV will come out a winner. A player
who consistently makes decisions with negative expectations will, over the long run,
lose money.
As another example, consider the hold ’em ﬂush draw situation mentioned previ-
ously: You have four to a ﬂush after the ﬂop and know the odds against making your
ﬂush (on the turn or the river) are 1.86 to 1. If you are contemplating calling a bet, the
simple EV analysis outlined above would tell you to call the bet if the pot is offering
you more than 1.86 to 1. The EV analysis presented here is, of course, a simpliﬁcation.
Highly skilled players will also be familiar with and consider effective odds, implied odds,
reverse-implied odds, and other more advanced concepts.

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Game Theory and Poker
.............................................................................................................................................................................
In their seminal book on game theory, The Theory of Games and Economic Behavior
(1944), John von Neumann and Oskar Morgenstern devote an entire chapter to poker.
As one author asserts (Nasr 1998, 13–14), von Neumann believed that poker and
economics share a key connection.
A seemingly trivial and playful pursuit like poker, von Neumann argued, might
hold the key to more serious affairs for two reasons. Both poker and economic
competition require a certain type of reasoning, namely the rational calculation of
advantage and disadvantage based on some internally consistent system of values
(“more is better than less”). And in both, the outcome for any individual actor
depends not only on his own actions, but on the independent actions of others.
Game theory is a ﬁeld of mathematics that models conﬂicts and strategic interactions
between competing agents. It attempts to solve games, help players avoid mistakes, and
discover mathematically best strategies. A game in the everyday sense might be deﬁned
as a competitive activity in which players contend with each other according to a set
of rules, a pastime or diversion. In game theoretic sense a game is any rule-governed
situation with a well-deﬁned outcome characterized by strategic independence. Firms
competing in a market are players in a game; countries involved in international trade
or ﬁnance negotiations are players in a game; so are poker players seated around a
poker table. Though ﬁrst applied to the theoretical study of economics, game theory
has broadened in scope to include applications in such diverse ﬁelds as international
relations, social science, political science, military science, psychology, biology, and
poker.
A particularly important and informative example of how game theory can be used in
poker is the determination of an optimal blufﬁng strategy, the strategy through which
you will average the same amount won regardless of whether your opponent calls
or folds. Game theory shows that the optimal blufﬁng strategy is a mixed strategy—
one where you randomly choose between multiple possible actions (here, blufﬁng
or folding) a predetermined percentage of the time. As David Sklansky (1999, 190)
summarized
When using game theory to decide whether to bluff, you must determine the pot
odds your opponent is getting if you bet and then randomly bluff in such a way that
the odds against your blufﬁng are identical or almost identical to your opponent’s
pot odds. If your opponent is getting 5-to-1, the odds against your blufﬁng should
be 5-to-1. By playing this way, you give your opponent no correct decision. He does
just as well—or badly—in the long run by calling or folding.
Game theory can also be used to decide whether to call a possible bluff (assuming your
hand can beat only a bluff and assuming your judgment doesn’t give you a hint). The

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appropriate mixed strategy here is to make the ratio of your calls to your folds the same
as the odds your opponent is getting on a bluff. For example, if your opponent is getting
3-to-1 odds on a bluff, then randomly calling three out of four times will make that
bluff unproﬁtable.
Many scientists have used a game theoretic approach to study poker. These
approaches typically use game theory to carefully analyze simpliﬁed models, or spe-
ciﬁc aspects or situations, of real poker in order to try to understand the fundamental
nature of the game. The interested reader is referred to chapter 19 of von Neumann
and Morgenstern (1944), chapter 19 of Sklansky (1999), chapter 22 of Ethier (2010),
and Ferguson and Ferguson (2007) for illustrative examples of such analyses. Chen and
Ankenman (2006) combines mathematical analysis with a heavy dose of game theory
in an attempt to create“near-optimal”strategies and enhance the player’s ability to win
money at real poker.
Artificial Intelligence and Poker
.............................................................................................................................................................................
As a game of imperfect information and nondeterministic dynamics where multiple
competing agents deal with probabilistic knowledge, risk assessment, and possible
deception, poker is both fertile ground and a challenging problem for artiﬁcial intel-
ligence research. By modeling various elements of skill and appealing to advanced
mathematical and statistical techniques, such as game theory and Bayesian proba-
bilistic models, scientists have had some success at designing champion-level artiﬁcial
intelligence poker agents.
One of the leading research groups in this area is the Computer Poker Research
Group (CPRG) at the University of Alberta. In designing intelligent poker bots to play
Texas hold ’em, the CPRG has speciﬁcally attempted to incorporate six skill-related
aspects:
• Hand strength assesses how strong your hand is in comparison to what your
opponents may hold and is computed on the ﬂop, turn, and river.
• Minimum skill—a function of your cards and the community cards.
• Moderate skill—also takes into account the number of players still in the game,
position at the table, and the history of betting in the hand.
• Maximum skill—also considers the different probabilities for each possible
opponent hand, based on the likelihood of each hand being played to the current
point in the game. Skill levels can be improved even further by varying hidden
hand probabilities for each player depending on that player’s model of play.
• Hand potential assesses the probability of the hand improving (or being overtaken)
as additional community cards appear.
• Minimum skill—a function of your cards and the community cards.

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betting strategy
• Maximum skill—also considers the number of players still in the game, position
at the table, history of betting in the hand, different probabilities for each possible
opponent hand, and each player’s model of play.
• Betting strategy determines whether to fold, call/check, or bet/raise.
• Minimum skill level—based on hand strength.
• Maximum skill level—also considers hand potential, pot odds, blufﬁng,
opponent modeling, and unpredictability.
• Blufﬁng makes it possible to proﬁt from weak hands and can create a false
impression about your play that can improve the chances of winning subsequent
hands.
• Minimum skill level—blufﬁng a ﬁxed percentage of all hands.
• Maximum skill level—incorporate opponent modeling.
• Opponent modeling determines a likely probability distribution for opponent’s
hidden cards or betting strategy.
• Minimum skill level—uses a single model for all opponents in a given hand.
• Maximum skill level—modiﬁes the probabilities based on a classiﬁcation of
each opponent (e.g., weak or strong, passive or aggressive), betting history, and
collected statistics.
• Unpredictability makes it difﬁcult for opponents to form an accurate model of your
strategy by varying playing style over time to induce opponents to make mistakes
based on inaccurate models.
In 2008 a CPRG-designed poker robot dubbed Polaris played six matches of two-player
limit Texas hold ’em against some of the best players in the world and managed to
outperform them by $200,000, winning three matches, losing two, and tying one. The
previous year Polaris played a duplicate match consisting of four 500-hand sessions
against two top professional poker players and ﬁnished with a record of 1–2–1.
A Caveat---House-Banked Poker Games
.............................................................................................................................................................................
The size of the skill component in Texas hold ’em is such that it can be fairly character-
ized as a game of skill—that is, a game in which skill predominates over chance. This
is true for many other player-versus-player poker games, such as seven-card stud and
Omaha. But the same cannot be said of house-banked poker games, such as Caribbean
stud, three-card poker, and video poker machines. The player of these games is playing
against the house and an associated house advantage, and while a certain element of skill
is necessary to minimize losses—except for a few types of video poker the player in these
games is always at a disadvantage—mastering optimal strategy in these house-banked
poker derivatives does not require the level of skill as in such player-versus-player poker
games as Texas hold ’em.

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For example, the reported advantages or payback percentages for a video poker
machine assume perfect optimal strategy and maximum coin played, but the effective
house advantage depends on the skill of the player. The reported house advantage can
be achieved only if playing optimal strategy, which varies depending on the particular
machine or game. Although playing video poker can be challenging, the skill levels of
video poker and Texas hold ’em are signiﬁcantly different. Skills such as psychologi-
cal insight, assessment of competition, the ability to read hands, recognize tells, and
exploit position as well as money management are conspicuously absent in video poker.
Another notable difference is that almost all video poker games, even when played at
optimum strategy, result in the player losing over time.
Skill in Poker
.............................................................................................................................................................................
Scientiﬁc studies on the relative roles of skill versus chance in poker have used a variety
of approaches to examine the issue, and the body of research on the subject points to
the conclusion that poker is a game predominately of skill. The following summarizes
the conclusions from some of the key studies:
• In an analysis of more than one billion hands of real poker, Robert Hannum,
Matthew Rutherford, and Teresa Dalton (2012) presented a method for isolating
the effect of systemic chance by taking advantage of knowledge of players’ hole
cards to predict their return on investment in a Texas hold ’em game devoid of all
elements of skill. Using a regression approach to compare players’ actual returns
on investment (ROIs) to their expected returns on investment in the chance-only
hold ’em game, they found that only 0.03 percent of the variation in players’
actual ROIs could be attributed to systemic chance and so 99.97 percent could be
attributable to skill. They further found that 85.2 percent of all hands were resolved
without a showdown, and of the 14.8 percent that did go to showdown, nearly half
(46.8%) were won by a player at the table who did not have the best hand (because
the player with the best hand folded prior to showdown).
• Steven Levitt and Thomas Miles (2011) used World Series of Poker data to address
the issue of skill versus chance. Having designated skill of players based on prior
year performance, they considered the average rate of return on investment in the
poker tournament. Their ﬁndings revealed that skilled players had, on average,
a 30 percent ROI while all other players had a loss of 15 percent. They used
this difference in ROI for skilled players over all other players as support for the
proposition that poker is a game of skill.
• Presenting evidence of skill differentials among 899 poker players ﬁnishing in one
of the ﬁnal two tables in 81 high-stakes Texas hold ’em tournaments between 2001
and 2005, Rachel Croson, Peter Fishman, and Devin Pope (2008) concluded (a)
that there appears to be a signiﬁcant skill component to poker: previous ﬁnishes

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betting strategy
in tournaments predict current ﬁnishes; and (b) that skill differences among top
poker players are similar to skill differences across top golfers.
• Comparing players who were taught strategies based on expert opinion with other
players who were taught no strategies, Michael Dedonno and Douglas Detterman
(2008) found that participants who were instructed outperformed those who were
not instructed. They concluded that the skill involved in poker is complex and
that luck (random factors) disguises the fact that poker is a game of skill and also
declared the unequivocal ﬁnding that poker is a game of skill.
• Based on the rationale that chance elements cancel out in the long run while skill
elements do not, Ingo Fiedler and Jan-Philipp Rock (2009) proposed a critical
repetition frequency—the threshold of repetitions at which a game becomes pre-
dominantly inﬂuenced by skill rather than by chance. Analyzing data from an
empirical survey of 51,761 poker players, they concluded that poker lies in the
continuum between being a game of chance and being a game of skill and that for
their sample, poker is a game of skill.
• In a mathematical analysis supported by computer simulations of a random player
versus a skilled player in Texas hold ’em, Hannum Anthony Cabot (2009) found
that the skilled player won nearly 97 percent of all hands and 1.6 big blinds per
hand. Additional full-table simulation games of Texas hold ’em and seven-card
stud with highly skilled and lesser skilled players showed that the highly skilled
players convincingly beat unskilled players. The authors concluded that poker is a
game predominantly of skill with the skill elements expressed through the player’s
betting strategy—that is, the decisions on whether to check, bet, call, raise, or fold.
• In computerized experiments in a simpliﬁed version of stud poker comparing
12 different strategies, ranging from a simple strategy that plays randomly (a
player with no skill) through progressively more sophisticated strategies utilizing
varying degrees of skill, Patrick Larkey et al. (1997) found a wide range of out-
comes across the different strategies, with better outcomes generally associated
with higher degrees of skill. They also determined that simple random strategy
(zero skill) is the worst overall performer in terms of winnings.
• Using a game theoretic approach to study the relative roles of skill and chance in
games, Peter Borm and Ben van der Genugten (2001) concluded that the level of
skill in the three popular variants of poker, seven-card-stud, Texas hold ’em, and
draw poker, is greater than that in roulette, craps, and blackjack.
Summary
.............................................................................................................................................................................
The science and economics of poker derive from the mathematics underlying the game
and the various and considerable elements of skill needed to be successful over the
long term. The mathematics of probability, odds, and expected value are intimately

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the science and economics of poker
401
associated with proper decision-making, a key objective in poker. Principles of game
theory shed further light on optimal or near-optimal strategies for winning money.
A spate of recent scientiﬁc studies on the subject provides compelling evidence that
skill is the major factor, and predominates over chance, in determining the outcome
in poker.
References
Borm, Peter, and Ben van der Genugten. 2001. On a relative measure of skill for games with
chance elements. Trabajos de Investigacion Operative [TOP—Ofﬁcial Journal of the Spanish
Society of Statistics and Operations Research] 9(1):91–114.
Chen, Bill, and Jerrod Ankenman. 2006. The mathematics of poker. Pittsburgh, Pa.: ConJelCo
LLC.
Croson, Rachel, Peter Fishman, Devin G. Pope. 2008. Poker superstars: Skill or luck? Chance
21(4):25–28.
Dedonno, Michael A., and Douglas K. Detterman. 2008. Poker is a skill. Gaming Law Review
12(1):31–36.
Ethier, Stewart N. 2010. The doctrine of chances: Probabilistic aspects of gambling. Berlin:
Springer-Verlag.
Ferguson, Chris, and Tom Ferguson. 2007. The endgame in poker. In Optimal play: Mathemat-
ical studies of games and gambling, edited by Stewart N. Ethier and William R. Eadington.
Reno: Institute for the Study of Gambling and Commercial Gaming, University of Nevada,
Reno.
Fiedler, Ingo, and Jan-Philipp Rock. 2009. Quantifying skill in games—Theory and empirical
evidence for poker. Gaming Law Review and Economics 1(3):50–57.
Hannum, Robert C., and Anthony N. Cabot, A. (2009). Toward legalization of poker: The skill
vs. chance debate. UNLV Gaming Research & Review Journal 13(1):1–20.
Hannum, Robert, Matthew Rutherford, and Teresa Dalton. 2012. Economics of poker: The
effect of systemic chance. Journal of Gambling Business & Economics 6(1):25–48.
Larkey, Patrick, Joseph B. Kadane, Robert Austin, and Shmuel Zamir. 1997. Skill in games.
Management Science 43(5):596–609.
Levitt, Steven D., and Thomas J. Miles. 2011. The role of skill versus luck in poker:
Evidence from the World Series of Poker. National Bureau of Economic Research
Working Paper No. 17023. Cambridge, Mass.: National Bureau of Economic Research;
www.nber.org/papers/w17023.
McManus, James. 2009. Cowboys full: The story of poker. New York: Farrar, Straus, and Giroux.
Nasar, Sylvia. 1998. A beautiful mind. New York: Simon & Schuster.
Parlett, David. 1991. A history of card games. Oxford: Oxford University Press.
——. 2005. A history of poker; www.pagat.com/vying/pokerhistory.html.
Sklansky, David. 1999. The theory of poker. Henderson, Nev.: Two Plus Two Publishing.
von Neumann, John, and Oskar Morgenstern. 1944. The theory of games and economic
behavior. Princeton, N.J.: Princeton University Press.

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## Page 423

chapter 22
........................................................................................................
THE KELLY CRITERION WITH
GAMES OF CHANCE
........................................................................................................
leonard c. maclean and william t. ziemba
1 Introduction
.............................................................................................................................................................................
In games of chance, a bettor must determine how much capital to bet in risky games
at each play, with a focus on the accumulation of maximum capital after a sequence
of plays. An important betting strategy is based on the Kelly criterion, through which
the expected logarithm of wealth is maximized. (Kelly 1956.) Log utility dates to 1738,
when Daniel Bernoulli postulated that marginal utility was monotone increasing but
declining with wealth and, speciﬁcally, was equal to the reciprocal of wealth, w, which
yields the utility of wealth, u(w) =log(w). Prior to this it was assumed that decisions
were made on an expected value or linear utility basis. This idea ushered in declining
marginal utility or risk aversion or concavity which is crucial in investment decision-
making. In his paper, Bernoulli also discussed the St. Petersburg paradox and how
it might be analyzed using log(w). This problem concerns how much to pay for the
following gamble:
A fair coin with 1
2 probability of heads is repeatedly tossed until heads occurs, ending
the game. The investor pays c dollars and receives in return 2k−1 with probability
2−k for k = 1,2,... should a head occur. Thus after each succeeding loss, assuming a
head does not appear, the bet is doubled to 2,4,8,... and so on. Clearly the expected
value is 1
2 + 1
2 + 1
2 + ··· or inﬁnity with linear utility.
Robert Bell and Thomas Cover (1980) argued that the St. Petersburg gamble is attractive
at any price c but that the investor wants less of it as c →∞. The proportion of the
investor’s wealth invested in the St. Petersburg gamble is always positive but decreases
with increasing cost c. The rest of the wealth is in cash.

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the kelly criterion with games of chance
403
Bernoulli offered two solutions since he felt that this gamble is worth a lot less than
inﬁnity. In the ﬁrst solution, he arbitrarily set a limit to the utility of very large payoffs.
Speciﬁcally any amount over 10 million was assumed to be equal to 224. Under that
bounded utility assumption the expected value is
1
2 (1) + 1
4 (2) + 1
8 (4) + ··· +
1
2
25 
224
+ ··· = 12 + the original 1 = 13
When utility is log the expected value is
1
2 log1 + 1
4 log2 + 1
2 log4 + ··· = log2 = 0.6915.
As Karl Menger (1934) pointed out, the log, the square root, and many other, but not all,
concave utility functions eliminate the original St. Petersburg paradox, but it does not
solve one where the payoffs grow faster than 2n. So if log is the utility function, one can
create a new paradox by having the payoffs increase at least as fast as log reduces them
so one still has an inﬁnite sum for the expected utility. With exponentially growing
payoffs one has
1
2 log(e) + 1
4 log

e2
+ ··· = ∞.
The super St. Petersburg paradox, in which even ElogX = ∞, is examined in Cover
and Thomas (2006, 181, 182), where a satisfactory resolution is reached by looking at
relative growth rates of wealth.
J. L. Kelly Jr. (1956) is credited with using log utility in gambling and repeated
games. His analysis uses Bernouli trials. He established that log is the utility function
which maximizes the long run growth rate, and is myopic in the sense that period by
period maximization is optimal. Latané (1959) introduced log utility as an investment
criterion to ﬁnance independent of Kelly’s work. Leo Breiman (1961) established the
basic mathematical properties of the expected log criterion: (i) wealth for the Kelly
strategy overtakes almost surely that of any other essentially different strategy as the
horizon becomes inﬁnitely distant, (ii) the strategy attains arbitrarily large wealth goals
faster than any other strategy, and (iii) with a ﬁxed opportunity set a ﬁxed Kelly strategy
is optimal.
In an economy with one log bettor and with all other bettors having essentially
different strategies, the log bettor will eventually get all of the economy’s wealth (Hens
and Schenk-Hoppé 2005). The drawback of log, with its essentially zero Arrow–Pratt
absolute risk aversion, is that in the short run it is the most risky utility function one
would ever consider. Since there is essentially no risk aversion, the wagers it suggests are
very large and typically undiversiﬁed. Simulations show that log investors have much
more ﬁnal wealth most of the time than do those using other strategies, but those
investors can essentially go bankrupt a small percentage of the time, even facing very
favorable choices (Ziemba and Hausch 1986). One way to modify the growth-security

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betting strategy
proﬁle is to use either ad hoc or scientiﬁcally computed fractional Kelly strategies that
blend the log optimal portfolio with cash. For instance, a fractional Kelly strategy will
keep accumulated capital above a speciﬁed wealth path with high probability given
log normally distributed payoffs. This is equivalent to using a negative power utility
function whose coefﬁcient (analogous to a risk aversion index) is determined by the
fraction and vice versa. Thus one moves the risk aversion away from zero to a higher
level. This results in a smoother wealth path but has less growth. For non-lognormal
payoff distributions, the fractional Kelly is an approximate solution to the optimal
risk-return trade-off, but the approximation may be inaccurate (MacLean, Thorp, and
Ziemba 2011).
2 Games of Chance and the
Kelly Strategy
.............................................................................................................................................................................
A game of chance is a game whose outcome depends on a random process. Consider
a set of K games whose outcomes are stochastic, that is, they are deﬁned on the
probability space (, B, P). Assume there is a payoff or return from a play of game i,
given the outcome ω ∈, deﬁned by by ri(ω),i = 1,...,K. A gamble is a bet placed on
the outcome of the game. For a unit of capital bet on game i the return is
Ri(ω) = 1 + ri(ω), i = 1,...,K.
(22.1)
In the gambling market games are played at points in time and the return on bets leads
to the accumulation of capital for a bettor. In the analysis of betting strategies, the
following structure is assumed:
(a) All games have limited liability.
(b) There are no playing costs, taxes, or problems with indivisibility of capital.
(c) Capital can be borrowed or lent at a risk-free interest rate r.
(d) Negative betting (borrowing against the game outcome) is allowed.
The returns on outcomes from the K games generate random vector R′ = (R0,...,RK),
where R0 = 1+r. Suppose a bettor has wt units of capital at time t, with the proportions
bet in each game given by and ˜X = (x1(t),...,xK(t))′. If the fraction of capital not bet
is x0(t) and earns the risk-free rate, then a betting strategy at time t is the vector process
X(t) = (x0(t), ˜X′(t))′.
(22.2)
Given the bets wtX(t) at time t, the accumulated capital at time t + 1 is
W (t + 1) = wtR′X(t).
(22.3)

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the kelly criterion with games of chance
405
For a sequence of T plays of the set of games starting with capital w0, wealth at time T is
W (T) = w0
T
.
t=1
R′X(t).
(22.4)
Alternatively wealth is
W (T) = w0

exp

1
T
T

t=1
ln(R′X(t))
T
.
(22.5)
Theexponentialformhighlightsthe growthrate withthestrategyX = (X(1),...,X(T)),
GT(X) = 1
T
T

t=1
ln(R′X(t)).
(22.6)
If the distribution of accumulated capital (wealth) at the horizon is the criterion for
deciding on an investment strategy, then the rate of growth of capital becomes the
determining factor when the horizon is distant. Consider then the average growth rate
EGT(X) = 1
T
T

i=1
E ln(R′(t)X(t)).
(22.7)
The case usually discussed is when the incremental returns are serially independent. So
the maximization of EGT(X) is
max
$
E ln

R′ (t)X (t)
%
,
(22.8)
separately for each t. If the returns distribution is the same for each t, a ﬁxed strategy
holds over time. The strategy that solves (22.8) is called the Kelly or optimal growth
strategy.
2.1 Kelly Formulas
The Kelly strategy is optimal for the asymptotic growth rate criterion, but there are
other measures of performance of interest. In table 22.1, some measures are deﬁned,
with a classiﬁcation by wealth and time. In the deﬁnitions in the table, the notation
τ(W (X) ≥u) is the ﬁrst passage time to the set [u, ∞).
The wealth and time dimensions of the stochastic process {W (X),t ≥0} are alter-
native perspectives, with the time component emphasizing growth speed and wealth
emphasizing growth magnitude. The distributions for the random quantities are
illustrated in ﬁgure 22.1.

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betting strategy
Table 22.1 Performance Measures
Criterion
Mean
Percentile
Wealth
φT (X) = E

in[WT (X)]
1
T
 
γT (X) = pr [ln(WT (X)) ≥1n(wT )]
Time
ηu (X) = E {τ (W (X)) ≥u}
βl,u (X) = pr [τ (W (X)) ≥u < τ (W (X)) ≤l]
Wealth
u
Time
T
First passage time
Final wealth
figure 22.1 Wealth and time dimensions of wealth process.
The Kelly strategy is deﬁned by the expected value, but the risk characteristics are
signiﬁcant as well. Risk is deﬁned by the chance of falling short of targets. By the wealth
criterion, a value-at-risk WT is speciﬁed at the horizon T, so risk is deﬁned by a VaR
condition. In the case of ﬁrst passage time, the chance of achieving a desired wealth
target before falling to an undesirable level is assessed.
The Kelly strategy is optimal for the expected values ϕ and η but may not do well
on risk measures γ and β. These performance measures have been considered in
several papers in the ﬁnance and probability literature (see, for example, Hanoch and
Levy (1969), Hakansson (1970), Kallberg and Ziemba (1981, 1983, 1984), Grauer and
Hakansson (1985, 1987), Jorion (1986, 1987), Browne (1997), Dohi et al. (1995), Ethier
and Tavaré (1983), Luenberger (1993, 2009), MacLean and Ziemba (1991, 1999, 2000),
MacLean, Ziemba, and Blazenko (1992), Hakansson and Ziemba (1995), Stutzer (2003)
and MacLean, Ziemba and Li (2005)). The evaluation of these measures is the basis for
selecting an appropriate betting strategy that satisﬁes our preferences. If the strategy
has constant investment proportions, which includes the Kelly, then standard results
on random walks (discrete time) and diffusions (continuous time) can be adapted to
provide computational formulas for the measures.

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the kelly criterion with games of chance
407
Discrete Time
The discrete time formulas for the measures were developed in MacLean, Ziemba, and
Blazenko (1992). They apply to any constant proportions strategy. They are presented
in table 22.2 using the following notation:
(i) X = (x0,x1,...,xK)′ is the constant betting policy.
(ii) J(X) = log(R′X).
(iii) ZT (X) = T
t=1 Jt (X), where J0(X) = log W0.
(iv) JM(X) = inf J(X),JM(X) = sup J(X).
(v) l∗= log(l), u∗= log(u), for lower and upper targets l,u.
(vi) L∗(X) = l∗+ Jm(X), U ∗(X) = u∗+ JM(X), U∗(X) = u∗−Jm(X).
(vii) θ is the non-unit root of EθJ(x) = 1, where E is expectation.
(viii) [•] is the cumulative normal distribution.
Continuous Time
The performance measures for repeated plays of games can be approximated by con-
tinuous time formulas. That is, the random walk of log wealth is approximated by a
diffusion. For the evaluation of measures in the continuous time formulation of the
log wealth process we refer to Dohi et al. (1995). Consider the following notation:
(i) The total bets in risky games is λ(X) = K
i=1 xi.
(ii) The risky games are combined into a single game fund with instantaneous rate
of return R = k
i=1 aiRi, where ai =
xi
λ(X).
(iii) The mean and variance of the instantaneous rate of return on the game fund
are μ
 ˜X

and σ 2  ˜X

, respectively.
(iv) D (X) = (μ(X) −r)λ −σ 2(/X)λ2(x)
2
, where it is assumed that D(X) > 0.
(v)  [• “•” ] is the cumulative normal distribution.
The expressions in tables 22.2 and 22.3 are similar and usually yield similar values.
One advantage of the discrete time formulas is the ﬂexibility over the rate of return
distributions on risky assets, since we can work with any distribution with ﬁnite sup-
port. For the exact continuous time model, the return distributions are assumed to
be lognormal, and that may not give an acceptable approximation. However, in the
continuous time approximation, where the payoffs on risky games have a lognormal
distribution, the decision is determined from
max
$
(μ −re)′ X
%
+ r −1
2
0X	0X

,
(22.9)
with mean returns μi, i = 1,...,K, and covariance of returns 	 = (δij). Also, 0X
′ =

x1,...,xk

are the bets in risky games. For this continuous time problem, the Kelly
strategy has the closed form
0X∗= 	−1 (μ −re).
(22.10)

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betting strategy
Table 22.2 Discrete Time Formulas
Measure
Formula
ϕT (X)
Elog (R’X)
γT (X)

⎛
⎜⎜⎝
TEJ (X) −log
WT
w0

√T σ (J)
⎞
⎟⎟⎠
ηu (X)
θ
2EJ (X)
+ U∗(X)
θu∗(x)
,
−
z0
EJ (X)
βl,u (X)

θz0 −θu∗
θu∗−θL∗(X) +

θz0 −θL∗(X)
θu∗(X) −θl∗
2

θu∗(X) −θl∗
θu∗−θL∗(X)
Table 22.3 Continuous Time Formulas
Measure
Formula
ϕT (X)
((μ(X) −r)λ(X) + r)T
γT (X)

⎛
⎜⎜⎝
T .D (X) −log WT
w0
3
T σ
0X

λ(X)
⎞
⎟⎟⎠
ηu (X)
1
D (X)log
 u
W0

βl,u (X)
1 −

u
W0
2D(X)
σ2(0X)λ2(X)

1 −

u
T
2D(X)
σ2(0X)λ2(X)

The Kelly or log optimal portfolio is X∗′ =

x∗
0 ,0X∗
′
, where x∗
0 = 1 −k
i =1 x∗
i . The
continuous time formula can be viewed as an approximate solution to the discrete time
betting problem. The Kelly strategy is a ﬁxed mix. That is, the fraction of wealth bet in
games is determined by X∗but rebalancing as wealth varies is required to maintain the
fractions.
2.2 Some Important Properties of the Kelly Strategy
The considerable interest in the Kelly strategy, particularly in the gambling, invest-
ing, and probability literature, has produced a number of important good and bad

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the kelly criterion with games of chance
409
properties. Some are listed below; for more details refer to MacLean, Thorp, Zhao, and
Ziemba (2010, 2011).
Good: Maximizing ElogW (X) asymptotically maximizes the rate of asset growth
(Breiman (1960, 1961); Algeot and Cover 1988).
Good: The expected time to reach a preassigned goal u is asymptotically as u increases
least with a strategy maximizing ElogW (X) (Breiman 1960; Algeot and Cover
1988; Browne 1997).
Good: Under general conditions Maximizing ElogW (X) also asymptotically maxi-
mizes the median ﬁnal wealth (Ethier 2004).
Good: The ElogW (X) bettor never risks ruin (Hakansson and Miller 1975).
Good: The absolute amount bet is monotone increasing in wealth (Thorp 2006).
Good: The ElogW (X) bettor has a myopic policy (Kelly 1956; Hakansson 1971).
Good: The ElogW (X) bettor’s fortune pulls ahead of other “essentially different”
strategies’ wealth for long sequences of plays (Thorp 1975/1971; Ziemba and
Hausch 1986; Aucamp 1993; Browne 1997).
Good: Kelly gambling yields wealth W ∗such that E W
W ∗≤1 for all other strategies
(Bell and Cover 1980, 1988; Grifﬁn 1984).
Good: The chance that the Kelly bettor is ahead of any other bettor after the ﬁrst play
is at least 50 percent (Bell and Cover 1980).
Good: The Kelly bettor is never behind any other bettor on average in 1,2,... trials.
(Finkelstein and Whitley 1981).
Bad: The bets are extremely large when the wager is favorable and the volatility of
returns is very low (Ziemba and Hausch 1986).
Bad: One over bets when the probabilities for events are in error (Chopra and Ziemba
1993, MacLean, Foster, and Ziemba 2007).
Bad: For coin tossing, if the number of wins equals the number of losses then the
bettor is behind (MacLean and Ziemba 1999).
Bad: The average Kelly return converges to half the optimal arithmetic return (Ethier
and Tavaré 1983).
Bad: The total amount bet swamps the winnings—that is, there is much churning
(Ethier and Tavaré 1983).
3 Fractional Kelly Strategies
.............................................................................................................................................................................
A challenging aspect concerning the performance of the Kelly strategy is that it is good
on some measures and poor on others. If we refer back to table 22.1, the good properties

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410
betting strategy
of the Kelly are with the means (or long-term growth) and the less desirable properties
are with percentiles (or the security of the acceptable results).
A variation on the Kelly strategy is the fractional Kelly strategy deﬁned as 0
Xf =
f 0X∗,0 ≤f ≤1, so it is a blend of the Kelly strategy and cash. The fractional Kelly
strategy has the same distribution of wealth across risky gambles as the Kelly but varies
the fraction of wealth invested in those risky assets. The strategy 0Xf has ﬁxed fractions,
and therefore the formulas in tables 22.2 and 22.3 apply. That is, the fractional Kelly
strategies can be evaluated based on performance on the measures of expected growth
rate and security of growth (or low risk).
3.1 Bi-Criteria Problems
The problem of determining the optimal trade-off of expectation and risk can be
formalized by using a utility function over these two attributes similar to that in mean-
variance analysis; see, for example, Markowitz (1952, 1987). Leonard MacLean et al.
(2004) did this another way by adding probability constraints on the drawdown; then,
using scenario analysis, an optimal fractionalized Kelly strategy can be determined. The
examples in section 4 illustrate this trade-off choice.
Analogous to static mean-variance analysis (see Markowitz 1952, 1987), a growth–
security combination pair is inefﬁcient if another pair in that combination has either a
higher mean growth and no lower security level or a higher security level and no lower
growth rate. A strategy is inefﬁcient if its growth–security combination is inefﬁcient.
Efﬁcient growth–security combinations are those that are not inefﬁcient. The efﬁcient
growth–security frontier is the set of all efﬁcient growth–security pairs. An efﬁcient
trade-off between growth and security occurs along the efﬁcient frontier. The efﬁciency
problems based on the performance criteria in table 22.1 are given in table 22.4. The
constraint on security sets an acceptable risk α for not meeting the performance target.
In addition to the growth–security problems, an expected utility problem M1 is
deﬁned. The power utility plays an important role in the Kelly and fractional Kelly
strategies. The log is the power utility as p →0. The coefﬁcient ρ is a risk aversion
Table 22.4 Alternative Decision Models
Model
Criterion
Problem
M1
Expected power utility, with risk aversion
index: 1 −ρ, ρ <1..
Max

E

1
p

W (T )p −1
 
M2
Optimal growth subject to a VaR
constraint.
Max{φT (X)|γT (X) ≥1 −α}
M3
Optimal growth subject to wealth goals
constraint.
Min
$
ηu (X)|βl,u (X) ≥1 −α
%

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the kelly criterion with games of chance
411
parameter, and the Arrow–Pratt relative risk aversion index is (1−ρ). If 0X∗is the Kelly
strategy for risky gambles, then 0Xρ =
1
1−ρ 0X∗, ρ < 0, is the optimal solution to problem
M1 in the continuous time case where returns are log-normally distributed. That
formula gives an indication of the risk aversion property of fractional Kelly strategies.
The optimality property applies to the other problems. The subclass of fractional
Kelly strategies is deﬁned as
0x∗=

0X∗
f |0X∗
f = f .0X∗, 0 ≤f ≤1
 
.
(22.11)
The signiﬁcance of the fractional Kelly strategies lies in their optimality for the problems
in table 22.4, assuming the geometric Brownian model for returns is correct.
Theorem
Let XMj be the optimal solution to growth problem Mj, j = 1,2,3 deﬁned in table 22.6.
Then XMj ∈0x∗, that is, the solution is fractional Kelly.
For proof see MacLean, Zhao, and Ziemba (2005).
In the continuous time formulation, the optimal investment strategies for the
various problems have the same form. However, the actual fraction in each prob-
lem, which controls the allocation of capital to risky and risk-free instruments,
depends on the decision model and parameters.
The formulas for the frac-
tions for different models are in table 22.5. The notation 0μ = (μ −re)′ 0X∗+ r,
and 0σ 2 = 0X∗′	0X∗is used for the mean and variance of the rate of return on
the Kelly strategy. Also at time t,y∗
t is the minimum positive root of the equation
γ yct +1 −y + (1 −γ ) = 0, for ct = log(u)−log(wt )
log(wt )−log(l) . Coefﬁcients are
$
A1 = (μ −re)′
	−1 (μ −re), B1t = A1 + za
&
A1
T−t ,C1t = r −(T −t)−1 log

wT
wt

, and

H = 0μ−r
0σ 2 ,
ht =
log(wt )−log(l)
log(wt )−log(y∗t .l)
 
.
Table 22.5 Investment Fractions
Model
Parameters
Kelly Fraction
M1
ρ
f1 =
1
1 −ρ
M2
(wT , α)
f2t
B1t +
3
B2
1t + 2A1C1t
A1
M3
(l,u,α)
f3t = ht.H +
&
[ht.H]2 + 2rht
0σ 2

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betting strategy
The solutions displayed in table 22.5 are derived from the continuous time wealth
equation, though the strategies are calculated at discrete decision points in time. The
alternative problems in table 22.4 can be based on the discrete time wealth equation,
but the optimal solution is not necessarily fractional Kelly. However, the fractional Kelly
solution may be near-optimal. If the feasible strategies for the discrete time problem
are restricted to the class of fractional strategies, the solutions are effective (MacLean,
Ziemba, and Blazenko 1992). That is, as the fraction changes, the growth (objective)
and security (constraint) move in opposite directions so that growth is monotone
nonincreasing in security. Speciﬁcally, 0 ≤f ≤1,
 d
df φT

X∗
f

≥0, d
df γT

X∗
f

≤0

,
 d
df ηu

X∗
f

≥0, d
df β1,u

X∗
f

≤0

.
(22.12)
The implication of this monotonicity is that growth can be traded for security using
the fraction allocated to the optimal growth portfolio. So the growth–security trade-off
can be observed for various fractional Kelly strategies and suitable fractions (meet-
ing investor preferences) can be determined. This will be demonstrated with some
applications.
4 Applications
.............................................................................................................................................................................
4.1 Blackjack
The game of blackjack, or 21, evolved from several related card games in the nineteenth
century. It became fashionable during World War I and has since become enormously
popular, played by millions of people in casinos around the world. Billions of dollars
are lost each year by people playing the game in Las Vegas alone. A small number of
professionals and advanced amateurs, using various methods such as card counting, are
able to beat the game (Thorp 1962). See Janacek (1998) for a computer program that
evaluates game statistics, such as advantage depending on the card-counting system
used and casino rules. The software is also available online (see Statistical Blackjack
Analyzer 5.5). The object is to reach, or be close to, 21 with two or more cards. Scores
above 21 are said to bust or lose. Cards 2 to 10 are worth their face value: Jacks, queens,
and kings are worth 10 points, and aces are worth 1 or 11 points, at the player’s choice.
The game is called blackjack because an ace and a 10-valued card was paid three for two
and an additional bonus accrued if the two cards were the ace of spades and the jack of
spades or clubs. While this extra bonus has been dropped by current casinos, the name
has stuck. Dealers normally play a ﬁxed strategy of drawing cards until the total reaches
seventeen or more, at which point they stop. A variation is when a soft 17 (an ace with
cards totaling six) is hit. It is better for the player if the dealer stands on soft 17. The
house has an edge of 1–10 percent against typical players. The strategy of mimicking the

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the kelly criterion with games of chance
413
dealer loses about 8 percent because the player must hit ﬁrst and busts about 28 percent
of the time (0.282 ≃0.08). However, in Las Vegas the average player loses only about
1.5 percent. The edge for a successful card counter varies from about −5 percent to
+10 percent, depending on the favorability of the deck. By wagering more in favorable
situations and less or nothing when the deck is unfavorable, an average weighted edge
is about ½–2 percent.
An approximation to provide insight into the long-run behavior of a player’s fortune
is to assume that the game is a Bernoulli trial with a probability of success p = 0.51
and a probability of loss 1 −p = 0.491 −p = 0.49′′−= 0.49. Then with outcomes
 = {0,1} , the payoffs are K(0,x) = x with probability p, and K (1,x)= −x with
probability 1 −p1 −p “–”. The mean growth rate is Elog (1+K(w,x)) = plog (1 + x) +

1 −p

log (1 −x). The optimal ﬁxed fraction strategy is x∗= 2p −1 if EK > 0; x∗=
0 if EK ≤0. This optimal strategy may be interpreted as the edge divided by the odds
(1–1 in this case). In general, for two outcome win-or-lose situations where the size of
the wager does not inﬂuence the odds, the same edge divided by the odds formula holds.
Hence with a 2 percent edge, betting on a 10–1 shot, the optimal wager is 0.2 percent
of one’s fortune. The growth rate of the investor’s fortune is shown in ﬁgure 22.2. It
is nearly symmetrical around x∗= 0.02. A security measure is also displayed in ﬁgure
22.2 in terms of the probability of doubling or quadrupling before halving. Since the
growth rate and the security are both decreasing for x > x∗, it follows that it is never
advisable to wager more than x∗. However, one may wish to trade off lower growth
for more security using a fractional Kelly strategy. For example, a drop from p = 0.02
to 0.01 for a 0.5 fractional Kelly strategy decreases the growth rate by 25 percent but
increases the chance of doubling before halving from 67 to 89 percent.
1.0
Probability
Relative growth
Prob. double
before half
Prob. quadruple
before half
Optimal Kelly wager
Fraction of Wealth Wagered
0.8
0.6
0.4
0.2
0.0
0.0
0.01
0.02
0.03
figure 22.2 Relative growth versus probability of doubling before halving (blackjack).

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betting strategy
In the blackjack example, the additional information provided by the security mea-
sure was important in reaching a ﬁnal investment decision. In a ﬂexible or adaptive
decision environment competing criteria would be balanced to achieve a satisfac-
tory path of accumulated wealth. Professional blackjack teams often use a fractional
Kelly wagering strategy with the fraction = 0.2 to 0.8. See Gottlieb (1985) for further
discussion including the use of adaptive strategies.
4.2 Horse Racing
In a race with n horses there are positive returns for show wagers made on the ﬁrst three
ﬁnishers. The set of all outcomes with probability pijk is  = (1,2,3),...“...”, (i,j,k),...
“...”, (n−“−”2,n−“−′′1,n). If is the probability that horse i wins, then Harville (1973)
gave the probability of an (i,j,k) ﬁnish as pijk =
qiqjqk
(1−qi)(1−qi−qj) = qi ×
qj
1−qi ×
qk
1−qi−qj .
That is the probability that i wins times the probability that j wins a race without i times
the probability that k wins a race that does not contain i or j. (For a bias correction to
the Harville formulas see Hausch, Lo, and Ziemba 1994/2008. The bias comes from the
fact that horses that do not win come in less frequently for second and third than the
Harville formulas suggest. The correction replaces qj and qk by0qj =
qa
j
qa
k , 0qk =
qa2
k
qa2
j
,
respectively. The selection a = 0.81 is recommended.) An investor wagers the fractions
(xi1,xi2,xi3) of his or her fortune w0 on horse i to win, place, and show, respectively.
One collects on a win bet when the horse is ﬁrst, on a place bet when the horse is ﬁrst or
second, and on a show bet when the horse is ﬁrst, second, or third. The order of ﬁnish
does not matter for place and show bets. All bettors, wagering on a particular horse,
share the net pool in proportion to the amount wagered, once the original amount
of the winning bets are refunded and the winning horses share equally the resulting
proﬁts.
A particular anomaly is the place and show wager (Ziemba 1987). Let the player bets
be (xi2,xi3) for horse i to place and show, respectively. Also let (Xi2, Xi3) be the total
place and show bets of other people and the particular (i,j,k) outcome is
K

i,j,k

,x

= Q

X2 + n
l=1 xl2

−

xi2 + xj2 + Xi2 + Xj2

2
×

xi2
xi2 + Xi2
+
xj2
xj2 + Xj2

+ Q

X3 + n
l=1xl3

−

xi3 + xj3 + xk3 + Xi3 + Xj3 + Xk3

3
×

xi2
xi3 + +Xi3
+
xj3
xj3 + Xj3
+
xk3
xk3 + Xk3

+ w0
−
⎛
⎝
n

l=1,l̸=i,j,k
xl2 +
n

l=1,l̸=i,j
xl3
⎞
⎠+ γ
 n

l=1
xl2 +
n

l=1
xl3

.

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## Page 436

the kelly criterion with games of chance
415
where Q = 1−the track take and γ is the rebate fraction. This return function is
developed in Hausch, Ziemba, and Rubinstein (1981). The return is net of transactions
costs (track take) and includes the track rebate and the effect of bets on the odds.
The optimal Kelly wager is determined from the problem
Maxl
⎧
⎨
⎩
n

i=1
n

j=1,j̸=i
n

k=1,k̸=i,j

pi,j,klog

K

i,j,k

,x

⎫
⎬
⎭
subject to
n

i=1
(xi2 + xi3) ≤w0.
xi2 ≥0,xi3 ≥0, i = 1,...,n.
The Kelly bet test was performed in 2004 by John Swetye and William Ziemba, who
searched for bets at 80 U.S. racetracks Ziemba and MacLean (2011). A $5,000 initial
wealth returned a proﬁt of $30,000. There was a lot of churning, with a total of more
than $1.5 million bet. The Dr Z system actually lost 7 percent, but with a rebate of
9 percent there was a 2 percent gain. Figure 22.3 presents the wealth trajectory, with a
comparison to the outcome for fractional wagers of 1
2 Kelly and 1
3 Kelly. The smaller
betting fractions provide more security but have less growth and lower ﬁnal wealth.
Implicit in the above example is the ability to identify races where there is a substantial
edge in the bettor’s favor. There has been considerable research into that question
(as surveyed by Hausch, Lo, and Ziemba 1994/2008; Hausch and Ziemba (1985, 2008)).
30000
25000
20000
15000
10000
5000
0
2/9/02
2/16/02
2/23/02
3/2/02
3/9/02
3/16/02
3/23/02
3/30/02
4/6/02
4/13/02
4/20/02
4/27/02
5/4/02
5/11/02
5/18/02
5/25/02
BRFull
BR1/2
BR1/3
figure 22.3 Wealth results for Dr Z place and show bets in 2004.

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416
betting strategy
Donald Hausch et al. (1981) demonstrated the existence of anomalies in the place and
show market. At thoroughbred racetracks, about 2–4 proﬁtable wagers with an edge of
10 percent or more exist on an average day. The proﬁtable wagers occur mainly because
(1) the public has a distaste for the high probability–low payoff wagers that occur on
short-priced horses to place and show and (2) the public is unable to properly evaluate
the worth of place and show wagers because of their complexity—for example, in a
10-horse race there are 120 possible show ﬁnishes, each with a different payoff and
chance of occurrence. In Hausch et al. (1981) and more fully in Hausch and Ziemba
(1985), equations were developed that approximate the expected return and optimal
Kelly wagers based on minimal amounts of data to make the edge operational in the
limited time available at the track. The Kentucky Derby is discussed by Bain, Hausch
and Ziemba (2005).
The bias correction to probabilities of second and third (Hausch, Lo, and Ziemba
1994/2008) approximately cancels the favorite-longshot bias, where long shots have
lower expected value and favorites have higher ones for place and show bets. However,
this bias is important in other wagers. (For more information on the favorite-longshot
bias refer to Hausch and Ziemba 2008).
Since the Dr Z system was derived in the 1980s it has changed the character of the
place and show and other racetrack betting markets. The recent changes have to do
with the rebate—the return of a fraction of the amount bet, long, and short betting
in Betfair in London and other locales. Track betting, some of which is done by well-
funded racing syndicates, has become a tougher market to win; see Benter (1994), who
discusses the world’s most successful such syndicate. See Ziemba (2014) for more details
on various racetrack bets.
4.3 Lotto Games
In lotto games players select a small set of numbers from a given list. The prizes are
shared by those with the same numbers as those selected in the random drawing. The
lottery organization bears no risk in the pari-mutuel system and takes its proﬁts before
the prizes are shared. Hausch and Ziemba (1995, 2008) surveyed these games. Ziemba
et al. (1986) studied the 6/49 game played in Canada and several other countries. (The
analysis was updated in Ziemba 2008 and other papers in Hausch and Ziemba 2008).
Numbers ending in eight and especially nine and zero tend to be unpopular. Six tuples
of unpopular numbers have an edge with expected returns exceeding their cost. The
expected value approaches $2.25 per dollar wagered when there are carryovers (that is,
when the Jackpot is accumulating because it has not been won.) However, investors
may still lose because of mean reversion (the unpopular numbers tend to become less
unpopular over time) and gamblers’ ruin (the investor has used up his resources before
winning). MacLean, Ziemba, and George Blazenko (1992) investigated how an investor
might do playing sets of unpopular numbers with a combined advantage using the data
in table 22.6.

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the kelly criterion with games of chance
417
Table 22.6 Lotto 6/49 Data
Prizes
Prob
Value
Contribution %
Jackpot
1/13983816
$6M
42.9
Bonus
1/2330636
$0.8M
34.3
5/6
1/55492
$M
9.0
4/6
1/1032
$5,000
14.5
3/6
1/57
$150
17.6
Edge
18.1%
Kelly bet
0.00000011
Number of Tickets with 10M bankroll
11
Source: MacLean, Ziemba, and Blazenko (1992).
The optimal Kelly wagers are extremely small. The reason for this is that the bulk of
the expected value is from prizes that occur with less than one in a million probability.
A wealth level of $1 million is needed to justify even one $1 ticket. Figure 22.4 pro-
vides the chance that the investor will double, quadruple, or tenfold this fortune
before it is halved using Kelly and fractional Kelly strategies. These chances are in
the range of 40–60 percent. With fractional Kelly strategies in the range of 0.00000004
and 0.00000025 or less of the investor’s initial wealth, the chance of increasing one’s
initial fortune tenfold before halving it is 95 percent or more. However, it takes an
average of 294 billion years to achieve this goal, assuming there are 100 draws per year
as there are in the Canadian lotto 6/49.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0E+00
9.7E–08
1.9E–07
2.9E–07
Tenfold
Quadruple
Double
Growth rate
Probability
Optimal Kelly wager
Fraction of wealth wagered
figure 22.4 Lotto 6/49—Probability of multiplying before losing half of one’s fortune versus
bet size.
Source: Maclean, Ziemba, and Blazenko (1992).

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## Page 439

418
betting strategy
The conclusion is that except for millionaires and pooled syndicates, it is not possible
to use the unpopular numbers in a scientiﬁc way to beat the lotto and have high
conﬁdence of becoming rich; these aspiring millionaires are also most likely going to
be residing in a cemetery when their distant heir ﬁnally reaches the goal.
4.4 Investing in the Turn-of-the-Year Effect
The trade-off between growth and security with the Kelly criterion was used by Ross
Clark and Ziemba (1987) in their analysis of investment in the turn-of-the-year effect in
the futures markets. The excess return of small cap stocks minus large cap stocks is most
pronounced in January. The distribution of gains at the turn of the year from holding
long positions in the Value Line futures Index of small stocks and short positions in the
Standard & Poor’s (S&P) futures index of large cap stocks is given in table 22.7, where
each point is worth $500. The data covers the period 1976–1977 to 1986–1987.
The Kelly strategy calculated from this distribution invests 74 percent of one’s fortune
in the trade. This is very aggressive considering the possible estimation errors and the
market volatility.
In ﬁgure 22.5 is a graph for fractional Kelly strategies with the turn-of-the-year trade,
showing the chance of reaching a wealth of $10 million before ruin, starting from
various initial wealth levels. The graph for 0.25 Kelly is much more secure. Similarly
in ﬁgure 22.6, the trade-off between relative growth and probability of achieving a
desired wealth level is displayed. Going from Kelly to quarter Kelly realizes a probability
gain (security) of about 0.25 and an almost equivalent loss in relative growth. Ziemba
used an approximate 0.25 Kelly strategy with consistent success in actual trades on this
commodity in the 14 years from 1982/1983 to 1996/1997, winning each year.
Because the declining Value Line volume makes the trade risky, Ziemba did not
participate in the trade from 1997 to 2008; see Ziemba (1994), Hensel and Ziemba
(2000), Rendon and Ziemba (2007), and Ziemba (2011). An update on the turn-of-
the-year effect is provided in Ziemba (2012), including successful trades of the turn-of-
the-year effect in 2009, 2010, and 2011 using the Russell 2000 small cap futures index
(long) and the S&P large cap futures index (short). Figure 22.7 shows the performance,
where 100K grew to 147K in two years. See the large portfolio jumps on the far left and
far right plus the middle jump for the three turn-of-the-year trades in the Anomalies
Test Account. An interesting aspect of this anomaly is the shift from January to a
December effect.
Table 22.7 Returns Distribution for VL/S&P Spread
Point Spread
7
6
5
4
3
2
1
0
−1
Probability
.007
.024
.07
.146
.217
.229
.171
.091
.045

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## Page 440

the kelly criterion with games of chance
419
1.0
Probability
Growth Rate
Double
Triple
Tenfold
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Investment Fraction
figure 22.5 Turn-of-the-year effect: Probability of reaching $10 million before ruin for Kelly,
half Kelly, and quarter Kelly strategies.
Source: MacLean, Ziemba, and Blazenko (1992).
1.0
Probability
1/4 Kelly
1/2 Kelly
Kelly
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
10
Wealth
figure 22.6 Relative growth versus probability of goal attainment.
Source: MacLean, Ziemba, and Blazenko (1992).

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## Page 441

420
betting strategy
15
14
13
12
11
10
9
Nov 2009
Nov 2010
S&P
WTZ
Nov 2011
figure 22.7 Private account of WTZ using anomalies, 2009–2011.
5 The Great Investors
.............................................................................................................................................................................
A large game of chance is the stock market. Much has been written about the efﬁciency
of the market, but clearly there are opportunities for excess returns. (Ziemba 2012
surveys U.S. calendar anomalies.) The legends of investing have a number of common
features: excellence in selecting/evaluating opportunities, focus, deep pockets to ride
out downturns, and successful investment strategies. Interestingly some great investors
have followed a Kelly type investment strategy. The outperformance of some legends
is documented in this ﬁnal section. Details on these and other investors is given in
Gergaud and Ziemba (2012).
5.1 John Maynard Keynes
Keynes ran the King’s College, Cambridge University, endowment fund from 1927 until
1945. Ziemba (2003) estimated that Keynes had about an 80 percent Kelly or a negative
power utility of u(w) = −w−0.25. That is an aggressive strategy, and he lost a lot (over
50%) in the early years. The trajectory of the Cambridge Chest is shown in ﬁgure 22.8.
Over the 19 years of his management, the fund had a geometric mean return of
9.12 percent compared to the market index of −0.89 percent. So he had superior
long-term performance.

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the kelly criterion with games of chance
421
600.0
500.0
400.0
300.0
Return
200.0
100.0
0.0
1926
1928
1930
1932
1934
1936
1938
1940
1942
1944
1946
Year
UK Market
T-Bill
Chest
figure 22.8 Portfolio performance: Keynes.
Source: Ziemba (2005).
5.2 Warren Buffett and George Soros
Two full Kelly investors who hold few and concentrated positions are the famousWarren
Buffett and George Soros. The wealth paths for their funds, Berkshire Hathaway and
Quantum, respectively, are shown in ﬁgure 22.9. As with Keynes, these billionaire
Value
1000.00
100.00
86
88
90
92
94
96
98
Year
Quantum
Berkshire-Hathway
figure 22.9 Portfolio performance: Buffett and Soros, 1985–2000.
Source: Ziemba 2005.

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## Page 443

422
betting strategy
15
Price (U.S. dollars)
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
11/68
10/73
11/77
10/81
10/85
12/88
U.S. T-Bill
S&P 500
PNP
figure 22.10 Portfolio performance: Thorp.
Source: Ziemba 2005).
investors had many gains but also many losses. Out of the 172 months represented in
the ﬁgure, Berkshire Hathaway had 58 and Quantum 53 losing months. However, the
gains were very high, as happens with the Kelly strategy. Both funds had annual growth
rates in excess of 15 percent during the years 1977 to 2005.
5.3 Edward O. Thorp
Ed Thorp is famous for his work on blackjack and for applying his ideas on mispriced
options and warrants and the growth optimal approach to the stock market (Rotando
and Thorp 1992, Thorp and Kassouf 1967). In fact he coined the term “fortune’s
formula” for the Kelly strategy. Thorp ran the Princeton Newport Partners (PNP)
hedge fund from 1968–1988. He had an amazing record of just three monthly losses
over a 20-year period. The smooth path of PNP is presented in ﬁgure 22.10. The fund
had an annual growth rate of 13.5 percent, a bit lower than that of Buffett and Soros
but without dips. Thorp’s later results in other hedge funds are equally impressive.
5.4 James Simon
The Renaissance Medallion fund uses ideas such as the Kelly criterion to achieve
superior returns. Working under mathematician James Simons, a staff of technical
researchers and traders devises edges to generate successful trades, most of which are
short-term (lasting only seconds). Amazingly, the fund had only 17 monthly losses
in 148 months, 3 losses in 49 quarters, and zero losses in 12+ years of trading to

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## Page 444

the kelly criterion with games of chance
423
6000
Total
Renaissance Medallion
5000
4000
3000
2000
1000
00
50
100
150
Month
figure 22.11 Portfolio performance: Simons.
Source: Ziemba and Ziemba 2007).
2005. So Renaissance Medallion had an annual growth rate of more than 30 per-
cent, and the path slope is basically monotone increasing (ﬁgure 22.11). (See Ziemba
and Ziemba 2007 for an analysis of this fund and Gergaud and Ziemba 2012 for an
update.)
6 Conclusion
.............................................................................................................................................................................
The Kelly strategy, where the expected logarithm of returns is maximized, subject to
constraints on betting proportions, has a rich tradition in the analysis of games of
chance. The strategy has many desirable properties that are mainly related to long-run
asymptotic growth. Use of this strategy over many plays of favorable games usually
results in unparalleled wealth. However, the strategy is aggressive since its Arrow–
Pratt risk aversion index is essentially zero. This leads to violent wealth paths, and a
string of bad luck can wipe out the bettor. Smoother wealth paths are obtained with
fractional Kelly strategies that blend the Kelly strategy with cash. This chapter has
presented the concepts in the Kelly strategy and described its good and bad properties.
The strategy and its fractional Kelly modiﬁcation have been applied to some familiar
games of chance, such as blackjack, horse racing, commodity markets, and lotteries.
The growth and security aspects of the strategy have been illustrated with tabulations
and graphs, and the records of some great investors that have Kelly-like portfolios have
been presented.

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betting strategy
References
Algeot, Paul H., and Thomas M. Cover. 1988. Asymptotic optimality and asymptotic
equipartition properties of log-optimum investment. Annals of Probability 16(2):876–898.
Aucamp, Donald C. 1993. On the extensive number of plays to achieve superior performance
with the geometric mean strategy. Management Science 39(9):1163–1172.
Bain, Roderick S., Donald B. Hausch, and William T. Ziemba. 2006. An application of expert
information to win betting on the Kentucky derby, 1981–2005. European Journal of Finance
12(4):283–301.
Bell, Robert M., and Thomas M. Cover. 1980. Competitive optimality of logarithmic
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chapter 23
........................................................................................................
EXPLOITING EXPERT ANALYSIS?
EVIDENCE FROM EVENT STUDIES
IN AN INFORMATION-RICH
MARKET ENVIRONMENT
........................................................................................................
michael a. smith
Introduction
.............................................................................................................................................................................
Almost ten years ago I conducted a study of horse racing tipsters, focusing primarily
on Pricewise of the Racing Post (Smith 2003).1 The study sought to evaluate the record
of media forecasters in selecting winners, with returns judged against the benchmark
of information efﬁciency as speciﬁed in the efﬁcient-market hypothesis (Fama 1970).
TheideabehindthePricewisecolumnistoidentifyoverlays,thatis,horseswhosetrue
probability of winning is understated by the market odds. The column recommends
an average of between two and three win bets on a typical Saturday, sometimes more
than one in a race, with additional midweek tips for prestige meetings, such as Royal
Ascot. Selections are mostly restricted to races of high public interest, associated with
high betting turnover, which along with the reputation of the column serve to further
the goal of maintaining acceptable or high circulation of the newspaper. Pricewise has
been portrayed in the media as a feature that leads to signiﬁcant odds movements,
and it claims to be a notably proﬁtable column, which has been a successful feature
of the Racing Post’s racing coverage since that paper’s inception in the mid-1980s.
Pricewise’s function and status in U.K. racing are comparable to those of, for example,
the Value Line research organization with respect to ﬁnancial investments. Pricewise
selections are routinely reported on Channel 4’s Morning Line racing program as well
as its afternoon racing coverage, always in the context of reported odds movements.
I visited the Racing Post’s ofﬁces in Canada Square (Canary Wharf, London) 10 years

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429
ago and was impressed by the range of information resources available to journalists
working on the paper. Subsequent technological developments can be expected to have
further enhanced the arsenal of information sources and analytical capabilities of such
media experts.
The prior analysis alluded to above found that newspaper tips appeared to have a
signiﬁcant impact on odds movements from early morning to starting price2 (SP) and
that knowledge of Pricewise selections in particular was a useful predictor of large
contractions in odds. Furthermore the performance of such horses was understated by
the best available early morning odds, indicated by high positive returns at those odds.
The high rates of return to Pricewise horses at the best early odds suggested that the
bookmakers’ initial appraisal of the chances of these horses was erroneous and that the
Pricewise assessment superior.
The evidence suggested that media journalists have a high degree of expertise and/or
privileged information in regard to such runners relative to the early bookmaker assess-
ment, at least concerning some runners. The returns at SP for such horses, however,
though proﬁtable, were not signiﬁcantly different to zero, implying semi-strong form
efﬁciency with respect to ﬁnal odds. A number of other studies have found that pari-
mutuel ﬁnal odds and SP, in relation to U.S. and U.K. horse racing, respectively, are
efﬁcient in discounting published factual information and published race forecasts
based on expert analysis (Figlewski 1979; Vaughan Williams 2000).
The prior Smith study did not consider evidence concerning market efﬁciency with
respect to arbitrage opportunities as the market progresses from media publication
time to race time. Thus a systematic analysis of odds over time, rather than two points
in time, is desirable to chart the dynamics of the market. The more quickly early odds
assimilate the information held in media forecasts, the more informationally efﬁcient
the market is.
The purpose of this chapter is to update, with a new and bigger dataset, the analy-
sis of Pricewise in order to establish whether or not the feature’s impressive record
has been maintained and to exploit new market information sources that permit
insights into the dynamics of horse race betting markets over time to reveal the
extent of arbitrage opportunities with respect to the Pricewise selections. This will
permit a fuller evaluation of the degree of information efﬁciency in relation to these
“events.”
First I will consider an abstract framework for judging the degree of information
efﬁciency with respect to the “events” impacting the market for individual horses, in
thiscaseselectionbyPricewise. Thereadershouldbearinmindthattheoddsconsidered
before commencement of the event, when SP rules, are known and ﬁxed at the point
of wager. Further, arbitrage/hedging trades of betting assets are now possible via the
medium of betting exchanges in those countries where such market formats are legal;
the discussion which follows assumes use of the exchanges, and the mechanism of such
trading is considered in a later section.
Figure 23.1 charts some of the possible paths of odds over time from publication of
media race selections at time t1 on the x axis to race commencement at t2. Odds are

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betting strategy
O2
F
O1
A
B
C
D
Odds
t1
Time
t2
E
figure 23.1 Alternative paths of odds to SP
represented on the y axis, with fair odds shown as F. Fair odds will vary with selections
by odds category, but for any odds level an efﬁcient SP market at t2 will yield zero proﬁt
at odds F over a representative number of selections. Should ﬁnal odds instead average
O1 long-term proﬁts will be earned, while average odds of O2 will lead to losses, both
cases representing semi-strong information inefﬁciency.
If odds A at the commencement of trading are known to systematically understate
the true chance of the outcome occurring, these odds will quickly contract on publica-
tion of the media selection. An informationally efﬁcient market will approximate the
path of odds to the event of AFD; variations on this L-shaped pattern are consistent
with efﬁciency provided they do not contain secondary or tertiary trends that can be
systematically exploited. The alternative path AD is not efﬁcient, as it permits bets to
be placed at high odds and subsequently laid off at lower odds. This hedging process is
equivalent to buying a claim to an asset at a low price then selling at a higher price.
The path AE depicts a case in which the market ﬁnds the Pricewise arguments for
the selection unconvincing and consequently the odds extend to race time; as odds F
are fair, the market would be wrong and ﬁnal odds of E would yield proﬁts. The earlier
study (Smith 2003) suggested that, in fact, this class of horse (drifters in the market)
leads to proﬁts very close to the average for all Pricewise selections at SP, suggesting that
the error of judgment lies in the Pricewise column, and the market is able to correct for
this error. In ﬁgure 23.1 this would be represented by a line parallel to AE culminating
in point D.
Finally, ABCD illustrates a situation where the information in the selection is quickly
assimilated by the market, followed by a period of overbetting and later correction,
perhaps by hedging trades as early back-to-win traders lay off at lower odds from point
C onward.
Clearly these paths, and other variations, may be observed in speciﬁc cases. For
semi-strong information efﬁciency to exist, however, proﬁtable arbitrage and hedging

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exploiting expert analysis?
431
opportunities must not be systematic and predictable. In the results section below the
actual path of price outcomes for a sample of Pricewise selections are considered.
The Betting Exchanges:
An Information-Rich Market Environment
.............................................................................................................................................................................
This section considers the nature and functionality of betting exchanges as a prelude
to analyzing market information relating to Pricewise selections. The exchanges are
information-rich in terms of odds, volumes traded at different odds, and sequence
of trades over time and therefore permit clear insights into the betting period before
and after publication of the Pricewise column. Similar market transparency is not
evident in the corresponding bookmaker markets largely because of lack of information
about trading volumes and uncertainty about the availability of odds (bookmakers
frequently impose strict bet limits in relation to advertised odds pertaining to Pricewise
selections).
In 2000 a small number of experienced city traders combined their expertise in sports
betting to create Betfair.While not the ﬁrst betting exchange, Betfair quickly established
itself as the market leader—it currently has approximately 90 percent of the betting
exchange market. Its turnover grew exponentially in the early years—growth generated
not only from market share taken from bookmakers but, in addition, from the inﬂux
of a new cadre of traders attracted to the potential proﬁts to be reaped from exploiting
price volatility in arbitrage and hedging activities; such growth could not be maintained
indeﬁnitely, and Betfair has now consolidated its position as the leading exchange and
a permanent and highly inﬂuential market mechanism in sports betting. Betfair is
the eBay of betting; it permits the many-to-many double auction of state-contingent
claims based on sporting events. It is Internet based and has spawned a whole new
derivative software industry in the development of associated applications and trad-
ing software that enhance and customize the primary properties of the site itself. This
related software permits market monitoring, order placing, direct trades, and hedging
to be executed on a range of mobile electronic devices, including mobile phones and
iPads in addition to desktops and laptops. Functionality will now be outlined, pri-
marily by reference to Betfair; other exchanges have similar characteristics with minor
variations.
A betting exchange does not act as market maker; rather it fulﬁlls broking and
exchange functions, displaying odds offered by layers and requested by bettors and
permitting execution of bets based on these odds. Layers wager that an outcome will
not happen, for example, a horse will lose, whereas backers wager to win, that is, that the
speciﬁed outcome will occur. The exchange itself assumes no risk, its income generated
from commission charged to clients, typically at a rate between 2–5 percent (most

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betting strategy
Betfair clients pay 5%, whereas high-volume traders pay less) applied to net winnings
on an event (horse race, cricket match, game of tennis—here, horse racing).
Clients can back a horse to win, lay a horse at speciﬁed odds, or request odds, all at
client-speciﬁed stake limits. Stakes are pooled by odds value so that individual matched
trades are not necessary, reducing the incidence of thin markets; trades and parts of
trades are allocated on a ﬁrst-requested and ﬁrst-offered basis. Betfair securely holds
monies corresponding to net potential liabilities, which must be fully funded from
clients’ accounts in advance of the event, thus ensuring the integrity of trades.
Once a race commences the market goes “in play.” Unmatched trades can be with-
drawn at this point or kept open. In play, that is, in running markets are characterized
by bigger aggregate margins (higher overround on the back side and underround on
the lay side), more frequent and rapid price movements, and greater price volatility
than pre-event markets.
Odds changes can be monitored directly or with dedicated trading software, some
of which is freely available from the Internet; much of this software downloads mar-
ket information from Betfair, updating at user-speciﬁed intervals of as little as once
per second. Automated trading is possible with such software, governed by decision
rules speciﬁed by the trader, often triggered by associated spreadsheets linked to the
software.
The ability to back and lay the same outcome also means that a range of hedg-
ing strategies, and arbitrage between the exchange and bookmaker markets, can
be employed by traders. Such extensive functionality, price transparency, and low
commission (relative to that implicit in bookmaker overround averaging over 1.5 per-
cent per runner in the United Kingdom) draws in serious bettors, reducing the
proportion of turnover attributable to casual bettors. As a consequence the mar-
ket is more efﬁcient, with low margins on the back and lay side. Price competition
increases with volume as the market progresses, thereby reducing the amount of
bias; Smith, Paton, and Vaughan Williams (2006) showed that unlike bookmaker
horse race markets, Betfair odds contain very little longshot bias. This result is
consistent with the literature on the economics of auctions (e.g., Klemperer 1999,
2004), which suggests that the decentralized nature of the decision-making processes
in such markets can accomplish the aggregation of information in a very efﬁcient
manner.
Figure 23.2 shows a typical Betfair horse race market shortly before going in play.
This race, run at Salisbury, was a modest handicap, which would attract relatively
low betting volumes in the bookmaker market compared to the higher class races
from which Pricewise selections are typically drawn. Nonetheless, the volume of
matched trades on Betfair (top right) for this race exceeded £300,000. To put this
in perspective, the tote win pool for this race amounted to only £8,428. The volume
traded on the exchange is so much greater than that in the tote pool because of the
large amount of trading that occurs in the exchanges, involving hedging strategies
of one form or another enabled by the possibility of backing and laying the same
outcome.

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exploiting expert analysis?
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figure 23.2 Example of a Betfair horse race market
The side of the display headed “Back” shows the best three prices available for each
runner being offered by layers to clients wishing to make win bets, with stake limits.
The stake limits are the pooled amounts various clients are prepared to accept on back-
to-win bets at the speciﬁed odds values. Prices on the exchange are expressed with a
unit stake included, so at this point in the market the best bet-to-win odds available
for Sciampin are 2.65/1 (3.65 minus 1, to a nominal unit stake) up to a maximum
stake of £949 (with a minimum stake requirement of £2). Should a client wish to offer
odds of 5.3 to 1 (price of 6.3) against Oriental Girl to a maximum of, say, £10, this
would become the new best price. Alternatively the client could specify an offer to lay
at lower odds, which would be pooled with existing values. The sum of probabilities
on the back side in the illustrated market stands at 101 percent, that is, 1 percent
overround, ensuring that a proﬁt cannot be earned by backing all runners to stakes
proportionate to odds probabilities. Should the book total less than one momentarily,
such “dutching” strategies will quickly mop up the higher odds across the ﬁeld until an
overround position is restored.
Similarly, on the lay side, prices represent invitations, or requests, to lay at higher
odds than are available on the back side—clients who place these orders wish to bet-
to-win but are not prepared to do so at odds indicated on the back side. Other clients
may choose to lay a horse at these odds should they believe that they overstate the
chances of that horse or as part of a hedging strategy. For example, a client who believes
that the true chance of Prime Mover winning is 20/1 may choose to lay that horse at
11.5/1 (12.5 minus 1), marginally higher than the best odds currently on offer, to a
stake of up to £80. The sum of probabilities on the lay side, based on the lowest odds
requested, stands at 98.1 percent, ensuring that a proﬁt cannot be guaranteed by laying
all horses to stakes proportionate to probabilities. Should this value temporarily exceed

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434
betting strategy
one, proﬁt-seeking traders will quickly eliminate the excess, laying all horses in the race
at the requested odds. Further details of betting exchange characteristics can be found
in Jones et al. (2006), Smith and Vaughan Williams (2008) and Koning and van Velzen
(2009).
Bettors may of course place conventional win bets on the exchanges as they would
with a bookmaker. The advantage to them is that on average Betfair odds exceed
bookmaker odds by more than the commission payable should the horse win; this is
particularly so in the case of long shots (horses with a low probability of winning). In
contrast, many traders attempt to lock in value arising from price movements, fully or
partially hedging back or lay bets against the ﬁeld.
Consider an initial back bet of stake sB made on a horse at exchange price pB,
corresponding to odds oB plus 1, and at a later time the back bet is partly or fully
hedged by laying the same horse at the lower price, pL equal to odds oL plus 1.
Assume that the trader aims to carry no net exposure to liabilities and that liquidity
at pL is sufﬁcient to achieve this aim. Let α be a hedging preference coefﬁcient reﬂecting
the degree of hedging across the ﬁeld sought by the trader, such that 0 ≤α ≤1.
Finally let r be the ration of best back to best lay prices, pB
pL
.
The value of sL wagered at pL is a function of the initial back bet, the relative back
and lay prices, and the hedging preference of the trader, as expressed in equation 23.1:
sL = sBr −α (sBr −sB)
= sB (r −α [r −1]).
(23.1)
If α = 0 the resulting lay trade hedges the initial bet fully against the ﬁeld and
the outcome is not state-contingent. Alternatively, if α takes a positive value the
paired trade closes the exposed position, but the monetary outcome remains state-
contingent. In the former case (α = 0) the trader will win an equal amount
whatever the outcome of the race. If α = 1, barring a dead heat, there are
two possible outcomes: zero proﬁt/loss if the horse loses and a proﬁt if he
horse wins. The proﬁt πW , should the horse win, is expressed in equations 23.2
and 23.3.
πW = sB

pB −1

−sL

pL −1

.
(23.2)
Substituting equation 23.1 in equation 23.2,
πW = sB

pB −1

−sB (r −α [r −1])
= sB

α

pB −pL

−[r −1][1 −α].
(23.3)
Should the horse lose, the net proﬁt on the paired trade, πL, is expressed in equations
23.4 and 23.5.
πL = sL −sB.
(23.4)

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Table 23.1 Outcomes of a Matched Trade with Various Degrees of Hedging
α
pB
pL
sB(£)
sL(£)
πW(£)
πL (£)
0
5
4.9
490
500
10
10
0.2
5
4.9
490
498
17.8
8
0.4
5
4.9
490
496
25.6
6
0.6
5
4.9
490
494
33.4
4
0.8
5
4.9
490
492
41.2
2
1
5
4.9
490
490
49
0
Substituting equation 23.1 in equation 23.4 to yield an expression containing α,
πL = sB (r −α [r −1]) −sB
= sB (r −α [r −1]) −1
= sB (r −1)(1 −α).
(23.5)
Table 23.1 shows a simple application of the above formulas, assuming bet and lay prices
for a horse of 5 and 4.9, respectively, with an initial back stake of £490. The impact on
proﬁts of different values of α is shown for the outcomes of the horse winning or losing.
The anticipated direction of price movement can of course be reversed, with a lay bet
being executed ﬁrst followed by a back bet to complete the paired trade. Rearrangement
of the above expressions permits calculation of back stake levels and their consequences
for proﬁts in such cases.
Variations of the above formal expressions are built into algorithms contained in
commercial derivative software that interfaces with the exchange markets, permitting
the various trader preferences and bet instructions to be executed.
Thesuccessof thetraderprimarilydependsontheabilitytopredictapricemovement
and its direction, when it will occur, and how long to leave exposed trades before closing
a position. Should a trader predict and bet on a price movement wrongly, he or she can
exit the trade as per the staking and proﬁt expressions above, but losses will be incurred
for one or other of the win/lose race outcomes. These factors will be considered below
in relation to the charts showing the dynamics of prices over time for a number of
Pricewise selections.
Results and Discussion
.............................................................................................................................................................................
The original sample from the Smith (2003) study, covering the period 1998–2000,
is referred to as sample 1; for the new database covering 2002–2011, sample 2.

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betting strategy
Table 23.2 Statistics for Pricewise Selections, 1998–2000 and 2002–2011
Sample 1 (1998–2000)
Sample 2 (2002–2011)
N
344
591
Average odds (early max)
14.3/1
12.9/1
Average odds (SP)
9.7/1
8.4/1
Average winning odds
(early max)
10/4/1
8.9/1
Average winning odds (SP)
6.8/1
5.8/1
Winning strike rate
(winners/runners)
0.1424
0.1506
Price movement from
early max odds to SP
−0.043∗∗∗
(0.0025)
−0.054∗∗∗
(0.0022)
Sample 1 Returns
Sample 2 Returns
Early Max
Starting
Price
Early Max
Starting
Price
Unit stake
0.617
0.118
0.497
0.023
Unit stake after
deductions
0.520
0.051
0.497
0.023
Unit stake (weighted by
odds probability)
0.559∗∗∗
(0.2058)
0.113
(0.1467)
0.421∗∗∗
(0.1441)
0.115
(0.1046)
Unit stake (weighted),
after deductions
0.466∗∗
(0.1934)
0.046
(0.1379)
0.421∗∗∗
(0.1441)
0.115
(0.1046)
Note: Values in parentheses are robust standard errors.
∗∗denotes p = 0.05.
∗∗∗denotes p = 0.01.
Comparisons between sample 1 and sample 2 are initially facilitated by reference to
bookmaker odds, as exchanges did not exist during the sample 1 period.
The descriptive statistics of odds and returns are summarized in the ﬁrst seven rows
of table 23.2. Average odds of Pricewise horses at both best early odds (early max)
and at SP are lower in sample 2 than in sample 1, possibly an indirect consequence
of the reduction in average ﬁeld sizes in U.K. racing between the two periods (Smith
and Vaughan Williams 2010). This tendency is also reﬂected in the lower average SP
of winning Pricewise selections and increased strike rate in the latter period. All these
aspects can be explained by declining runners per race as opposed to strategic changes
in the approach of the column, which are otherwise not evident.
Odds movements from early max to SP for each Pricewise horse were recorded in
both datasets by means of a measure, pm, adapted from Law and Peel (2002), shown

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in equation 23.6.
pm = log

1
1 −p1

−log

1
1 −p2

,
(23.6)
where p1is the odds probability corresponding to the early maximum odds available for
aPricewiseselectionandp2 istheoddsprobabilityatSP.Thevirtueof thismethodisthat
it places greater emphasis on movements from shorter odds and therefore more closely
approximates a trade-weighted measurement. A negative value of pm indicates that the
Pricewise selection contracted from early odds to SP; the mean values for samples 1 and
2 are −0.043 and −0.054, respectively. To add perspective to these numbers, a value
of −0.05 corresponds to a contraction from 20/1 to 10/1 against or from 6/1 to 9/2
against. The odds against Pricewise selections therefore typically contract substantially
from early morning to SP.
Table23.2showsthatPricewiseselectionsduringbothperiodsearnedpositiveproﬁts,
to a unit stake, of around 50 percent at early max odds, even after deductions in the
case of sample 1.3 The corresponding returns at SP are much lower, as a consequence
of strong odds contraction, but remain positive, even after deductions in sample 1. In
ordertogeneratemeasuresof statisticalsigniﬁcancetheunitstakereturnswereweighted
by the reciprocal of the odds plus one to reduce the impact of heteroskedasticity. All
returns at early max odds are signiﬁcant at p = 0.05 or better, though the SP positive
proﬁts are insigniﬁcant. The before deductions SP returns are similar between the two
samples, however, and are suggestive of a semi-strong form inefﬁciency.
Table 23.3 shows the results of tests of independence between the two sets of sample
returns at both sets of odds. There is no evidence of signiﬁcant differences in mean
returns between the samples, although the contraction of odds from early max to SP in
sample 2 appears to have become more marked than in sample 1.
Overall the evidence from this comparative study of returns strongly suggests that it
is possible for an expert to identify wrongly priced horses yielding high positive proﬁts
prior to public dissemination of the selection decisions. The possibility of subsequent
undervaluation of the information contained therein at ﬁnal market odds also remains
open, given the continued positive SP returns across the two samples, their lack of
statistical signiﬁcance notwithstanding.
Exchange prices and traded volumes were acquired for 193 Pricewise horses that ran
during the period September 2010–July 2011, a subset of sample 2 outlined above, with
Table 23.3 Difference of Sample 1 and Sample 2 Means: Independent Sample
T -test Results
Early Max (t-values)
Starting Price (t-values)
Unit stake (weighted by odds probability)
0.27
−0.047
Unit stake (weighted), after deductions
−0.092
1.10
Price movement from early max odds to SP
−24.03∗∗∗

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betting strategy
the paths of exchange prices charted from the commencement of each market through
time of publication of the Pricewise selections and the remainder of the pre-event
trading period. Detailed market data were sourced from Fracsoft, an organization
which employs specialist software to record the exchange markets for most of their
duration. Recordings begin typically between 8.30 a.m. and 10 a.m. on the day of the
race, tracking the remainder of the pre-event period and continuing into the in play
segment through to the conclusion of the race. Only the pre-event data were required
for the current study.
The problem with this data source is that the column is published, both in the hard
copy Racing Post and on the corresponding website, some time prior to the commence-
ment of Fracsoft recordings. Newspaper outlets nationwide typically will hold stocks
of the paper from 5 or 6 a.m., early editions being available in London and its region
much earlier. A market recording that commences at 8.30 a.m. will therefore not trace
impacts at the point of publication. To overcome this problem, additional price data
from early in the pre-event market period were acquired direct from Betfair’s historical
data electronic archive for the analyzed races. These additional data have their own
limitations in that for each horse only ﬁrst and last times traded for each price are
given along with aggregate amounts traded by price per horse across the whole of the
market period for these prices. Prior to the time of the detailed Fracsoft recordings,
therefore, the corresponding segments of the charts derived from the data exhibit node
points in an envelope encompassing ﬁrst- or last-price values traded over time, with no
details of price ﬂuctuations over time at values already traded. Nonetheless it is possible
to reconstruct primary price movements during the early market period sufﬁcient to
observe the ostensible impact of Pricewise selections before and after their publication.
Figures 23.3 through 23.7 depict exchange price movements for ﬁve Pricewise selec-
tions chosen from the 193 charts constructed as exemplars of frequently occurring
patterns. There are some clear characteristics evident in the pattern of exchange price
movements that apply to the vast majority of Pricewise selections. First, prior to publi-
cation of the column’s tips they are often subject to initial speculative offers of low odds
when the market opens, usually on the day before the races are scheduled to be run.
Of course at this point there is no public knowledge of the Pricewise tips, which are
published the following day. The offer of poor odds at the start of the market for the
majority of a ﬁeld of runners, with resulting high levels of overround, is commonplace
on the exchanges. This tendency can be seen in four of the ﬁve exemplar charts for
Pricewise horses. As competition and liquidity increase, more realistic prices for most
runners in the typical ﬁeld will be offered quite quickly following this initial period,
again evident in the charts.
Following this early period of speculative pricing, inspection of the path of prices
for Pricewise horses reveals a second phase during which there is, in the majority of
cases, a sustained contraction in exchange odds. Of the 193 horses for which charts
were constructed, 85 percent revealed a marked reduction in odds at this stage of the
market. The exact timing of such market support varies considerably, as shown in table
23.4, which details the distribution of days/times when these sustained odds reductions

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12
10
8
6
4
2
Two Minute Time Periods
Volume
Odds
8
7.5
6.5
6
5.5
5
4.5
4
Odds + 1
7
Log Volume (£s)
0
1
9
17
25
33
41
49
57
65
73
81
89
97
105
113
121
129
137
145
153
161
169
177
185
193
201
figure 23.3 Steamer
Horse: Desert Law
12.5
11.5
10.5
9.5
8.5
7.5
6.5
5.5
Odds + 1
12
10
8
6
4
2
Two Minute Time Periods
Log Volume (£s)
0
1
9
17
25
33
41
49
57
65
73
81
89
97
105
113
121
129
137
145
153
161
169
177
185
193
201
Volume
Odds
figure 23.4 S-Shaped
Horse: Minella Four Star
commence; the ﬁrst and last time traded data accessed directly from Betfair enable
easy identiﬁcation of these changes in primary trend. The ﬁve exemplar charts exhibit
marked odds contractions of this type, generally following the initial speculative pricing
period and prior to the period of Fracsoft recording.
Only 15 percent of observed charts exhibited no signiﬁcant contraction; this category
also includes observed contractions which were judged to be consistent with subsequent

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betting strategy
Two Minute Time Periods
1
10
0
3
5
7
9
11
13
15
17
2
4
6
Log Volume (£s)
Odds+ 1
8
10
12
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
181
190
199
208
217
226
Volume
Odds
figure 23.5 L-Shaped
Horse: Hawkeyethenoo
Two Minute Time Periods
Log Volume (₤s)
0
2
4
6
8
10
12
5.5
6
7
Odds+ 1
6.5
7.5
8
8.5
9
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
Volume
Odds
figure 23.6 Cup-Shaped
Horse: Pastoral Player
price volatility and trends in the odds over time for the horses concerned and for that
reason were not counted as signiﬁcant.
To further consider the remaining 85 percent of observations that did contract, a
word on distribution arrangements for the Racing Post is in order. A consequence of
the overnight declaration system whereby runners for the following day’s races must
be declared by trainers by midday on the day prior to the races is that full and focused

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Two Minute Time Periods
Volume
Odds
1
10
0
7
9
11
13
15
17
19
21
1
2
3
4
5
Log Volume (£s)
Odds+ 1
6
7
8
9
10
19
28
37
46
55
64
73
82
91
100
109
118
127
136
145
154
163
172
181
190
199
208
217
226
figure 23.7 Drifter
Horse: Empirico
coverage of a day’s race meetings by Racing Post cannot feasibly be published prior
to the day of the races concerned. Racing Post hard copy is distributed early on the
morning of the races to be run that day, typically as early as 5 a.m. via newspaper
outlets nationwide. Distribution in London may begin earlier than this, and therefore
midnight to 5 a.m. is assumed here as the period of initial distribution. Racing Post tips
are also made available online but not until well after hard copy distribution commences
so as not to compromise circulation ﬁgures of the newspaper.
Table 23.4 shows that only 18.6 percent of charts surveyed exhibited a marked con-
traction in odds commencing in the post-distribution period (from midnight of the
day of the races onward). As many as 11.4 percent of the observations exhibited sharp
Table 23.4 Starting Time of Odds Contractions (Primary Trend)
Time
Frequency
Percentage of Total Charts Surveyed
Two days before the race
22
11.4
Morning of day before race
9
4.7
1200<1600, day before race
34
17.6
1600<2000, day before race
74
38.3
2000<midnight, day before race
16
8.3
Midnight<0500, day of race
3
15.5
0500 or later, day of race
6
3.1
No evidence of signiﬁcant contraction
29
15.0
Total
193

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betting strategy
contractions in price commencing two days before the races concerned were run,
typically being races attracting substantial ante post betting interest. Whereas Pricewise
does give ante post recommended bets for some races, the present study excluded these,
being careful to include only tips published on the relevant race day, the better to iden-
tify potential cause and effect in an event study methodology. Most primary trend price
contractions commenced in the period from noon to 8 p.m. (1200 < 2000) of the day
prior to publication, accounting for 56 percent of the charts surveyed. Most of the sub-
sequent price contraction in such cases appears to have occurred by the time Fracsoft
recording commences, typically between 8.30 and 10 a.m. on race day, at which point
a new lower price ﬂoor characterized by less volatility compared to trading prior to
publication is invariably evident, at least until the ﬁnal 10 to 20 minutes of the market.
No explicit control against corresponding non-tipped horses was carried out, but the
fact that overround on odds offered decreases over time in these markets (levels of
50% or more are commonplace early in the market) to approaching zero at race time
implies that price extensions over time, not contractions, are the norm for runners in
general. More signiﬁcantly, actual trades as opposed to offers on average exhibit little
trend across the market as a whole.
There are several possible explanations for these strong price contractions prior to
publication.
1. One of the key criteria in the selection process for the Pricewise column may be
existing evidence of strong market support; that is, odds contraction precedes
selection, in which case the assumed cause and effect (that Pricewise selection
causes the relevant odds to contract) is reversed.
2. Pricewise selection and odds contraction are strongly associated but indepen-
dent, implying that market participants employ information search and analysis
techniques equivalent to those applied by the Pricewise column.
3. The exhibited price contractions arise from betting by insiders, having priv-
ileged knowledge of Pricewise horses prior to publication, either to retain
as win bets or to subsequently hedge following the anticipated reduction in
odds.
4. The explanation may lay in a combination of the above, as they are not mutually
exclusive.
Whatever the explanation, it would appear that watching the market in its early stages
for primary trend contracting odds, against the tide of general price extension through
competition between layers, may give signals as to which horses may turn out to be
Pricewise selections.
The phases of the market considered thus far have been conﬁned to the price envelope
containing ﬁrst and last odds value trades4 from Betfair’s historical data archive. The
discussion now moves to an examination of the remaining period of pre-event trading,
for which the charts depict exchange price values (odds plus one), traded at two-minute
intervals, and volumes wagered during those intervals. On the exemplar charts, ﬁgures

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Table 23.5 Advised Odds, SP, and Amounts Traded on Pricewise Horses in the
Exemplar Charts
Pricewise
Selection
(chart-depicted
horses only)
Bookmaker Odds
Advised and (SP)
Total Traded on
Horse Prior to
Commencement
of Fracsoft
Recording (£000)
Total Traded on
Horse at End of
Pre-Event Period
(£000)
Ratio of Totals
Traded
(end-period/
Fracsoft-start)
Desert Law
6/1 (3/1)
76.05
458.14
6.02
Minella Four Star
10/1 (5/1)
45.37
231.50
5.10
Hawkeyethenoo
16/1 (8/1)
12.53
129.51
10.34
Pastoral Player
6/1 (13/2)
31.13
146.27
4.70
Empirico
14/1 (14/1)
18.08
55.91
3.09
23.3 through 23.7, the primary vertical axis measures volume traded expressed as a
natural logarithm (to make the scale manageable), and exchange prices (odds plus one)
are expressed on the secondary vertical axis. Table 23.5 shows the amounts traded on
the exemplar horses to give perspective to the log scale and trading volumes over time.
It is clear from the charts that in each case volume traded accelerates substantially
duringtheﬁnalstagesof thepre-eventmarket; thesecharacteristicsaretypicalof the193
horses for which charts were constructed. Inspection of the charts in total lends itself
to identiﬁcation of a typology of market dynamics; ﬁve generic categories were created
to represent market types commonly observed. Each Pricewise horse was allocated to
one of the categories (or more than one if the market appeared to be a hybrid, which
was the case for about 5% of horses). The categories were named as follows: Steamer,
S-Shaped, L-Shaped, Cup-Shaped, and Drifter. These categories are now described.
Steamer: Primary trend of exchange price (odds plus one) throughout the pre-
event market period is downward. This trend is often, but not always, steeper in the
pre-Fracsoft recording period. Steamer is exempliﬁed by ﬁgure 23.3.
S-Shaped: Following a signiﬁcant decline in exchange price in the pre-recording
period, a period of price stability and low volatility extends throughout the day. As
volume increases toward the end of the pre-event period, a further primary trend
decline in odds occurs. S-Shape is exempliﬁed by ﬁgure 23.4.
L-Shaped: In most cases a signiﬁcant decline in exchange price occurs in the pre-
recording period, though in a small number of cases the exchange price extends
signiﬁcantly instead. A long period of price stability and low volatility continues
throughout the day, to the end of the pre-event period. L-Shaped is exempliﬁed by
ﬁgure 23.5.
Cup-Shaped: Following a signiﬁcant decline in exchange price during the pre-
recording period, a long period of price stability and low volatility follows throughout
the day. As volume increases toward the end of the pre-event period, the early primary

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betting strategy
trenddeclineinoddsisreversed. Asmallnumberof casesapproximatesthestereotypical
quadratic cup shape. Cup-Shaped is exempliﬁed by ﬁgure 23.6.
Drifter: There may or may not be an initial primary trend reduction in odds prior
to the Fracsoft recording period. The recording period is characterized by a primary
trend extension of exchange price throughout the pre-event market period; that is, odds
increase over time to the conclusion of the market. Drifter is exempliﬁed by ﬁgure 23.7.
The frequency distribution of this allocation of horses to categories is shown in table
23.6. Traders who back a Pricewise selection that subsequently contracts in odds early
in the market, which occurs in the majority of observed selections, can exploit their
position by laying, either fully or partially or in a staged sequence of hedging bets later
in the pre-event period. However, as 85 percent of these horses exhibit the bulk of
primary trend contractions prior to publication, this strategy is easier to identify than
to execute.
In terms of the market shapes suggested above these are primarily distinguished by
the path of prices during the Fracsoft recording period. The L-Shaped category offers
the best ﬁt with an efﬁcient market in terms of arbitrage opportunities. Table 23.6 shows
this to be empirically the mean outcome, with the Steamer and S-Shaped categories
(exhibiting odds contractions during or late in the market) and the Cup-Shaped and
Drifter categories (exhibiting odds extensions during or late in the market) distributed
approximately normally around the L-Shape type. This distribution is consistent with
market efﬁciency, from an arbitrage over time perspective, suggesting the path of
prices for the sampled horses to be a random variable normally distributed around the
L-Shaped pattern.
Traders not fortunate enough to place win bets prior to publication are therefore
presented with the usual dilemmas when attempting to predict price movements and
associated trading strategies. Should the trader back Pricewise selections shortly after
publication, hoping to lay at lower odds later on? If so they are betting on the emergence
of the S-Shaped or Steamer patterns or are relying on favorable random movements
sufﬁcient to offset the margin between back and lay prices. Or should the trader lay
Pricewise selections shortly after publication, hoping to back at higher odds later on?
Table 23.6 Pricewise Horses Distributed according to
Market Shape Typology
Category
Frequency
Percentage of Total Charts
Steamer
36
18.7
S-Shaped
30
15.5
L-Shaped
49
25.4
Cup-Shaped
48
24.9
Drifter
30
15.5
Total
193

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This strategy relies on the emergence of the Cup-Shaped or Drifter patterns or, again,
favorable random price changes. Implicit in this strategy is the assumption that the
market has overreacted to the Pricewise information and that a market correction will
occur in the form of drifting odds. The empirical evidence suggests, however, that
the exchange prices at the end of the pre-event period accurately reﬂect the value of
Pricewise information: for the subsample from which charts were derived the Betfair
SP return was −0.05 percent, factoring in 5 percent commission (compared to a loss
of 9.9% at bookmaker SP). The distribution of charts around the L-Shaped market
type, and a zero exchange return at ﬁnal odds, imply no systematic overreaction or
underreaction earlier in the recording period of the pre-event market.
Another common strategy employed by exchange traders, known as scalping, seeks to
exploit volatility in price movements. Traders can amass frequent low-margin positive
returnsfromsuchtradingduringperiodswhenthepriceexhibitsnotrend. Theproblem
with this trading approach is that gains can quickly be wiped out by the emergence of
a trend in the prices; in addition, traders have to be skillful in timing decisions about
the optimum point in time to exit trades and at what levels of proﬁt and loss open
positions should be closed. The evidence is that many traders ﬁnd this balance difﬁcult
to achieve; empirical studies of ﬁnancial asset trading suggest that traders hold on
to losing positions too long and not long enough to winning positions—the so-called
disposition effect (Shefrin and Statman 1994; Weber and Camerer 1998). This tendency
is explained by prospect theory, which posits that the utility function for gains is less
steep than that for losses (Kahneman and Tversky 1979). Scalping can be seen simply
as noise trading; it is not central to the pursuit of value from Pricewise selections but
does explain much of the market activity between step changes in price observed in the
middle segments of the recording periods in many of the charts.
Traders employ analyses of volumes offered, requested, and traded to predict the
direction and extent of exchange price changes. Weight of money indicators are rou-
tinely calculated and updated in the derivative trading software available on the market.
A common technique is to monitor the relative percentages of money associated with
price offers (back side) and price requests (lay side), including the best three prices
on each side. For example, considering Sciampin in the Salisbury race illustrated in
ﬁgure 23.2, the total amount of unmatched orders for the best three prices on either
side is £5417, of which £4159, or 76.8 percent, is on the back side, with the remaining
23.2 percent on the lay side. Prima facie, many traders would interpret these speciﬁc
values as a predictive indicator of imminent odds extension.
Signiﬁcant primary trend price contractions (S-Shaped) or extensions (Cup-Shaped)
are likely to occur in the ﬁnal stages of the pre-event market; consistent success in pre-
dicting the direction of these changes would clearly be of considerable trading value.
Bookmakers are permitted to run betting exchange accounts and frequently use these
to lay off unwanted liabilities that may unduly balance their books. In the ﬁnal stages
of the pre-event market bookmaker odds movements (though not the associated vol-
umes) are well publicized; evidence of marked price contractions in the bookmaker
market for speciﬁc horses may signal corresponding falls in exchange price. If such

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support in the bookmaker market is for the Pricewise horse(s) in a race, then volumes
ﬁnding their way into the exchanges to reduce bookmaker liabilities may consider-
ably outweigh volumes arising from traders hedging their early back to win positions
on Pricewise. Such a scenario will lead to downward pressure on prices and a sub-
sequent S-Shaped market type. Conversely, if late support in the bookmaker and
exchange markets has been for other horses in the ﬁeld, price extension of the Price-
wise horse(s) may occur, especially if higher than normal exchange trading volumes
associated with the early odds contraction of Pricewise selections leads to high levels of
hedging.
Conclusions
.............................................................................................................................................................................
This chapter has reported the results of a study of returns and odds movements asso-
ciated with an inﬂuential media horse racing pundit. In the comparative study of odds
at two points in time, early morning and at race time, both samples considered suggest
that expert analysis can yield highly proﬁtable, statistically signiﬁcant returns prior to
public dissemination of the results of such analysis. These “abnormal returns” arise
from bookmaker mispricing and the fact that the market drives down returns at SP as
a consequence of strong odds contraction. Even at SP, however, proﬁts of over 10 per-
cent remain. While not statistically signiﬁcant (the associated p value is 0.18 for the SP
returns pooled over both samples), these positive returns persist over both samples and
are very similar, a result at variance with most large-sample studies of betting markets
selection strategies, which invariably yield losses. The persistence of positive returns
over time is indicative also of a lack of learning from past experience. On these grounds
the results at both points in time arguably permit a conclusion of semi-strong form
inefﬁciency.
Thesecondpartof thechapterconsideredthedynamicsof themarketfromearlyodds
to SP. This was based on charts derived from betting exchange data, and there appears
to be prima facie evidence that exchange traders are collectively skilled in accurately
incorporating the information contained in the Pricewise column into odds; given
the broadly normal distribution of path-of-price types around that typifying market
efﬁciency, there do not appear to be systematic opportunities for proﬁtable hedging
strategies. It may be, however, that skillful traders employ more sophisticated methods
based on, for example, weight of money, to proﬁtably exploit the expert analysis of
tipsters.
More robust statistical measures would be possible with a full record of Pricewise
selectionsgoingbackover25years. Theseareavailableviathearchivesof theRacingPost,
and perhaps one day I will indulge the wish to complete the set. In the meantime, the
remarkable reputation of the Pricewise column continues to exert a powerful inﬂuence
on U.K. horse race betting markets.

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exploiting expert analysis?
447
Notes
1. The Racing Post is the leading racing newspaper by circulation in the United Kingdom.
The study in question employed the nom de plume “Winsome” for Pricewise; in retro-
spect the reasons for being so guarded in identifying the real name of the feature are
unclear.
2. Starting price is the odds value at which bets are settled in the absence of a ﬁxed-odds
agreement between bookmaker and bettor. The SP for each horse is determined by inspec-
tors who monitor the range of on-course odds available from competing bookmakers close
to the time of the race.
3. During the period of sample 1 bookmakers made deductions to cover the betting tax of
6 percent of winnings and an additional 3 percent to cover operating costs; this deduction
ceased when betting tax was abolished in October 2001.
4. Many of the last observed odds values do not appear in the early stages of the charts as they
are captured in the recorded Fracsoft phase.
References
Fama, Eugene F. 1970. Efﬁcient capital markets: A review of theory and empirical work.
Journal of Finance 25(2):383–417.
Figlewski, Stephen. 1979. Subjective information and market efﬁciency in a betting market.
Journal of Political Economy 87(1):75–88.
Jones, Peter, David Turner, David Hillier, and Daphne Comfort. 2006. New business models
and the regulatory state: A retail case study of betting exchanges. Innovative Marketing
2(3):112–119.
Kahneman, Daniel, and Amos Tversky. 1979. Prospect theory: An analysis of decisions under
risk. Econometrica 47(2):263–292.
Klemperer, Paul. 1999. Auction theory: A guide to the Literature. Journal of Economic Surveys
13(3):227–286.
——. 2004. Auctions: Theory and practice. Economics Papers 2004-W09. Economics Group,
Nufﬁeld College, University of Oxford.
Koning, Ruud H., and Bart van Velzen. 2009. Betting exchanges: The future of sports betting?
International Journal of Sport Finance 4(1):42–62.
Law, David, and David A. Peel. 2002. Insider trading, herding behaviour and market plungers
in the British horse race betting market. Economica 69(274):327–338.
Shefrin, Hersh, and Meir Statman. 1994. Behavioral capital asset pricing theory. Journal of
Financial and Quantitative Analysis 29(3):323–349.
Smith, Michael A. 2003. The impact of tipster information on bookmakers’ prices in UK
Horse-Race Markets. In The economics of gambling, edited by Leighton Vaughan Williams.
London: Routledge, 67–79.
Smith, Michael A., and Leighton Vaughan Williams. 2008. Betting exchanges: A technological
revolution in sports betting. In Handbook of sports and lottery markets, edited by William T.
Ziemba. Amsterdam: Elsevier, 403–418.
——. 2010. Forecasting horse race outcomes: New evidence on odds bias in UK betting
markets. International Journal of Forecasting 26(3):543–550.

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Smith, Michael A., David Paton, and Leighton Vaughan Williams. 2006. Market efﬁciency in
person-to-person betting. Economica 73(292):673–689.
Vaughan Williams, Leighton. 2000. Can forecasters forecast successfully? Evidence from UK
betting markets. Journal of Forecasting 19(6):505–513.
Weber, Martin, and Colin F. Camerer. 1998. The disposition effect in securities trad-
ing: An experimental analysis. Journal of Economic Behavior & Organization 33(2):
167–184.

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## Page 470

s e c t i o n v
........................................................................................................
MOTIVATION,
BEHAVIOR, AND
DECISION-MAKING IN
BETTING MARKETS
........................................................................................................

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chapter 24
........................................................................................................
BETTING MOTIVATION
AND BEHAVIOR
........................................................................................................
alistair bruce
1 Introduction
.............................................................................................................................................................................
This chapter is concerned with exploring individuals’motivations for betting and other
aspects of their behavior as bettors. These topics have generated a substantial literature
over the past four decades. While the study of betting behavior has been dominated
by the lens of economic analysis, it has also occupied the attention of psychologists,
sociologists, and those interested in designing the legal and regulatory regimes within
which betting takes place or those tasked with addressing and treating the negative
effects of excessive exposure to betting from a medical or social care perspective.
A major contemporary factor behind the interest in and motivation for academic
research on betting is the large increase in gambling activity in many countries (see,
for example, Gambling Commission 2011). This ﬁnds expression via an increasingly
wide diversity of betting media, forms of betting markets and forms of engagement
with betting markets. This has in part been fueled by, and in part has fueled, changes
in the regulatory and legal frameworks within which betting takes place. In the United
Kingdom, for example, the deregulation of betting and other forms of gambling has
been as much a feature of the past 30 years as the rise in betting as a participative leisure
pursuit, though which drives which is neither clear nor, probably, straightforward. For
example, 30 years ago, the typical U.K. betting ofﬁce had sound-only access to betting
shows and race commentary, an overwhelmingly male-dominated and working-class
clientele, a highly limited range of betting media focused on horse, and to a lesser
degree greyhound, racing, no seating or refreshments. The interiors of betting ofﬁces
were, by regulatory design, invisible from the street. Betting was regarded as an activity
at the margins of social acceptability—indeed betting ofﬁces had only been legalized
in 1960. The contrast with the contemporary betting ofﬁce is striking. Premises today

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motivation, behavior, and decision-making in betting markets
enjoy sophisticated technological support, typically with multiple TV screens relaying
a diversity of information, live broadcasts of betting-related events, expert analysis,
and guidance. The modern clientele reﬂects, to a far greater degree, a cross section
of society in general. We can see into betting shops, which offer a bright, clean, and
welcoming image, inviting clients to participate in what is now seen as a mainstream
leisure experience, with the opportunity to sit down and enjoy refreshments as they
bet. The menu of betting opportunities has increased signiﬁcantly to embrace most
mainstream sports as well as much wider media, such as outcomes in political elections,
game shows, and ﬁnancial markets. More strikingly, perhaps, the mode of engagement
of bettors with betting markets is in a state of ﬂux, with the rapid emergence of betting
via Internet and mobile devices, while new forms of betting market, most notably
person-to-person betting exchanges, are also a feature of a rapidly changing landscape.
The above is just one illustration of the transformative change, in the United King-
dom and elsewhere, that forms the context for this survey. The approach adopted here
in addressing motivational and behavioral issues relating to betting is naturally shaped
by the author’s disciplinary background and experience as a researcher in the ﬁeld
over the past 25 years and, as such, reﬂects a personal perspective on the issues under
scrutiny. Accordingly, the emphasis in this chapter is on examining betting motivation
and behavior principally, though not exclusively, through
(i) the application of economic analysis to betting;
(ii) insights based on naturalistic rather than experimental research;
(iii) the lens of horse race betting;
(iv) the author’s (and his collaborators’) own work and insights.
Clearly the above basis for addressing motivational and behavioral issues cannot claim
to offer a comprehensive coverage of available insights; it does, though, attempt to
provide a consistent and manageable approach to a complex and diverse ﬁeld.
The chapter is organized as follows. Section 2 explains the approach outlined above
by examining economists’ particular interest in betting as a research medium and the
susceptibility of betting to economic analysis. This is followed by a discussion of the
merits of naturalistic vis-à-vis other methodological traditions in the study of betting
behavior. Finally, the focus on horse race betting as the principal medium of interest
addressed in the chapter is explained.
This provides the basis in Section 3 for considering how individuals might be moti-
vated to engage in betting as an activity and to become active participants in betting
markets, as consumers. A variety of core motivations are considered, including some
that have been the subject of empirical inquiry. An important consideration here is the
belief that we can often infer something of the motivation of the individual bettor by
examining the particular circumstances of that bettor’s betting activity, such as how,
when, or where the bet was made.
Section 4 moves beyond betting motivation per se to explore some of the inﬂuences
on and relationships between further aspects of betting behavior. This discussion is

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betting motivation and behavior
453
centered on the concepts of risk-taking and betting performance and the factors that
appear to inﬂuence each of these aspects. It will become clear that many of the insights
into behavior that are developed and discussed herein are the by-products of studies,
the principal objectives of which lie elsewhere. So, for example, while a large pro-
portion of the empirical analysis of betting has occupied itself with issues of betting
market efﬁciency, variously deﬁned, the roots of inefﬁciency at the level of the mar-
ket lie in individual bettors’ and/or bookmakers’ behavior. As such, studies with these
more macro-level objectives have the capacity to enrich greatly our understanding of
micro-level behavior. Finally, in section 4, some observations are offered on that most
widespread and researched behavioral phenomenon in betting, the favorite-longshot
bias. Brief concluding remarks follow.
2 Studying Betting Motivation and
Behavior: Economic Analysis, Naturalistic
Inquiry and Horse Race Betting
.............................................................................................................................................................................
As noted above, the approach adopted in this chapter reﬂects the author’s particular
“take” on the body of theoretical and empirical work in the area of betting motivation
and behavior, in terms of its disciplinary orientation, methodological preference, and
the dominance of a particular betting medium within the literature.
2.1 The Economic Analysis of Betting
The justiﬁcation for adopting a largely economic approach to the study of betting
reﬂects both the willingness of economists to engage with the phenomenon and
the preeminence of economics as a disciplinary basis for investigation within the
literature.
Economists’ interest in betting has been motivated by a variety of factors. First
there is the apparent violation of the received view of economic rationality that is
embodied in betting as an activity and which explains, in particular, the interest of
behavioral economists. There is also interest in the study of decision-making in an
economic context and under uncertainty, how decisions are framed and made and
how such issues as the complexity of decision problem are managed by individuals.
As a form of decision context, betting is of particular interest to economists as bets
generate unequivocal outcomes with clear ﬁnancial implications, which facilitate mea-
surement of decision performance under a range of conditions. Third, economists have
an enduring interest in the functioning and efﬁciency characteristics of markets and
how these may be affected by biases in market participants’ behavior or by information
asymmetries.

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motivation, behavior, and decision-making in betting markets
In this section the emphasis is on exploring how economists seek to make sense
of the apparent irrationality of betting. In a sense, developing an understanding of
this issue clariﬁes the origins of economists’ interests both in the details and processes
associated with decision-making and the consequences for market efﬁciency which
reﬂect decision-making in aggregate.
2.1.1 Betting and Economic Rationality
The fact that betting is an activity in which individuals voluntarily engage, using their
own money, and which in the long run will almost inevitably lead to ﬁnancial loss,
poses difﬁculties for economists who feel the need to explain all economic behavior as
motivated by narrowly deﬁned, seemingly rational economic considerations. To such
“purist” economists, therefore, betting is regarded as constituting eccentric behavior
that deﬁes rational explanation. The irrefutable fact that betting is a mass-participation
and increasingly popular pursuit with material ﬁnancial consequences, however, means
that it over the past twenty years in particular, the behavioral economics tradition has
become an increasingly important and vibrant sector of the discipline. In many areas of
economic life an inconvenient truth is that human behavior appears to accommodate
motivations other than the maximization of a narrowly deﬁned welfare function. In
the particular context of the analysis of decision-making, Richard Thaler (1991, xii)
captured the limitations of the “purist” economic perspective.
What I kept noticing was that people did not seem to behave the way they were
supposed to .... I was constantly confronted with the contrast between the models
my colleagues were constructing and the behaviour I was so frequently observing.
Thaler went on to describe his discovery of the work of Daniel Kahneman, Amos
Tversky, and others (see, for example, Kahnemann and Tversky 1979; Gilovich, Grifﬁn,
and Kahnemann 2002, xxi) on judgment, heuristics, and biases, which he saw as key
to developing a more inclusive perspective on decision-making, one that embraced
concepts from economics and psychology. His conclusions on what he has termed
“quasi rational behavior” are worth repeating.
Quasi rational behavior exists, and it matters. In some well-deﬁned situations,
people make decisions that are systematically and substantively different from those
predicted by the standard economic model. Quasi rational behavior can be observed
under careful laboratory controls and in natural economic settings such as the stock
market. Market economies and their institutions are different from the way they
would be if everyone were completely rational.
Even in the relatively short period since Thaler made these observations, the dialogue
and development of trust and mutual respect between the disciplines of psychology
and economics has been noticeable, encouraged by a growing acceptance that each can
enrich the understanding of a phenomenon of common interest by accommodating

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betting motivation and behavior
455
perspectives from the other. This increased readiness to remove the disciplinary blink-
ers is epitomized by the popularity of journals that span the boundaries of psychology
and economics, most notably the Journal of Economic Behavior and Organization. Also,
in the context of betting in particular, even the most casual engagement by an academic
economist with the behavior of a betting ofﬁce clientele or an on-course betting market
would likely encourage the academic to seek to rationalize betting activity in terms of
far more complex and shifting motivations than merely the desire to make money. This
translates into an interest in motivation, as characterized by the bettor’s utility function
and, in particular, elements of utility that work against ﬁnancial returns maximization
in ﬁnancial decision-making. Economists have shown considerably greater tolerance
than has the academic ﬁnance community for the possibility of broader utility func-
tions, and consequently there is greater acceptance by economists that deviations from
market efﬁciency can be rationalized in terms of noneconomic or nonﬁnancial drivers
of behavior.
The judgmental heuristics and resultant biases to which Thaler refers form an
important element in the plethora of empirical studies that focus on the efﬁciency
characteristics of betting markets. As noted above, a pervasive, and some might say
obsessive, feature of work in this area has been the investigation of the phenomenon
of the favorite-longshot bias as a contributory factor in market inefﬁciency. Favorite-
longshot bias describes the tendency of favorites (shorter odds horses) to be underbet
and long shots (longer odds horses) to be overbet relative to their objective probability
of success. The causes of this particular bias are an issue of some debate within the
literature, and while psychologically rooted factors are held to be important in some
quarters, other contributors view the bias more as simply the function of a rational
economic response to the threat of adverse selection under conditions of asymmetric
information (see Shin 1991, 1992, 1993). The issue of the favorite-longshot bias is
discussed in the concluding section.
2.2 Naturalistic and Laboratory-Based Inquiry
in Betting Research
Thaler points to the incidence of, and opportunity to observe, quasi rational behavior
in both controlled laboratory and natural contexts, and at this point it is appropriate to
explore some of the methodological issues relating to the economic analysis of betting.
One view is that, in essence, laboratory-based and naturalistic insights are comple-
mentary and mutually corroborative methods. As Bernard Baars (1980) has observed,
“without naturalistic facts, experimental work may become narrow and blind . . . with-
out experimental research, the naturalistic approach runs the danger of being shallow
and uncertain.” Although the literature on betting behavior is indeed well represented
by both laboratory-based and naturalistic analysis, it seems fair to suggest that, in

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motivation, behavior, and decision-making in betting markets
contrast to the inclusive tone of the view expressed above, there remains some implicit
skepticism from each tradition regarding the contribution of the other.
From a personal perspective, implicit in a preference for naturalistic investigation is
a failure to be entirely convinced by the ability of the laboratory setting to capture the
full richness of the natural decision environment or to replicate the incentive-penalty
conditions experienced by the bettor in a real setting. The susceptibility of individual
decisions to small changes in aspects of the decision environment has been observed
(see, for example, Payne 1982). Equally there is some skepticism as to whether observed
behavior, in the laboratory, of relatively small groups of incentivized subjects who are
unfamiliar with the decision task assigned sheds much light on our understanding of
real bettors committing their own resources in a decision context with which they are
more or less familiar.
A preferred method of investigation with colleagues has been the interrogation of
large datasets of actual betting decisions, generally made available via data-access agree-
ments with large bookmaking organizations. This preference may be a function of an
economics disciplinary base to some degree, but from a methodological perspective
there is a strong appeal in being able to observe and analyze decisions that are made
• in a natural setting
• by decision-makers who are to a greater or lesser degree task-familiar,
• by decision-makers oblivious to scrutiny
• committing their own money
• with attendant real ﬁnancial gains/losses
• in a large and diverse set of individual betting markets
• with attendant opportunity for multifaceted cross-market comparison
• with the opportunity to input complementary market information.
Working with datasets that embody the above characteristics permits an unparalleled
range of avenues of inquiry. Typically, for each bet made, we have self-documented
details of the selection made as well as the stake and the type of wager (e.g., win or
each-way) supplemented by data on the evolution of odds in the market, location (e.g.,
on-course, off-course, telephone), and precise date and time of bet placement; race-
related data, such as racecourse location, number of runners, race type (handicap/non-
handicap, etc.), race class (grade of race), position of race in the race card, ground
conditions (“going”), race result with associated starting prices (SPs), and returns
to each betting decision. These data offer rich potential for developing insights into,
inter alia, betting motivation, levels of participation, risk appetite (in terms of size of
investment,inherentriskinessof bettypeorselectionmade),theeffectof complexity(in
terms of race type, number of runners), and relative performance, variously measured.
While the appeal of working with this type of resource is compelling, there are
associated limitations. One is the anonymity of subjects in a natural setting. This has
the advantage of ensuring the absence of distortive observation effects on behavior,
but it denies the opportunity to interrogate subjects directly as to their motivations

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betting motivation and behavior
457
for gambling. Here, by contrast, laboratory studies can shed light on the factors and
processes underpinning decisions made by interrogating subjects ex post. Equally,
laboratory simulations can sharpen the focus on the relationship between particular
variables in a controlled environment without the noise and turbulence which attend
the natural setting. To the extent that the noise and turbulence materially inﬂuence the
processes involved in decision-making, however, isolation of particular variables might
be regarded as an abstraction from reality.
Ultimately there are advantages and drawbacks associated with each method, and a
consensus around the complementarity of each is probably fair.
The above discussion, with its focus on the contrast between laboratory-based and
naturalistic inquiry, reﬂects a further methodological bias, that is, a preference for quan-
titative versus qualitative analysis of betting behavior. This requires some comment. In
large part the preference for naturalistic over laboratory-based inquiry turns on the
appeal of data elicited anonymously in a natural decision setting versus data generated
in a synthetic decision environment as a basis for seeking to explain naturally occur-
ring aspects of decision behavior. Questions regarding the reliability of the quantitative
interrogation of laboratory-generated data are ampliﬁed where qualitative analysis is
concerned. Necessarily, whether via instruments such as questionnaire-based inquiry
or interviews, eliciting qualitative information from bettors on aspects of their betting
behavior requires conscious self-reﬂection by subjects. This may, particularly for an
activity which has only recently moved from the margins of social acceptability, invite
responses that reﬂect subjects’ perceptions of socially acceptable norms in relation to
betting activity or unwarranted and unrealistic self-perceptions rather than frank and
honest reporting of motivation or other behavioral aspects. Equally, as with laboratory-
based quantitative inquiry, there are potentially distortive effects associated with the
investigator’s framing of the qualitative instrument. These types of reservations may
explain, in part, the dearth of qualitative studies of bettor behavior in the empirical
literature.
2.3 Horse Race Betting as a Focus
The justiﬁcation for using, in this chapter, horse race betting as the dominant form
of betting medium through which to offer more general insights rests on a number of
factors.
First, in many countries where betting is a signiﬁcant pastime, such as the United
Kingdom, horse race betting remains the single most popular betting medium. Equally,
for most of the largest bookmaking organizations, horse race betting remains the single
most important element in their core business. That said, a striking feature has been
the rapid innovation in both new betting media (i.e., types of events on which bets
can be placed) and new forms of betting market (such as betting exchanges and digital
market media). So, in the context of these changes, can the focus on horse race betting
markets be justiﬁed? It is argued here that it can be justiﬁed in the sense that a signiﬁcant

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motivation, behavior, and decision-making in betting markets
element of the betting clientele that engages with new betting media is also engaged
with (and likely began betting on) horse race betting markets. As such the populations
are far from discrete, and we might therefore expect their underlying motivations and
behaviors to be similar.
Second, although its origins were in traditional bookmaker-based markets, horse rac-
ing is a dominant betting medium in new market forms. For example, Betfair, the
leading person-to-person (betting exchange) operator in the United Kingdom and an
innovator in sports betting, returned over 43 percent of its core revenue from horse race
betting in ﬁnancial year 2010/2011.
A third reason for adopting this focus reﬂects the fact that the majority of aca-
demic studies of betting have, over the years, used horse race betting data in their
analysis. This reﬂects the richness and accessibility of continually expanding data on
individual markets complemented by the availability of comprehensive and detailed
market-relevant information. As such, in reﬂecting on and drawing insights from this
literature, horse race betting is the naturally dominant milieu.
3 Economic Analysis of the Motivations
for Betting
.............................................................................................................................................................................
This section addresses the issue of betting motivation based on economic analysis. It
is important at the outset to acknowledge that betting motivation is itself a complex
and multifaceted issue. For example, bettors are characterized both by those who are
solely interested in a recreational experience for a trivial outlay/return and those who
regard themselves as professionals, placing high stakes. There are highly experienced
and sophisticated participants as well as complete novices; extremely well-informed
bettors and wholly uninformed and whimsical decision-makers. There are on-course,
off-course, online, and telephone bettors; bettors who prefer bookmaker markets, pari-
mutuel markets, or betting exchanges; male and female bettors and many more bases
for disaggregating bettors as a population. These spectra of diversity are matched by
a breadth of motivational drives for participation, and no doubt for many bettors
the motivation comprises a blend of factors. It seems reasonable to suggest that the
aggregatepopulationof participantsinbettingmarketsisconsiderablymorediverseand
motivationally complex than the populations associated with most ﬁnancial markets,
where a more uniform and ﬁnancially focused motivation would generally appear
appropriate.
As a route into this complex world, we begin this section by discussing a paper by
Alistair Bruce and Johnnie Johnson (1992) that represented an early attempt to validate
a four-way classiﬁcation of off-course bettors’ motivations. Bruce and Johnson exam-
ined the proposition that different dominant motivations to bet might be associated
with betting in distinct time windows of the betting day and with whether the bettor

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betting motivation and behavior
459
elected to“take” the price (odds) on offer at the time of bet placement rather than have
a winning bet settled at starting price (SP) (the independently adjudicated market price
at the close of the market). Four motivations were identiﬁed: ﬁnancial gain (drawing,
for example, on Cornish 1978), intellectual challenge (Downes et al. 1976; Langer 1983;
Letarte, Ladouceur, and Mayrand 1986), social interaction (Filby and Harvey 1989;
Saunders and Turner 1987), and excitement (Gilovich and Douglas 1986, Anderson
and Brown 1984). It was argued that each motivation could be associated with a partic-
ular time frame within the betting day or a combination of time frame and price-taking
behavior. So, for example, it was suggested that those bettors principally motivated by
social interaction would be more likely to bet at times when the betting ofﬁce was rela-
tively heavily populated, whereas those for whom ﬁnancial return was most important
might be expected to operate immediately prior to a betting event, when the fullest
exposure of market-relevant information is available. Comparisons were then made
between the motivationally distinct subsets, and these generated results that appeared
to support the basis for subgroup deﬁnition. Accordingly, the ﬁnancial gain subgroup
was associated with both higher levels of staking and higher levels of proﬁtability. There
was also a tendency for this group to bias betting more toward favorites, suggesting their
more sophisticated understanding of the relationship between subjective (implicit in
odds) and objective (revealed by outcomes) probabilities or, in other words, a sharper
appreciation of “value” opportunities.
The identiﬁcation of intellectual challenge as a motivation for betting prompted
further investigation of the effect of different levels of complexity in betting event on
participation. In other words, to what extent are bettors either incentivized or deterred
by the challenge of more complex events? Most of the literature relating to this issue
would suggest that complexity should inhibit participation. Decision problems involv-
ing more alternatives and/or attributes increase the cognitive and computational stress
onthedecision-maker. Thepowertodiscriminatebetweenalternativesiscompromised.
Johnson and Bruce (1997a) later found, however, that alternative-deﬁned complexity is
positively correlated with participation in terms both of bets placed and stakes wagered.
That is to say, bettors appear to have an appetite for more complex events featuring
larger numbers of runners, and this would tend to support the intellectual challenge
motivation. The results relating to attribute-deﬁned complexity are more in line with
the consensus in the literature, suggesting that complexity in the attributes set deters
participation. The effects of complexity on other aspects of betting, such as risk-taking
and performance, are considered in a later section.
To the extent that complexity may be viewed, alternatively, as a negative and unattrac-
tive or a positive and attractive feature, that is, as a deterrent or incentive to engage with
a complex betting challenge, risk might be viewed similarly. Depending on an individ-
ual’s attitude to and appetite for risk, betting generally may be viewed as an unattractive
or attractive pursuit. Given that risk is inherent in betting, it seems reasonable to argue
that it might form part of the appeal, alongside other factors, to individuals who do bet.
Section 4 illustrates how the acceptance and management of risk, or risk behavior, in
betting might be inﬂuenced by a range of factors. In the meantime, it is worth making

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motivation, behavior, and decision-making in betting markets
two points about the nature of risk as an incentive to bet, which are materially distinct
from the satisfaction of an appetite for risk per se. First, betting offers an opportunity
to experience risk in a controlled setting, with self-determined limits on downside con-
sequences. This may be attractive to individuals who are uncomfortable with risk in
a general sense. Second, exposing oneself to ﬁnancial risk in relation to the outcome
of an event, a horse race for example, may amplify the enjoyment of the event. So,
by paralleling the experience of simply viewing the event with a ﬁnancial stake in the
event’s outcome, and associating one’s interests with a speciﬁc horse, the bettor adds
material to emotional engagement. This so-called mimetic dimension to participation
has been observed as important in a variety of contexts. Patrick Murphy, John Williams,
and Eric Dunning (1990), for example, observed this type of effect in relation to the
identiﬁcation with a particular team for soccer spectators.
The diversity of the aggregate population of bettors in terms of a range of behav-
ioral aspects has already been stressed and is a recurring theme in this chapter. For
many bettors themselves, of course, there will be an awareness of this diversity and,
in particular, an awareness of who their fellow bettors are. This in itself may form the
basis for betting motivation. For example, for more expert, informed, analytical, and
serious bettors, part of the motivation for betting may relate to their awareness that they
are playing in a market alongside novice, uninformed, irrational, purely recreational
bettors. Serious bettors will believe, and possibly with some justiﬁcation, that they are
likely to be better decision-makers than this group and that the presence of novices
may actually improve the odds available to the serious bettor. The presence of so-called
mug punters is, naturally, well understood by bookmakers and an important element in
guaranteeing their return. Bookmakers may even deliberately manipulate odds to tempt
“mugs”toward invariably fruitless investments. For example, a horse whose probability
of success in the view of the bookmaker is 1 in 300, may be priced at 50–1 to give the
novice punter the idea that its chances of success are not so remote as they actually
are. At the same time, bookmakers may lengthen the odds of short-priced horses to
induce betting revenue from novice bettors who tend not to be attracted by very short
odds and are unlikely to be aware of the relative “value” in the short odds range. More
serious, higher stakes bettors, with a more sophisticated understanding of the objective
probability of short odds horses, may thereby be able to beneﬁt from better prices in
the short odds range. In passing, it is worth noting that this sort of activity, of course,
contributes to the favorite-longshot bias. And even without manipulative bookmaker
behavior, the tendency toward a random distribution of betting across opportunities
by less informed or less sophisticated bettors would be inclined to contribute to the
favorite-longshot effect.
If one basis for identifying motivationally distinct subgroups relates to the
novice/expert axis, another may be the form of betting market in which they choose
to participate. In a U.K. context, the traditional distinction between bookmaker-based
and pari-mutuel markets has in recent years been augmented by the development of
new market media, most notably betting exchanges. It could be argued that each form
of market satisﬁes different motivations.

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Bookmaker-based markets may appeal more to those more traditional bettors who
appreciate the opportunity to know with certainty the return to a successful bet at the
time of bet placement. Pari-mutuel markets, by contrast, may tend to be more attractive
to more risk-loving bettors, who are content to accept the price dictated by the market,
or by those who prefer betting on outsiders, where the return to a winning pari-
mutuel bet is invariably higher, and sometimes signiﬁcantly so, than in the equivalent
bookmaker market. Exchange betting arguably taps into the motivations of a wholly
different set of bettors, those who enjoy the buzz of a direct screen-based interface with
a live market. In many senses the interactive opportunities offered by exchange betting
may be regarded as more akin to online poker in their more dynamic and interactive
nature. They are also likely to appeal to those who appreciate rapid access to the range
of information relevant to the market, given the linkages and real-time updates which
are a feature of most betting exchanges.
Another basis for discriminating between groups is the on-course/off-course dis-
tinction. In general terms it is tempting to suggest that those who incur the time and
ﬁnancial costs of attending a racecourse and who bet during their time there are likely to
be materially different from those whose betting is conducted via an off-course venue,
such as a betting ofﬁce, telephone account, or online. A reasonable assumption is that
on-course bettors may be attracted to the course principally by their enthusiasm for
the sport of racing, whereas betting for them may be an essentially secondary activity,
a function of their access to betting opportunities on-course rather than an innate
interest in betting. By contrast, it seems fair to suggest that those who choose to bet
off-course are more likely to be principally motivated by betting itself rather than the
underlying sport. Bruce et al. (2009) explored behavioral differences between on- and
off-course betting populations, and the results reveal evidence for stronger favorite-
longshot bias in the on-course population. This is seen as symptomatic of a population
that has a less sophisticated understanding of the relationship between objective prob-
ability and odds-implicit probability, which in turn suggests material distinctions in
betting motivation between on- and off-course bettors.
In relation to betting motivation in general, it is clear from the above that there is
a wide diversity of factors driving betting participation and, therefore, a high level of
motivational heterogeneity in the aggregate betting population. It seems reasonable to
suggest that a major inﬂuence underpinning this diversity has been the deregulation of
betting in many jurisdictions. As more liberal regulatory attitudes toward betting and
gambling more generally have developed, this has encouraged betting and gambling
operators to invest in the development of new forms of betting markets and new media
for betting beyond the traditional horse and greyhound racing focus. It is tempting
to argue that these innovations have encouraged previously untapped sections of the
population into betting and gambling. In addition, in a U.K. context, though doubtless
this also applies elsewhere, the introduction of the National Lottery as a gambling
opportunity made available to all on a regular and highly publicized basis appears
to have been an important factor in legitimizing gambling and betting as mainstream
leisure pursuits and challenging an entrenched stigma in British society. In other words,

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motivation, behavior, and decision-making in betting markets
many whose urge to gamble has been suppressed in the past have felt increasingly able
to express their desire through active participation.
4 Betting Behavior
.............................................................................................................................................................................
The range of observable and measurable behaviors associated with betting is consid-
erable. Apart from shedding light on the motivation to engage in betting, as discussed
above, aspects of the betting decision can offer insights into perceptions of and
responses to risk, variously deﬁned, attitudes to insurance, approaches to more and
less complex decision scenarios, subjective perceptions of probability, conﬁdence, and
decision performance. In this section, initially, attention is focused on two areas of
behavior—risk strategies adopted in the face of complex and uncertain decision prob-
lems, and decision performance. This focus is justiﬁed in terms of the fundamental
role of risk in the activity of betting and the key role of performance in evaluating deci-
sion outcomes. In each case alternative measures of the dependent variables, risk and
performance, are considered and how each is inﬂuenced by a variety of independent
variables is reported.
Itwillbecomeapparentduringthissectionthatthereareoftensigniﬁcantcorrelations
between particular betting motivations, as discussed above, and attitudes to risk and
performance. These associations are clearest where motivationally distinct subgroups,
whether deﬁned in terms of time of bet placement, location of bet placement, or some
other factor, are characterized by distinct attitudes toward/response to risk or patterns
of performance.
4.1 Risk
4.1.1 Measuring Risk in Betting
In considering how bettors respond to the presence of risk,it must ﬁrst be acknowledged
that the voluntary participation of individuals in betting markets suggests some degree
of inherent risk appetite. The variety of betting options available spans a very wide
range of risk exposures. It is this vast range which affords the opportunity to explore
attitudes toward and responses to different degrees of risk.
There are a number of perspectives on risk that translate into operational measures
of riskiness or risk-taking. We can focus, for example on the type of bet selected and
differentiate between higher- and lower-risk bets. Thus a “multiple” win bet, where
a return is dependent on predicting simultaneously and in combination the unique
outcome of a number of discrete events, is at one end of the risk spectrum. By contrast,
an “each-way” bet is a relatively low-risk investment, where the stake is split between
the probability of a horse winning and it being placed (second; second or third; second,

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463
third, or fourth or occasionally, additionally, ﬁfth place). This embeds an element of
insurance into the bet to mitigate risk. A whole range of so-called exotic bets offers a
wide menu of risk characteristics.
A second basis for measuring the riskiness of a bet is associated with the subjective
probability inherent in the odds at which the bet is struck, where clearly the implied
riskiness of a 16/1 selection (implied probability of success = <6%) is materially differ-
ent from a 5/4 selection (implied probability = c. 44%). A more sophisticated version
of this type of measure uses a version of odds adjusted by market context, that is, raw
odds/mean market odds as a measure of relative risk. Related to this is the position of
a selected horse in the betting market; that is, the market’s view of the horse’s ranked
probability of success within the ﬁeld, whereby comparative favorites are inherently less
risky propositions.
A third basis for judging risk relates not to the selection per se but to the amount of
money risked in the investment, the stake.
Although they are presented here as discrete insights into risk, it will be seen that there
are often important interactions between these risk variables whereby, for example,
increased risk exposure in one sense may appear to be offset by reduced exposure in
terms of an alternative risk measure.
In investigating the inﬂuences on the risk behavior of bettors, a number of factors
have come under consideration. Here the focus is on four main potential inﬂuences:
time of bet placement (variously deﬁned), location of bet placement, complexity of the
betting decision, and gender of the bettor.
4.1.1.1 Risk and Bet Timing
Johnson and Bruce’s (1992) empirical study of patterns of betting behavior investigated
the relationship between the time of bet placement and various bet characteristics. For
each of a sample of 1,200 bets placed in U.K. betting ofﬁces, the exact time of bet
placement was recorded. This formed the basis for splitting the population into three
subgroups. The ﬁrst subgroup comprised all bets placed prior to the ﬁrst report of the
active betting market in the betting ofﬁce (the “ﬁrst show”). The second comprised all
wagers placed during the active market period (typically around 15 minutes) minus all
bets placed in the last 30 seconds before the start of the relevant race. The ﬁnal sub-
group comprised all bets placed later than 30 seconds before the “off” time, including
any bets placed after the “off.” The results revealed a number of notable distinctions
between the periods. In terms of staking behavior, there was more evidence for sig-
niﬁcantly higher staking in the last time period than in either of the earlier periods,
suggesting a greater willingness to incur risk in terms of the level of investment at
risk by bettors in this group. This applied to bets placed at both starting price (SP)
and board price (BP), the prevailing market price at the time of bet placement. Bets
placed in the last period carried average stakes of £12.54 (BP) and £4.75 (SP) com-
pared with equivalent values, for the earliest period, of £4.76 (BP) and £1.83 (SP)
and, for the middle period, of £7.50 (BP) and £3.51 (SP), respectively. The results
were interpreted as identifying a group of late bettors who were prepared to incur

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motivation, behavior, and decision-making in betting markets
increased risk in terms of stake because they were conﬁdent that they had absorbed
all of the price-embedded information generated throughout the life of the markets
as a basis for their decision. The performance associated with this time-deﬁned sub-
group, reported below, supports the notion of an informationally privileged set of
bettors.
It was observed earlier that time-deﬁned subgroups of bettors could allow insights
into subgroups that were also distinctive in terms of their dominant motivation. As part
of this study, further aspects of risk exposure across time also were considered. These
included the comparative propensity, across four time-deﬁned subgroups this time, to
bet on relative favorites and relative long shots. The results indicated a signiﬁcant and
positive difference between the proportion of bets placed on ﬁrst and second favorites by
bettors in the latest time period (post-30 seconds before the “off-time”) at 60 percent
compared with bets placed in three earlier periods. Equally the percentages of bets
placed on horses outside the ﬁrst three positions of favoritism and on horses with odds
of 20/1 or more were signiﬁcantly lower for bettors in the latest time period. The results
of these two studies, taken together, suggest that risk exposure in terms of staking levels
is inversely related to the market’s assessment of risk.
Another insight into the relationship between risk-taking and time considers how
the propensity to take risk may vary through the course of a betting day rather than in
relation to a particular betting market. There is a strand of literature which suggests
that risk attitudes may change as a result of the (normal) experience of loss during
a betting day. One example of this is Gluck”s Second Law, which states that the best
time to bet the favorite is in the last race of the day, the reasoning being that most
impoverished bettors will incur greater risk by placing their money on relative “out-
siders” in later races in order to recoup losses incurred earlier. As such the odds of the
favorites in later races will be more favorable than would normally be the case. Johnson
and Bruce (1993) investigated this phenomenon and explored various comparisons of
subsets of earlier versus later races within a betting day. The results highlighted striking
differences between early and late behavior. It was clear that betting on favorites, at
30.9 percent of bets in the last three races, was signiﬁcantly higher than in the ﬁrst
three races (20.1%). This suggests greater risk aversion as later bettors default to the
market view. Mean staking levels, as an alternative insight into risk-taking, however,
tell a rather different story, with signiﬁcantly higher mean staking in the last three
races (£6.51) compared with the ﬁrst three (£4.34). Again, taken together the results
suggest offsetting behaviors in terms of the two perspectives on risk-taking, which
endorses the importance of adopting a range of insights into, and measures of, risk
behavior.
4.1.1.2 Risk and Bet Location
A further potential inﬂuence on the propensity of bettors to incur risk relates to the
location from which they place their bets, where the distinction between the on-course
andoff-coursebettingpopulationsappearstobesigniﬁcant. Bruceetal. (2009)explored
differential incidence of favorite-longshot bias between location-deﬁned subgroups

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465
of bettors, ﬁnding evidence for signiﬁcantly greater concentration of betting toward
relatively long-odds horses in the on-course market, compared with both the aggregate
off-course market and each of its component submarkets (betting ofﬁce, telephone,
“away” track). Similarly, off-course bettors displayed a signiﬁcantly greater propensity
to bet on relative favorites than their on-course counterparts. While these results may,
in some degree, reﬂect a greater risk appetite by on-course bettors, perhaps because of
the dominance of recreational and less ﬁnancially focused bettors within the on-course
group, it may equally reﬂect the superior awareness by off-course, more serious bettors
of the relationship between odds-implied and objective probabilities across the odds
range.
4.1.1.3 Risk and Complexity
Finally, it might be argued that the type of betting event, which affects the complex-
ity of the decision problem, may inﬂuence bettors’ attitudes toward/appetite for risk.
In the context of horse race betting markets, key factors in determining complexity
are the number of runners in the race and the race’s status as a handicap or non-
handicap event. For all races, and their associated betting markets, complexity is seen
as increasing with the number of runners (alternative-related complexity). Attribute-
related complexity is greater in markets relating to handicap races, where the value of a
key attribute (weight carried by the horse) is designed to compensate for other horse-
speciﬁc, ability-related attributes in order to contrive a competitive race. Comparison
of risk behavior across events of differing complexity suggests a range of effects. Using
a probit model, Johnson and Bruce (1997a) noted an increased tendency to limit risk
by betting on favorites as both alternative- and attribute-based complexity increase
but with a more marked effect evident as alternatives increase. Johnson and Bruce
(1997b) employed three further measures of risk-taking in investigating the determi-
nants of staking,absolute odds,and relative odds (odds relative to mean market odds) as
dependent variables, using both multivariate analysis of variance and separate univari-
ate analyses. Distinctions between win and each-way betting were explored also. The
results suggest that staking levels are not inﬂuenced by either alternative- or attribute-
based complexity. In terms of raw odds as a measure of risk, there is no signiﬁcant
difference between handicaps and non-handicaps, but there is a propensity for odds
to increase (i.e., greater risk) as the number of runners increases. Using relative odds,
there appears to be greater risk propensity in handicaps than non-handicaps but little
discernible effect on relative risk as number of runners varies. It is clear from this set
of results that effects are highly sensitive to the particular measure of risk employed.
There is a clear indication that the win/each-way decision forms an important element
in the management of risk, particularly in relation to bettors who appear to be risk
averse in terms of their choice of non-handicap (low attribute-based complexity) races.
For this group, the each-way option appears to facilitate betting on longer odds horses.
Perhaps the most important contribution of this paper, however, is to demonstrate the
importance of interactive effects between alternative and attribute-deﬁned complexity.

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motivation, behavior, and decision-making in betting markets
Most strikingly, the combination of high-attribute and high alternative–based com-
plexity, handicap races with very large numbers of runners, appears to elicit very high
levels of risk exposure, suggestive of a multiplicative relationship between complexity
forms.
4.1.1.4 Risk and Gender
The potential impact of a bettor’s gender on attitudes to risk and risk behavior is an
issue of increasing importance, as more women gamble (any numbers on this trend?).
The contemporary literature on gender differences in risk appetite among decision-
makers, suggesting a greater risk propensity among males (Keinan, Meir, and
Gome-Nevirovsky 1984; Levin, Snyder, and Chapman (1988), motivated an inves-
tigation of gender-based differences in risk-taking in betting by Bruce and Johnson
(1994). The results of this study were mixed. Males were signiﬁcantly more likely than
females to select “win” bets, rather than “each-way” bets, which embody an element
of insurance. While there was no signiﬁcant difference between genders in preference
for more complex (and inherently riskier) accumulator bets, there was evidence that
women preferred“any to come”accumulators, again suggesting a female preference for
some element of risk management as compared with men.
A follow-up study (Bruce and Johnson 1996) focusing simply on “single” bets
demonstrated a signiﬁcant tendency for women to select inherently riskier longer odds
selections as compared with men; 42 percent of men’s bets were placed on horses with
forecast odds of 5/1 or less compared with just 26 percent of women’s bets. On the
other hand, it appeared that women controlled their risk exposure in terms of odds
by demonstrating a preference for each-way betting, with the proportions of female
and male bets placed “each-way” being 39 and 25 percent, respectively. Perhaps the
strongest message to emerge from these investigations into gender inﬂuences on risk is
that perceptions and management of risk differ between men and women.
4.2 Performance
Just as the riskiness of a bet can be measured in various ways, so betting performance
can be viewed from a number of perspectives. Equally there are a number of factors
that have been identiﬁed by empirical inquiry as materially inﬂuential in determining
performance. This section begins with a consideration of performance measure before
addressing those factors which have been identiﬁed as signiﬁcant in determining or
affecting performance.
Very simply, in the context of a betting market, bets represent discrete decision
events so that one calculation of decision performance relates straightforwardly to
the rates of return realized by speciﬁc bets, individually or in aggregate. A related
measure measures proﬁtability per bet. Further measures include returns and proﬁts
per unit of stake wagered, which give a greater sense of the performance of bettors
in aggregate or subgroups of bettors. There are then measures of performance that

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467
focus on the proportion of bets or stakes which are successful in generating a return
or proﬁt.
In terms of the factors that might potentially inﬂuence performance, location and
timing of bet placement as well as the inﬂuence of complexity and excitement on
performance and the issue of gender-based performance differentials are considered.
4.2.1 Performance and Location of Bet Placement
One of the beneﬁts of working with betting data that segments bets according to
where they are placed is the insight this can generate into comparative performance
across locations. A recent study (Bruce, Johnson, and Peirson 2012) compared the
performance of “attendee” bets (bets placed at the racecourse on horse races run at the
venue) and bets placed remotely from the event venue (either off-course bets or bets
placed in an on-course setting on-course but on events at another course). The results
demonstrate a signiﬁcant performance advantage for remote bets. The interpretation
of these results centers on the likely distinctions between so-called professional and
recreational bettors, which are held to be dominant inﬂuences on the remote and
attendee populations, respectively. An interesting feature of this contribution’s results
is that they run contrary to an established empirical phenomenon observed in other
ﬁnancial market contexts, the home asset bias effect, which would tend to suggest
performance advantages where investors and assets are closely co-located (see, for
example, Coval and Moskowitz 2001). A potentially important element in the identiﬁed
performance differentials may relate to the highly charged atmosphere of the on-course
setting, which may militate against calm and rational decision-making, especially for
recreational bettors.
4.2.2 Performance and Timing of Bet Placement
A range of time-related effects on performance has been identiﬁed in the literature.
These include day of the week effects (e.g., Sung, Johnson and Peirson 2008), timing of
bet within the structure of the betting/racing day, and timing of bet within the duration
of individual betting markets.
In terms of performance effects associated with the timing of bet placement within
the betting day, as noted above, there is a literature relating speciﬁcally to last-race
effects (see, for example, Kopelman and Minkin 1991), where one contention is that
there are material changes in bettor behavior in the last race of the day, when bettors
will typically seek to recoup earlier losses. The comparative performance of bets in
early and late races as evidenced by Johnson and Bruce (1993) is generally suggestive of
a mild performance advantage for last-race bettors. Comparison of the proportion of
winning bets in the last race of the day (18.5%) with that in the ﬁrst three races (10.2%)
yields a striking and statistically signiﬁcant difference. These results may, in part, reﬂect
the relative risk aversion associated with later race betting.
Within the more strictly time-deﬁned conﬁnes of individual betting markets, an
interesting question relates to the degree to which markets yield performance-relevant

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motivation, behavior, and decision-making in betting markets
information through their evolution, as reﬂected in the changing patterns of available
prices. To the extent that this occurs, one might anticipate superior performance by
bets placed very late within the life of the market, where the exposure of event-relevant
information is most complete. In terms of the proportions of stakes producing both a
return and a proﬁt, Johnson and Bruce (1992) found highly signiﬁcant performance
advantages for end of market bettors as compared with earlier market bettors. Most
strikingly, more than half of the betting ofﬁce stakes wagered at “board price” (odds
guaranteed at time of bet placement) generated a net proﬁt compared with percentage
rates of proﬁt in the teens earlier in the market.
4.2.3 Performance and Complexity
Ithasbeenobservedthatbettingdecisioncontextswhicharecharacterizedbyhighlevels
of complexity may inﬂuence both levels of participation and the particular strategies
adopted in dealing with high levels of complexity. Unsurprisingly, perhaps, there is
also some evidence to suggest that complexity affects levels of performance in betting.
Bruce and Johnson (1996) employed two dimensions of complexity (alternative and
attribute-deﬁned) to discriminate between more and less complex betting events. The
results demonstrate that performance in complex events deﬁned in terms of alternatives
(here, the number of runners in a horse race) is signiﬁcantly compromised compared
with that in less complex settings. For races featuring 12 or fewer runners, performance
is signiﬁcantly better than in races featuring more than 12 runners. This is a consistent
result across both returns and proﬁts to bets and stakes, and in terms of comparative
average returns to stake, where the less and more complex sets of events yield ﬁgures of
0.92 and 0.52, respectively. Interestingly, using an attribute-based complexity measure,
where complex (by design) handicap races are compared with non-handicap events,
the distinction in performance effectively disappears, suggesting that bettors’ decision
performance is relatively invulnerable to attribute as compared with alternative-deﬁned
complexity.
4.2.4 Performance and Excitement
For many bettors it is fair to suggest that an important driver of participation is the
excitement associated with holding a ﬁnancial stake in an event of uncertain outcome
with the prospect of signiﬁcant ﬁnancial gain. This raises the question of the degree
to which bettor excitement may inhibit decision performance, in the sense that high
levels of arousal may be expected to compromise the capacity of for rational and
analytical consideration of the decision problem. One insight into this was offered by
Bruce and Johnson (1995), who sought to measure the cost (or value to the bettor)
of excitement. That paper reviewed the literature on the importance of excitement
to leisure experiences generally and noted the role of betting in amplifying the core
enjoyment of the leisure experience per se. A set of time intervals within the betting
day, deﬁned in terms of the intensity of associated excitement levels, was developed. The
results suggested quite strong distinctions between bets placed in the relatively tranquil

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469
morning period, remote from the buildup to and running of the race, and bets placed
in the turbulent and highly charged atmosphere associated with the second half of the
live on-course market, immediately prior to the race. These distinctions were evident
in terms of performance, with the high-excitement zone characterized by signiﬁcantly
poorer ﬁnancial outcomes. As noted above, levels of excitement might be expected to
vary with place as well as across time, and the results reported by Bruce, Johnson and
Peirson (2012) in relation to location of bet placement are suggestive of performance
penalties associated with high-excitement venues.
4.2.5 Performance and Gender
Gender differences in the form of betting, including preferences for particular types
of bet, were explored above. Comparisons of the performance of male and female
bettors also yield interesting results. The more recent general literature relating to
relative decision performance of men and women suggests negligible differences as
compared with earlier contributions (e.g., Priest and Hunsacker 1969), which identiﬁed
the performance superiority of males.
In terms of betting decision performance more speciﬁcally, Bruce and Johnson
(1994) reported highly signiﬁcant performance superiority for females in terms of
returns to both bets and stakes, though the advantage disappeared when proﬁts to
bets and stakes were considered. This study covered all forms of bet type and, as
such, it was speculated that the performance results may have been in large part
accounted for by female preferences for bets with an insurance component, which
would also help explain the distinction between returns to bets and stakes, on
the one hand, and proﬁts to bets and stakes, on the other hand. A further study
offered a “like-for—like” comparison by focusing on “single” bets only. Singles are the
simplest form of bet, where bet performance relates to one selection in a race. Strik-
ingly, all ﬁve performance measures demonstrated a signiﬁcant superiority of female
performance.
Reﬂecting on the inﬂuences on betting performance in general, it is clear that the
determinants of performance are multifaceted, not always straightforward and at times
counterintuitive. The above offers just a glimpse of the types of factor that may come
into play, variously speciﬁc to person, form of betting event, place, time or environmen-
tal aspects of the decision setting. Clearly there are often strong interactions between
these types of variables so that the tasks of disentangling and identifying the funda-
mental inﬂuences on betting performance remain a challenge for researchers in the
ﬁeld.
4.3 The Favorite-Longshot Bias as a Behavioral Phenomenon
While much of the above discussion relates to aspects of individual betting behavior,
it would be difﬁcult to end this contribution without a little further discussion on one

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motivation, behavior, and decision-making in betting markets
of the most pervasive and consistent phenomena in terms of aggregate behavior in
betting markets—the favorite-longshot bias. At the same time, such is the coverage of
this topic that it is difﬁcult to offer insights into favorite-longshot bias and its causes that
say anything new. This section is conﬁned, therefore, to some observations relating to
the origin of the bias. Speciﬁcally, it reports an alternative supply-side perspective on the
causes of bias, which differs in material respects from the received version, followed by
the introduction of the possibility that our understanding of the origins of the bias may
be enriched by incorporation of demand-side factors, which are capable of investigation
by studying the comparative behaviors of motivationally distinct subpopulations of
bettors.
By far the most inﬂuential contributor to the causes of the bias is Hyun Song Shin
(1991, 1992, 1993), whose focus on the possibility of insider activity in betting markets,
to which bookmakers are vulnerable, sees the particular pattern of (mis)alignment
between objective and subjective (implicit in odds) probabilities as arising from book-
makers’ pricing behavior in the face of this vulnerability, which varies with the number
of runners. Shin’s contribution in this area remains dominant but continues to invite
important questions.
First, to the extent that the bias is regarded as simply a supply-side phenomenon, does
the supply-side inﬂuence relate exclusively to the adverse selection issue and the factors
which affect vulnerability to adverse selection? Second, and more directly relevant to
anydiscussionof bettingmotivation,isitreasonabletosuggestthatdemand-sidefactors
have no inﬂuence on the bias? An examination of each of these questions follows.
In addressing the nature of the supply-side inﬂuence on the favorite-longshot bias,
while there is a fairly strong body of evidence to support the Shin view, to explain
the bias wholly in terms of bookmaker pricing being inﬂuenced by fear of adverse
selection seems too simple. Bookmakers have a variety of mechanisms independent
of the prices they offer to limit their risk exposure. They can, for example, refuse
to take bets, they can limit payouts, they can share risk with other bookmakers by
“laying off bets” where liability on one horse becomes uncomfortable. And as a pro-
fessional community, it is difﬁcult to view bookmakers as a vulnerable group that
is systematically at risk of exploitation by a diverse, differentially informed, and
overwhelmingly amateur clientele. Equally, there are other aspects of bookmaker
motivation, beyond fear of exposure to insiders, which might help to explain the
observed bias in the set of prices. So, for example, long shots may be shortened in
order to convey to recreational bettors that the chances of the horses in question
are not as remote as an “honest” assessment of odds might imply. Similarly, odds
relating to relative favorites may be lengthened to tempt more “serious” bettors to rec-
ognize the value in this part of the market. This may be particularly relevant where
bookmakers seek to attract the high revenues associated with this subgroup of the
betting population. The issue of collusive bookmaker behavior and its effects was
the subject of a recent investigation by Bruce and David Marginson (2012) in the
particular context of explaining the magnitude of the overround in betting markets.

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betting motivation and behavior
471
The overround reﬂects the degree to which the sum of implied probabilities embod-
ied in odds within a betting market exceeds one and offers a measure of bookmaker
margin. As a phenomenon it can be an inﬂuential factor in determining the degree of
favorite-longshot bias.
The rationale for exploring potential demand-side inﬂuences on the bias resides sim-
ply in the fact that prices, or menus of prices, are normally regarded as resulting from
the interaction of supply and demand factors and that odds or odds menus within bet-
ting markets are essentially no different. So, for example, the ability of bookmakers, as
suggested above, to inﬂuence bettors’activity toward particular areas of the market says
something about the way in which bettors perceive odds menus, and this in turn may
cast light on bettors’ motivations or utility functions. To the extent that bettors persist
in biasing their activity, or allowing their activity to be biased, toward less fertile (in
ﬁnancial terms) areas of the odds distribution, this suggests that their utility functions
are, indeed, populated by factors other than ﬁnancial return. In this context it has been
suggested that, for more recreational bettors, some utility may attach to the holding
of a betting slip which carries at least the theoretical possibility of a very substantial
return on investment even if the probability implicit in the odds is both very small in
absolute terms and smaller than the objective probability. This may suggest, in turn,
some appetite for increased risk independent of that which is regarded as the price paid
for a probability of higher return. Bruce et al. (2009) offered insights into the poten-
tial demand-side inﬂuences on bias by examining bias across subsets of an aggregate
pari-mutuel betting population. Their results suggest that motivational distinctions
between subpopulations affect the degree of bias and that relative transactions costs
and the nature of information and decision context inﬂuence the motivational com-
position of these subpopulations. As with the alternative perspective on supply-side
inﬂuences discussed above, these insights into demand-side factors suggest that there
are still aspects of the favorite-longshot bias which remain under researched and that
there are signiﬁcant limitations to a simple, adverse selection-base explanation of the
phenomenon.
Conclusion
.............................................................................................................................................................................
This chapter has provided a personal perspective on the related issues of betting
motivation and performance. Adopting this approach necessarily involves a subjective
emphasis, which reﬂects the author’s particular enthusiasm regarding certain topics,
themes, and methods. As such, this contribution makes no claim to offer an exhaus-
tive coverage of all aspects of motivation and behavior. Instead it provides an insight
into a rich, diverse, and growing ﬁeld of inquiry. While researchers will doubtless con-
tinue to strive for a deeper understanding of established behavioral curiosities, such
as the favorite-longshot bias, the continuing and rapid development of new forms of
engagement with betting markets, new betting media, and demographic changes in the

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472
motivation, behavior, and decision-making in betting markets
betting clientele introduce new questions that sustain and advance the research agenda
in this ﬁeld. This exciting broad research agenda is susceptible to inquiry from diverse
disciplinary and methodological perspectives, where different insights are increasingly
recognized as complementary and mutually enriching.
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chapter 25
........................................................................................................
MOTIVATION IN BETTING
MARKETS: SPECULATION,
CALCULUS, OR FUN?
........................................................................................................
les coleman
Betting markets are diverse but share several distinguishing traits.1 Generally they are
open for short periods and have an endpoint that relates to an event whose occurrence
(but not outcome) is known in advance. The events are conducted in public with strong
spectator interest, and bettors can expect to have or develop skill that gives them an
advantage. Bets are typically written by corporations or well-funded bookmakers but
are predominantly purchased by individuals. Due to substantial operating fees and
taxes, betting is a less-than-zero-sum transaction, and there are limited opportunities
to sell securities or to arbitrage positions. Betting markets, then, are very different from
ﬁnancial markets that trade long-lived securities whose value is set by events conducted
in private and which have sophisticated participants on both buy and sell sides and
parallel derivatives markets.
The unique structure of betting markets and the asymmetry between participants
on supply and demand sides raise the issue of the motivations of market participants. I
use motivation with the meaning of a force that is internal or external to the bettor that
triggers, directs, intensiﬁes, or leads to betting (Lee et al. 2007). My speciﬁc research
questions relate to what the literature tells us about the motivations of bettors and their
implications for betting markets.
Background
.............................................................................................................................................................................
Betting markets trade securities whose values are contingent on the outcome of a spec-
iﬁed event, typically the result of a contest between individual humans or animals,
sporting teams, political parties, or the like. In most cases the securities are issued

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motivation in betting markets: speculation, calculus, or fun?
475
over the counter by a bookmaker or pari-mutuel operator, though organized betting
exchanges, such as Betfair, are growing in scale. Payment for a successful bet can be
agreedinadvance(ﬁxedodds),bederivedfromotherbets(e.g.,themostfavorablestart-
ing price odds offered on the successful outcome), or be established by the proportion
of successful bets (as in a pari-mutuel system).
The typical assumption in ﬁnance about the value of any security is that it equals the
present value of its expected cash ﬂows discounted at a risk-adjusted rate (Damodaran
2002). This is less relevant to betting securities that relate to a single,near-term cash ﬂow
whose value is known or can be reasonably estimated. Moreover, the betting cash ﬂow
is contingent and will occur only in the event of particular outcomes among a num-
ber of possibilities. Bets, then, have more in common with options than bonds or
shares because options represent a contingent claim and because their payout, too, can
ﬂuctuate.
The typical approach to valuing bets is to multiply the expected payout from a
successful bet by its probability of occurrence. Consider an event that a bettor judges
has probability p of occurrence, which indicates a theoretical payout from a $1 bet
of $

1 + 1
p

. If the bettor can obtain a higher payout the bet has a positive expected
return and vice versa. In other words, rational bettors should place bets when their
expected probability of success is higher than that indicated by the odds on offer (i.e.,
Payout offerred > 1 + 1
p) and arbitrage should ensure that odds converge to reﬂect the
objective probability of success of each bet.
In practice, though, there is extensive evidence that betting markets are inefﬁcient in
the Fama (1970) sense. In particular, betting prices do not move randomly, or quickly
price in all publicly available information, and they do appear to offer opportunities
to proﬁt from private information. The many examples of irrationality or inefﬁciency
make it axiomatic that a signiﬁcant portion of bettors are not rational in the neoclassical
sense that they maximize expected utility. This is not surprising given that individuals
appear to be vulnerable to cognitive biases, which dominate the demand side of betting
markets. This allows rational bet sellers or large bettors to exploit the misjudgments
of individual bettors. There are several comprehensive reviews of anomalies in betting
markets (see Hausch and Ziemba 1995; Sauer 1998). Thus I will only brieﬂy summarize
several of the most important betting market biases, as they will support my contention
of inefﬁciency and form the basis for discussion of bettor motivations.
Perhaps the most consistent of all betting market anomalies is the longshot bias in
which high payout (that is, long odds or longshot) bets are priced above their expected
value and short odds bets are priced below their expected value. As a result the expected
return from short odds bets is greater than that from longshot bets, and expected return
rises with the probability of a win. This has been extensively documented in horse racing
(Coleman 2004) and in a variety of team sports, such as cricket, and individual contests,
such as boxing and tennis (Cain, Law, and Peel 2003).
A second near-universal bias relates to location of the contest. According to the
home team underdog bias, teams competing at home that have long odds of winning

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476
motivation, behavior, and decision-making in betting markets
are more successful than the market expects. There is also a home country bias
in contests with international participants such that odds on success by a com-
petitor of a given nationality are lower in that nation’s markets than in foreign
markets. This bias is sufﬁciently strong to justify formation of large international
syndicates that arbitrage bets in popular international contests, such as the various
world cups.
Semi-strong inefﬁciency is also said to exist in betting markets. The most obvious
example is that the payments for winning bets by pari-mutuel operators consistently
exceed those offered on identical runners by bookmakers (Gabriel and Marsden 1990).
This is not a true anomaly, however, as it is totally expected: bookmaker odds are
incremental because they apply only to current bets, whereas pari-mutuel odds are
cumulative, reﬂecting all bets to date. As odds on winners typically fall during the
betting period, at any point in the betting (incremental) bookmaker odds will be less
than (cumulative) pari-mutuel odds. Thus bookmaker starting price (SP) odds will be
less than the mean odds offered by the pari-mutuel operator.
Weak form inefﬁciency is evidenced by herding, where odds will trend in the same
direction for some time. In pari-mutuel markets this occurs when a disproportionate
volume of bets is placed on one outcome; in bookmaker markets it reﬂects the market
maker’s decision and so can be part of a strategy to induce herding.
There is also consistent evidence of strong form inefﬁciency in betting markets.
This exists due to chronic asymmetry in information among bookmakers, bettors,
and contestants and offers opportunities to proﬁt from private information, including
manipulation of the betting market and contest outcome.
Given the spread of economic analyses of betting market efﬁciency and biases it is not
surprising that some methodologies do not prove robust. Michael Cain, David Law, and
David Peel (2001), for instance, found that the Gabriel and Marsden anomaly does not
hold under different estimation methods. Another example is the inﬂuential method-
ology developed by Hyun Song Shin (1993) to calculate the extent of insider trading in
bookmaker markets. Shin, following the assumption that bookmakers manipulate the
supply side of the market to protect themselves against the risks of adverse selection,
derived a value, z, that represents the proportion of these bets. My own study (Cole-
man 2007b) showed that near identical values of z are obtained in bookmaker markets
and pari-mutuel markets. As the latter do not have a supply side and so should have
a zero value of z, the methodology’s premise is questionable. Similarly a number of
studies assume all bettors are risk averse, despite evidence that they embrace risk (with
its meaning of loss and higher volatility) and skew (e.g., Golec and Tamarkin 1998).
More broadly, but just as unlikely, are common assumptions that there is competition
between bookmakers (e.g., Cain, Law, and Peel 2001) and that skillful analysis of pub-
licly available information can lead to proﬁtable betting (e.g., Lessmann, Sung, and
Johnson 2009). Examples such as these suggest that betting studies are particularly sus-
ceptible to what Eugene Fama (1991, 1575) has termed “the joint hypothesis problem”
whereby models must rely on a priori assumptions that can be mis-speciﬁed and draw
invalid conclusions.

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motivation in betting markets: speculation, calculus, or fun?
477
The intuition behind this chapter is that biases and inefﬁciencies in betting markets
mean that bettors are not motivated solely by maximization of expected value. Thus
my research objective is to analyze bettors’ other possible motivations. This extends
previous studies which have usually involved only problem gamblers with a view to
mitigating the issue (see, for instance, Raylu and Oei 2002). These typically seek addic-
tive or psychological explanations, such as arousal effects, counters to depression, and
masochism. While these are important issues, most bettors are not addicts. Thus a
secondary research objective is to establish a framework to explain the motivations of
nonproblem bettors and hence contribute to a more complete depiction of behavior
that can help distinguish between those with and those without a betting problem.
Considerable research has been conducted on the motivation of gamblers, princi-
pally using slot machines and roulette and in both laboratory and naturalistic settings.
An open-ended study asked college students to list their top ﬁve reasons for gambling
and found the answers to be predominantly rational: money (22.1% of all motivations),
enjoyment/fun (18.4), social reasons (13.3), and excitement (9.8). Less than 12 percent
of all reasons related to such negative or pathological motivations as boredom, escape,
or drinking (Neighbours et al. 2002). Such studies support conventional, rational expla-
nations for betting, such as the ﬁnancial objective of winning, a preference for hedonic
fun and enjoyment, and the desire for stimulation and socialization. Another study con-
ducted a factor analysis of 51 possible motives for gambling and found that the most
important were excitement (including thrill and tension), socialization, avoidance of
negative feelings (troubles, loneliness, anger, anxiety), monetary gain, and amusement
(Lee et al. 2007). Other research, though, is less kind to bettors. Karim Benhsain, Alain
Taillefer, and Robert Ladouceur (2004, 399) begin their analysis with the claim that“the
majority of individuals behave and think irrationally when gambling.”
To summarize studies of the motivation of gamblers and bettors, Lee et al. (2006)
found three broad explanations. The ﬁrst involves social motives, such as participation
in gambling groups or escape from personal problems. The second is psychological
and perceives gambling as a self-determined pursuit of excitement or achievement,
including monetary reward. The third and ﬁnal base views gambling as an experience
that is consumed in the same way as tourism and watching movies.
To complement published sociological and psychological studies of bettor moti-
vations, the following sections discuss motivation from a ﬁnancial perspective,
particularly in terms of bettors’ attitudes toward risk, expected return, and socializa-
tion. I close with a brief discussion of the consequences for betting markets of different
bettor motivations.
Risk Attitudes in Betting
.............................................................................................................................................................................
For the average bettor, betting has a negative expected return of up to 30 per-
cent. This means that betting is highly risky, with risk taking on the meaning of

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478
motivation, behavior, and decision-making in betting markets
accepting the possibility of loss. Thus, with the exception of the few bettors whose
skill delivers signiﬁcantly more than the average return, it is hard to sustain a rational
economic motive for betting. This means that betting must provide some nonﬁnancial
beneﬁt.
A common explanation is in bettors’ attitudes toward risk, particularly as betting
offers a range of risk-return trade-offs. This is analogous to the concept in ﬁnan-
cial markets of speculation, which—though often ill-deﬁned—usually refers to the
purchase of securities or goods without an investment horizon, and without the expec-
tation of income, by a party who gains from their use or from a desire to hedge another
risk. A typical example is purchase of commodities or derivatives that do not gener-
ate income but ﬂuctuate widely in price. In conventional markets speculation involves
investing in risky (often leveraged) securities that have a high probability of negative
return but have an uncertain possibility of a disproportionate rise in price. Speculators
are generally thought to be risk prone and proﬁt by accepting risks from risk-averse
hedgers.
Parallels to ﬁnancial markets speculation can be seen in the actions of bettors who
buy option-like bets, including lottery-style longshot bets. The latter may reﬂect risk
embrace, but they can also meet a preference for skewness, or very high possible payout,
that is attractive to risk-neutral or even risk-averse bettors (Golec and Tamarkin 1998).
This preference of risk-averse bettors for lottery-like payouts is consistent with evidence
in other areas of life, such as investment (Kumar 2009).
This points to the existence of at least two discrete groups of bettors (Coleman
2004). The ﬁrst is informed or skilled, predominantly places low odds bets, and has
a positive (or near zero) expected return: this group is risk neutral. The second, and
larger, group is less skilled and informed, places longer odds bets largely in accordance
with chance, and has a signiﬁcantly negative expected return: these tend to be gam-
blers and risk lovers. The transition from risk aversion (positive expected return) to
risk embrace (negative expected return) occurs around an objective probability of a
positive outcome of about 0.2. This transition to risk embrace (or the overweighting
of long shots) matches the ﬁnding of Malcolm Preston and Philip Baratta (1948) that
probabilities of less than 0.25 are subject to systematic overestimation and is consistent
with ﬁndings on risk transitions by Colin Camerer (1995) and Amos Tversky and Craig
Fox (1995).
The importance of risk in bettors’ motivation poses an interesting challenge
to theories of decision-making under risk or uncertainty because it violates what
Tversky and Daniel Kahneman (1992) described as a key element: that in the
initial framing phase of a decision “transparently dominated prospects are elimi-
nated.” Bettors’ psychological makeup causes them to irrationally interpret available
information.
A risk-averse strategy is to follow changes in odds because those that reﬂect informed
trades move toward a closing price that more closely represents the actual outcome than
do opening odds at the start of betting. This is true of horse racing (Coleman 2007a),
basketball (Gandar et al. 1998), and other sports.

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motivation in betting markets: speculation, calculus, or fun?
479
Bettor Expectations of Return
.............................................................................................................................................................................
Extending the assumption developed earlier that rational bettors test the probability of
a win against odds on offer, information-driven expectations of return are important
motives for bettors and bet sellers. Irrespective of where the odds are set on contest
outcomes, if they rationally reﬂect available information the bet is only attractive to
bettors with different information that indicates a higher probability of winning.
There are a number of sources of superior bettor-speciﬁc information. It can be a
proprietary skill that more accurately calibrates the probability of a given outcome,
most obviously by using a superior process to interpret publicly available information.
In addition, some bettors have access to monopoly information. My guess is that it
would be hard to ﬁnd any bettor who does not believe that superior use of information,
particularly information that is not public, provides a source of incremental return to
betting on contests.
Looking ﬁrst at superior processing of public information, experts abound in betting.
Until the explosion of Internet-based wagering, virtually every newspaper published a
form guide or tip sheet on racing, football, and other popular betting contests. This
has prompted many analyses of betting experts’skill, particularly that of racing tipsters,
and the literature has been reviewed by John Peirson (2011) and Leighton Vaughan
Williams (2000). The general conclusion is that tipsters as a group are able to match
the accuracy and ﬁnancial return of the wagering market in racing. Because tipsters’
predictions are made without the beneﬁt of seeing the strength of others’ expectations
(for instance, through wagering market odds and changes in these odds) and well ahead
of the races’ commencement, it is easy to agree with Fergus Bolger and George Wright
(1994) that they have expertise.
It is not so easy to establish, though, whether or not this apparent expertise comes
from skill, as the sources of any skill are opaque. In an effort to identify the nature
of expertise or superior betting skill, Stephen Ceci and Jeffrey Liker (1986) recruited
30 men who were longtime patrons of a harness racetrack in Delaware, had extensive
knowledge of the industry, and purchased form guides ahead of race day. By comparing
the men’s ability to select starting favorites before any betting market formed, they
divided the group into 14 experts and 16 nonexperts who, respectively, picked at least 9
out of 10 favorites and less than 5 favorites. Means for the two groups were not different
when they were divided according to years of education (about 10), occupational
prestige, measured IQ (100), and years of experience in betting (15–17). After exploring
interactions, the researchers concluded that intelligence and learning do not determine
betting skill. Rather, it is related to use of a greater number of predictor variables, which
is equivalent to operating a more complex cognitive model.
There are more formalized evaluations of publicly available information. Michael
Kaplan (2002), for instance, provided an insight into the quantity and variety of data
collected by sophisticated betting syndicates. Stefan Lessmann, Ming-Chien Sung, and
Johnnie Johnson (2009) developed a two-stage betting model in which the ﬁrst stage

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480
motivation, behavior, and decision-making in betting markets
estimates the probability a horse will win by calculating its objective performance level
or ability and the second involves within-race ranking of horses’ relative ability.
Another source of superior valuations comes from the ability to manipulate bet-
ting markets, which was graphically illustrated by Camerer (1998). He hypothesized
that some bettors follow price signals and thus erroneous price signals could mislead
uninformed bettors and distort odds to the advantage of a market manipulator. The
author conducted a ﬁeld experiment using races which had two runners that matched
according to morning line odds and odds set in early betting. About 20 minutes before
the races started, he randomly chose one of the matched horses and placed a win bet
that was canceled about 15 minutes later. The second, unbet horse served as a control,
and odds on both horses were recorded. Betting $500 on 50 races showed no substantial
effect, and the experiment was modiﬁed to comprise two separate $500 bets at tracks
with smaller pools that were made later, at around 10 minutes before the start, and
canceled just before the start. This showed subsequent reduction in the odds of the bet
horse, which was more pronounced in maiden races where there was less information
available about the runners.
Conﬁrmation that this kind of market manipulation may be signiﬁcant comes from
the fact that pari-mutuel operators have changed their rules to limit the ability to cancel
bets in New Zealand (Camerer 1988, 460) and Australia (Templeton 2003).
A second source of manipulation is to affect the outcome of a contest rather than
market odds on the outcome. This can be to beneﬁt a team, such as in a round-robin
tournament where it may be advantageous to play poorly against a weak opponent
and allow them to progress to the next round ahead of a stronger opponent. Another
advantage to losing can come toward the end of a season when poorly ranked teams
can have an incentive to drop in the rankings to secure more favorable conditions in
picking next season’s players.
Sports can be corrupted by individuals for their own purposes. In cycling or motor
racing where individuals compete within a team, the ﬁnishing order can be agreed upon
in advance irrespective of individual performances. A speciﬁc example is provided in
a study by Mark Duggan and Steven Levitt (2002, 1595) of Japanese Sumo contests
over a decade, which found “overwhelming evidence that match rigging occurs in
the ﬁnal days of sumo tournaments.” Tournaments involve 15 bouts, and wrestlers
who win at least eight bouts are promoted in the rankings, which provides them with
signiﬁcant additional rewards. Duggan and Levitt found that wrestlers with seven wins
in a tournament are victorious more often than expected (and their opponents win a
disproportionate share of the next bouts, indicating payback) and are less successful
at the end of their careers. In addition, manipulation disappears when the media are
focused on match rigging.
Contest outcomes can also be manipulated to secure a higher return from gambling
on the result either by participants or by gamblers who use part of their winnings
to induce participants to rig the outcome. A good example of gambling corruption
involves U.S. basketball, which offers spread betting in which a bet on the shorter
priced team pays if the team wins by more than the spread (say 8.5 or 16.5 points)

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motivation in betting markets: speculation, calculus, or fun?
481
and a bet on the longer priced team pays if the team wins or loses by less than the
spread. The colloquial term for winning by less than the spread is point shaving, which
can promote manipulation because the team wins the game and secures championship
points but bookmakers do not pay out. An analysis by Justin Wolfers (2006) of 44,120
National Collegiate Athletic Association (NCAA) men’s basketball results in the period
1989–2005 concluded that as many as six percent of strong teams manipulated their
performance downward and thus that gambling-related corruption affected around
one percent of games. Richard Borghesi and William Dare (2009, 121) provided a list
of games that were found to have been manipulated and revisited Wolfers’s data to
conclude that “strong favourites . . . win as frequently as expected, but by a margin less
than anticipated.”
Wolfgang Maennig (2005), Ian Preston and Stefan Szymanski (2003), and Stefan
Winter and Martin Kukuk (2008) have provided a good range of examples of betting-
related corruption in sport. Manipulation is more likely when it does not affect the
outcome of the game (e.g., such within-game betting as which player makes the ﬁrst
score), when opponents face asymmetric rewards from winning (as is the case in leagues
with relegation or advancement of teams from one season to the next), or with spread
betting when the game can be won but the bet lost.
While the media in many countries carry frequent stories of betting-related corrup-
tion, there are surprisingly few proven cases. Borghesi (2008), for instance, reported
that it has been more than 50 years since there has been a documented case of corrup-
tion in the four major American professional sports of basketball, football, baseball,
and hockey. At the other extreme is cricket, against which numerous instances have
been documented, often alleged to be tied to bookmakers in India (Maennig 2005).2
In the middle is horse racing where there is a lot of anecdotal evidence of corruption
but relatively few proven cases (Coleman 2007a). Corruption seems more common in
countries where betting is weakly regulated and in sports where regulations are not
enforced.
A further source of superior valuations is monopoly, or insider, information that
is not generally available to other bettors, and this has stimulated a rich literature of
economic analyses that seek to identify the incidence of insider trading. A review of a
variety of betting markets by Cain,Law,and Peel (2003) using a methodology developed
by Shin (1993) estimated that insiders place between two and eight percent of bets,
which is consistent with results using a different technique by Les Coleman (2007a).
Betting as Socialization
.............................................................................................................................................................................
A commonly accepted nonﬁnancial motivation for betting arises in such factors as
socialization, fun, excitement, and other personal or recreational needs. Socialization
motives can be strengthened when betting is conducted around spectator sports—
cricket and football, horse and dog racing—or in entertainment complexes, such as

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motivation, behavior, and decision-making in betting markets
racinos. Supporting the importance of betting for fun and excitement is the fact that
this is the emphasis of most advertising for betting. Another possible explanation for
this tilt in advertising is that men are more likely than woman to place a bet, and
women may be attracted by its context. A related motivation is achievement where
bettors exploit a developable skill, such as counting cards in blackjack. In each case bets
are simply consumption goods and purchased in much the same way as a movie ticket
or language training.
Betting has another personal attraction, which is that participants have total control
over their decisions. This appeals to those with a preference for self-determination
and also feeds into the illusion of control, or the belief that bettors can foster a win
through their efforts, even in the face of conﬂicting evidence. This was a popular
subject of research during the 1960s and 1970s, and a number of exotic experiments
were performed to replicate the ﬁnding that people have most conﬁdence in events
they can control. Howell (1971) tested students who threw darts at a board and were
rewarded in proportion to their score multiplied by a number obtained at random from
spinning a roulette wheel. This resulted in multiple paired outcomes determined by the
combination of a factor within the students’ control (dart score) and a factor beyond
their control (roulette wheel’s result). After a familiarization period, students played
for money and—when able to choose the criteria for a win—consistently preferred
outcomes where the greatest uncertainty related to the dart; in other words, they
preferred to back their own skill rather than trust chance.
A consequence of extensive betting for nonﬁnancial motives is that these bets will be
distributed according to a relatively narrow range of factors (perhaps the leading jockey
or trainer in horse racing or a home team) or factors that are not commonly associated
with winning (contestant’s name or colors). This can induce an element of randomness
in bets that—in popular contests, such as the Super Bowl, or glamour races—can
swamp biases. That is, social bettors have different valuations of bet outcomes.
Consequences for Betting Markets of
Heterogeneous Bettor Motivations
.............................................................................................................................................................................
In closing, let me discuss the consequences of bettors’ varying motivations for betting
markets.
Perhaps the most important economic question is where the inefﬁciencies and biases
in betting markets arise. Obviously in pari-mutuel markets that do not have a supply
side, anomalies arise in the pricing decisions of bettors. But what is the relative contri-
bution of the different bettor populations? And, of course, in bookmaker markets there
is the added complexity of a sophisticated supply side: so where do biases arise here?
The most obvious point to make is that many of the biases in betting markets are
amenable to multiple explanations. Consider as an example the longshot bias, which

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## Page 504

motivation in betting markets: speculation, calculus, or fun?
483
is due to relative overpricing of low-probability winners. One common explanation
is risk, so that some bettors prefer the higher variance of long shots. Alternatively
the higher skew of long shots—where wins bring bragging rights—can be attractive
even to risk-averse bettors. The bias may be perceptual, where bettors overestimate
the probability of low-frequency events because they are more memorable. In any
case, bettor populations are segmented such that some bettors pay too much for low-
probability winners and induce the longshot bias. Other explanations for the longshot
bias that are consistent with heterogeneous bettors is that informed money bets on
favorites with long shots attracting less informed money from irrational, less-informed
bettors who suspect that public information is incomplete or erroneously discount the
attractiveness of favorites.
Most analyses of betting market biases look to demand-side causes,3 but an intu-
itively obvious source of bias in betting markets with a supply side (that is, bookmaker
markets, casinos, and lotteries) is the asymmetry between participants on the supply
and demand sides. Usually there are few suppliers of bets, and their prices are suf-
ﬁciently similar to suggest collusion (an alternative explanation of low, competitive
prices under perfect competition is inconsistent with reported proﬁtability of casinos,
lotteries, and bookmakers). They are, then, oligopolies, which give opportunities to
extract rent through biases in pricing. Another advantage is that it is expensive to
obtain private information (or manipulate results) for most contests that attract bets,
and the higher turnover of bet suppliers makes it easier for them to pay the high ﬁxed
costs for monopoly information on contests. Thus, biases and inefﬁciencies could arise
if bet suppliers use monopoly power to distort prices to their advantage and are better
able than bettors to form more accurate expectations of contest outcomes. This is a
totally rational outcome because the volume of transactions in betting markets makes it
very attractive for the most skilled and knowledgeable bettors to operate on the supply
side.4
A strong indication that biases arise on the supply side comes from the fact that bet
prices in markets with a supply side experience little change. Many are ﬁxed, particularly
games of chance, such as lotteries, roulette, or slot machines, which have a constant
payout. Operators of these ﬁxed-odds games have designed them to be attractive to
bettors, despite a negative expected return. Even in the case of betting markets prices
change relatively infrequently through the course of betting (Levitt 2004). In the case
of U.S. National Basketball Association games, for example, the point spread changes
by less than half a point in more than half the games; given that the mean opening line
spread is 4.8 points, this means that the spread is relatively constant (Gandar et al. 1998).
Moreover, except at the extremes, the odds offered differ little between bookmakers
and usually are similar to those in the pari-mutuel market. Thus casinos, lotteries, and
bookmakers are adept at setting prices—and hence expected returns—at a level that
is attractive to bettors, and fragmented participants on the demand side of betting
have no control over the bets’ structure and little inﬂuence on bet prices. In addition,
bet suppliers can leverage monopoly information and skill to bias odds in their favor.

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motivation, behavior, and decision-making in betting markets
As an example, knowing that bettors prefer local teams, bet suppliers could generate
abnormal return by offering high odds on foreign teams and low odds on local teams.
In short, market makers construct attractive and proﬁtable bets by catering explicitly
to the motivations and preferences of bettors and by besting bettors at forecasting
contest outcomes.
The implications of this are profound for betting market researchers. The latter
usually follow the assumption of Richard Thaler and William Ziemba (1988) that
wagering markets are mirrors of conventional markets, efﬁcient, and thus well suited
to ﬁnancial studies. The conclusions above are quite different, as they highlight the
heterogeneity of bet buyers and the large asymmetries between buyers and sellers of
bets that make betting markets totally different from conventional markets. Betting
markets have a negative expected outcome for bettors, whereas conventional markets
have a positive expected outcome over time for investors. Absent IPOs, conventional
markets have similar participants on buy and sell sides, whereas betting markets are
oligopolies. Information and skill are diffused through conventional markets but are
concentrated on the supply side of betting markets. Regulation of conventional markets
isgenerallystrong,whereasitappearsmuchlessrobustinbettingmarkets. Thus,models
of betting markets that assume competition, efﬁciency, and behaviors similar to those
in conventional markets can be mis-speciﬁed and hence, reach erroneous conclusions.
Notes
1. I use the terms betting market and bettor to emphasize that most of my material and
discussion relate to contests other than those involving games of chance (such as roulette,
lotteries, and slots) where participants are better described as gamblers. The expected
return from both bets on contests and gambles on games of chance is negative but skewed,
so a small proportion of players can expect to make money. However, because gambles
involve random events, only bettors can be rationally expected to have some inﬂuence
over the outcome.
2. A series of links to materials cataloging corruption in international cricket are provided
by the Australian Broadcasting Corporation at www.abc.net.au/4corners/content/2010/
s3047207.htm.
3. A prominent exception is the Shin (1993) methodology for calculating the amount of
insider trading that assumes it can be observed in bookmaker-induced biases to protect
against insider bettors.
4. Why does this situation not occur in conventional markets where it appears that the most
sophisticated investors—fund managers—are generally unable to beat the market?
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chapter 26
........................................................................................................
EVIDENCE OF BIASED
DECISION-MAKING IN
BETTING MARKETS
........................................................................................................
david mcdonald, ming-chien sung,
and johnnie johnson
Psychologists have long been aware of the limitations of normative models of judg-
ment and decision-making. Herbert Simon’s (1955) work on bounded rationality
criticized rational models of decision-making for disregarding such factors as the indi-
viduals’limited cognitive capacity. Subsequently experimental psychologists conﬁrmed
through a series of experiments that decisions are systematically biased in many ways,
with decision-makers adopting rules of thumb or “heuristics” in order to more rapidly
solve complex problems (Kahneman et al. 1982). However, the vast majority of research
in this area has involved experimental investigations conducted under controlled lab-
oratory conditions. This has led to researchers questioning the generalizability of the
results (e.g., Bruce and Johnson 2003; Levitt and List 2007). In particular it is well
understood that laboratory experiments cannot replicate the richness and complexity
of real-life situations. As Léon Festinger (1953, 141) noted: “In the most excellently
done laboratory experiment, the strength to which the various variables can be pro-
duced is extremely weak compared to the strength with which these variables exist and
operate in real life situations.” Naturalistic environments offer an attractive alternative
for examining decision-making behavior, featuring subjects who are experienced in the
task at hand (whereas most laboratory experiments involve naive subjects with little
domain knowledge) and who are not aware that their actions are being scrutinized (as
in most laboratory experiments).
Betting markets constitute naturalistic decision-making environments that offer
great potential for helping to understand individuals’ decision-making behavior. These
markets feature many of the aspects of real-world decision environments. In particular,
they are associated with rich, dynamic information sets, offer strong incentives to par-
ticipants for success, require the commitment of the individual’s own resources, and

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motivation, behavior, and decision-making in betting markets
involve repeated trials, offering signiﬁcant potential for learning. This chapter provides
a survey of previous studies that have employed betting markets of various kinds to
investigate the decisions made by bettors with particular reference to systematic biases
that were ﬁrst identiﬁed in the laboratory.
The remainder of this chapter is structured in four main parts. First we summa-
rize the debate over the generalizability of laboratory ﬁndings and identify the ways in
which naturalistic environments offer an alternative for studying the extent to which
individuals’decisions are biased. In particular we outline the usefulness of betting mar-
kets and review a range of studies that have demonstrated that bettors are in many ways
rational and well-calibrated decision-makers. Secondly, we brieﬂy discuss the widely
documented favorite-longshot bias, with particular attention to studies concerned with
the psychological factors that may cause the bias. Third, we address two decision biases,
anchoring and herding, each of which involve judgments of some unknown quantity
being unduly inﬂuenced by external stimuli. Finally, we survey studies that have inves-
tigated biases that result from a failure of individuals to recognise randomness: the
gambler’s fallacy and the hot hand fallacy.
1 Betting Markets as a Naturalistic
Environment in which to study
Decision-Making
.............................................................................................................................................................................
1.1 The Generalizability of Findings from Laboratory Studies
At the heart of this discussion is the distinction between experiments conducted under
controlled conditions in artiﬁcial laboratory settings and analysis of data obtained
from naturalistic environments, such as casinos, lotteries, and markets for betting on
horse races or other sports.
While experiments can be carried out under controlled conditions in artiﬁcial “real-
world” environments, we deﬁne a naturalistic environment to be one that “has not
been artiﬁcially manipulated (i.e., a nonexperimental setting)” (Johnson and Bruce
2001, 266). This distinction is crucial, and there is a long-running debate concerning
the relative merits of the two alternative methodologies when employed in experi-
mental psychology (e.g., Ebbesen and Koneˇcni 1980; Hogarth 1981; Funder 1987,
Bruce and Johnson 2003) or economics (Harrison and List 2004; Levitt and List
2007). Levitt and List (2007) pointed out that a critical assumption in experimen-
tation is that results generalize to the broader population. This generalizability or
“external validity” has been seriously questioned because of signiﬁcant variations in
observed behavior between laboratory and naturalistic environments (e.g., Ebbesen
and Koneˇcni 1980; Koehler 1996). The factors that have been identiﬁed as limiting

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evidence of biased decision-making in betting markets
489
the generalizability of laboratory experiments (cf. naturalistic studies) include the
following:
1. Context: The context in which decisions are evaluated is of central importance.
Laboratory environments often present simpliﬁed versions of tasks that may be more
complex in real-world environments. As a result laboratory experiments may uninten-
tionally omit variables that are inﬂuential in the natural setting. It has been reported
that signiﬁcant differences in behavior may depend only on small changes to the exper-
imental conditions (Ayton and Wright 1994), and Glenn Harrison and John List (2004,
1010) noted that
although it is tempting to view ﬁeld experiments as simply less controlled variants of
laboratory experiments, we argue that to do so would be to seriously mischaracterize
them. What passes for“control”in laboratory experiments might in fact be precisely
the opposite if it is artiﬁcial to the subject or context of the task.
In addition, there are things that the experimenter cannot control, such as past experi-
ences or social norms, which can affect the results (Levitt and List 2007). Furthermore,
laboratory experimentation is often conducted under a condensed time frame rather
than the extended period within which interaction occurs in naturalistic settings. In the
real world, cognitive processes are“trained”over time and individuals develop strategies
that can handle redundant and unreliable data. However, these strategies prove inap-
propriate when tackling the normal “static” tasks set in laboratory experiments. Biases
in judgment recorded in the laboratory may simply be a response to that particular lab-
oratory stimulus, and those same biases may not occur under ordinary circumstances
(even while resulting from the same cognitive processes). For example, when mistakes
are made in visual perception tasks in the laboratory, it is usually assumed that the
mechanisms that result in the error generally produce correct judgments in real life
(Funder 1987).1
2. Experience: Laboratory-based studies typically use university students, who may
be inexperienced in tackling the kind of tasks with which they are presented. It is
possible for inexperienced subjects to misinterpret the problem, whereas this is far
less likely among participants experienced with the task. Robin Hogarth (1981) high-
lighted the importance of feedback in making correct decisions over the continuous
time period often associated with real-world decision-making tasks. This is not pos-
sible in many “one-shot game” laboratory studies where there is no potential for the
participants to learn from their mistakes. Laboratory participants often lack exper-
tise in the tasks presented to them, so they fail to apply the correct strategies. Even
worse, they frequently carry “baggage”: behavior learned in the outside world entirely
unsuited to the problem at hand (e.g., Burns 1985). Furthermore, a number of
studies demonstrate large differences between the decision strategies of experts and
novices in terms of the way they think, the information set and the nature of the
decision models they employ, and the speed and accuracy of their problem solving
(e.g., Larkin et al. 1980).

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motivation, behavior, and decision-making in betting markets
3. Scrutiny: Participants in laboratory experiments, who are generally aware that
they are being investigated, may be keen to project a particular image (even if they
have no idea of the purpose of the experiment). The student volunteers studied in
most investigations are more likely to be “scientiﬁc do-gooders” (e.g., interested in the
research or seeking approval from the experimenter) with unusually high awareness of
the moral implications of their decisions (Levitt and List 2007). Scrutiny may therefore
exaggerate the importance of pro-social behaviors, such as altruism and fairness. Con-
versely, the anonymity that is often present in real settings may allow decision-makers
to feel that they are able to avoid being judged morally.
4. Incentives: Laboratory experiments are usually conducted with relatively trivial
rewards for success. However, in the real world, decision-makers are often involved in
high-stakes environments where they must commit their own or others’ resources and
where the results of their decisions can have signiﬁcant personal consequences. These
high-stakes environments can, therefore, involve a meaningful degree of risk. This can
lead to a marked difference in risk-taking behavior between laboratory and real-world
environments (Yates 1992). For example, the lack of excitement and low arousal levels
in laboratory studies may lead to behaviors that would not be present in real settings
(Anderson and Brown 1984).
The issues discussed above may all limit the potential for generalizing the biased
behavior often found among laboratory participants to the wider population. How-
ever, to discard laboratory ﬁndings outright would be naive (Hogarth 1981). Rather,
data gathered in the laboratory and under naturalistic conditions have their own
strengths and weaknesses, and these data should be considered complementary (Keren
and Wagenaar 1985). For instance, naturalistic work suffers from the inability to use
control groups and difﬁculties associated with the replication of results. In addition,
laboratory-based investigations are usually more cost-effective and afford the possibility
of isolating speciﬁc variables.
1.2 Betting Markets as Valuable Naturalistic
Environments
Betting markets, whether markets for bets on horse races, sports, or lotteries, offer
an ideal naturalistic environment in which to explore biased decision-making. A key
pragmatic advantage is the availability of extensive, rich, and detailed quantitative
data relating to bettors’ decisions. Since markets are ﬁnite in nature, there is a con-
tinually expanding set of “completed” markets, that is, a time period during which
betting continues up to a deﬁned endpoint, at which time all bets are settled in an
unambiguous manner.2 Furthermore, there is potential for comparative analysis across
different types of event or bet, according to such recognized criteria as the quality
(e.g., Smith et al. 2006), time of day (e.g., McGlothlin 1956), or complexity (e.g.,
Johnson and Bruce 1998) of the event. Thus it is possible to control for some aspects

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evidence of biased decision-making in betting markets
491
of the decision setting. Most importantly, betting markets include many of the factors
regarded as distinctive to naturalistic decision-making (Orasanu and Connolly 1993):
uncertain dynamic environments, poorly-structured problems, high stakes, time stress,
action/feedback loops, and multiple players. Each element of the decision-making event
(i.e., the bet) is unique: no two horse races or football matches are the same. Thus the
outcome is uncertain, and the information relating to that outcome is often (as it is in
many real-world decision environments) ambiguous, vague, or redundant. For exam-
ple, it is not obvious how to combine the various factors that might enable one to predict
participants’ performance. The dynamic nature of betting markets is evidenced by the
constantly updating prices as bettors with diverging opinions participate in the market.
Bettors, like many decision-makers in real-world environments, often risk mean-
ingful amounts of money while under stress from time pressures (the window of
opportunity in a betting market may last only minutes, or even seconds). A further
important feature of these markets is the repetitive nature of betting. Since events take
place regularly and often, there is potential for gaining familiarity and expertise with
the task. Betting markets involve action-feedback loops; once bets have been placed and
a market is closed and decided, bettors receive relatively unambiguous feedback on the
success of their decisions, and this can be incorporated into future decisions (Good-
man 1998). Also, betting markets involve multiple players, and it has been shown that
the interaction between individuals in markets can signiﬁcantly reduce errors (Wallsten
et al. 1997). This results from a variety of causes, not least the fact that different individ-
uals use different decision-making procedures and have diverse information gathering
skills. As a result, their reaction to the same information may vary. Consequently, the
ﬁnal prices that emerge in these markets take into account a wide range of informa-
tion and the forecasts of many individuals, and studies show that combining diverse
forecasts generally leads to signiﬁcantly more accurate predictions (e.g., Grant and
Johnstone 2010; Vlastakis, Dotsis, and Markellos 2009). In addition, betting markets
are not subject to several of the limitations of laboratory investigations listed above.
For example, bettors are unaware that their decisions may be scrutinized, as they are
not directly volunteering to take part in an experiment; instead, betting patterns are
analyzed in such a way as to observe their decisions unobtrusively.
1.3 Analyzing Decision-Making Using Betting
Market Data
The operation of betting markets is straightforward, which helps in the analysis of
decision-making behavior. Speciﬁcally, in a betting market individuals are able to place
bets on a set of outcomes of a particular event. For instance, in the simplest of markets
for betting on a horse race with n runners, n different bets are available, one for
each horse to win the race. After the market has closed and the race has taken place,
each bet pays a return, £ri, for each £1 staked if horse i wins the race but pays nothing

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motivation, behavior, and decision-making in betting markets
otherwise. While the returns, ri (usually referred to as the“odds”against each outcome),
are determined differently according to the type of market and event, generally they
depend on the relative amounts bet on each outcome by all the market participants.
Consequently, bettors have an incentive to continue to place money on each outcome
until the returns reﬂect the market’s best estimate of that outcome’s probability of
occurring (Figlewski 1979). Therefore, a typical approach to assessing decisions in
betting markets is summarized (with reference to horse race betting) by R. M. Grifﬁth
(1949, 290) as follows:
the odds on the various horses in any race are a functioning of the proportion of the
total money that is bet on each and hence are socially determined. On the other hand,
the objective probability for winners from any group of horses is given a posteriori
by the percentage of winners. Thus the odds express (reciprocally) a psychological
probability while the percentage of winners at any odds group measures the true
probability; any consistent discrepancy between the two may cast light not only on
the speciﬁc topics of horse-race betting and gambling but on the more general ﬁeld
of the psychology of probabilities.
So, the “socially determined” prices in betting markets reﬂect the “subjective proba-
bilities” assigned to each possible outcome by the bettors, in aggregate. The results of
the event then determine the “objective probabilities.” A comparison of subjective and
objective probabilities thus allows an evaluation of any biases in bettors’ decisions. If
the betting is such that the relative volumes of betting on each outcome introduce a
systematic bias, this can be detected by researchers.
A drawback of most betting market research is that, for ethical and/or practical
reasons, it is usually not possible to obtain information relating to the decisions of
individual bettors. Instead, subjective probabilities are an aggregation of opinions of
all bettors. Hence it is possible that “certain biases present in an individual bettor’s
decisions are being counterbalanced by opposite biases in other bettors’ decisions”
(Johnson and Bruce 2001, 280). Colin Camerer (1987, 982) noted that a common
argument for the rationality of market participants is that “random mistakes of indi-
viduals will cancel out” but also offered the counterargument that “biases found
by psychologists are generally systematic—most people err in the same direction.”
Thus the best we can hope for in betting market research is evidence of systematic
bias.
A further weakness of employing betting market data to examine decision behavior
is that psychologically signiﬁcant biases also hold an economic signiﬁcance. Conse-
quently, if some bettors (even a small group) become aware of an overall disparity
between subjective and objective probabilities, they can potentially proﬁt by bet-
ting against the bias. This could reduce the extent to which any systematic bias that
exists among bettors is detectable from aggregate betting market data. Fortunately for
researchers, transaction costs ensure that it is rarely possible to entirely arbitrage away
biases.

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evidence of biased decision-making in betting markets
493
1.4 Calibration of Bettors’ Judgments
Given the above discussion, it might be expected that bettors display signiﬁcantly
less biased judgment in their natural domain than that demonstrated among naive
participants in laboratory experiments. Indeed, a number of studies have investigated
bettors’ rationality and calibration. Speciﬁcally, Richard Rosett (1965) found that
horse race bettors are generally sophisticated and rational agents who will not forgo
combinations or sequences of bets when such bets offer a higher probability of win-
ning for the same return or a higher return for the same probability of winning.
Furthermore, results reveal a high correlation between expected returns and realized
winning probabilities, suggesting that bettors are familiar with their decision-making
environment and are able to accurately forecast risky outcomes.3 Rosett (1965, 596)
noted that
if these gamblers behave as though they know statistical prediction methods and
the probability calculus, it seems reasonable to suppose that, in a variety of other
circumstances, human beings can be expected to respond appropriately to risky
situations merely after having had sufﬁcient experience with them.
Johnnie Johnson andAlistair Bruce (2001) also investigated the calibration of horse race
bettors’ subjective probability judgments. They found that bettors’ subjective proba-
bilities are not signiﬁcantly different from the observed objective probabilities. They
noted that while there is substantial evidence of poor calibration among decision-
makers, this may reﬂect on the speciﬁc laboratory experiments involved. For example,
James Shanteau (1992) suggested that task characteristics may account for differences
observed in the quality of experts’ judgments; speciﬁcally, more competent perfor-
mance is likely if the decisions involve stimuli that are relatively constant, the tasks
undertaken are repetitive, and decision aids are widely available. Furthermore, it has
been empirically observed that violations of rationality are reduced under the multiple-
play conditions that exist at the racetrack (e.g., Keren and Wagenaar 1987). Johnson
and Bruce’s (2001) study therefore suggests that bettors are skilled in a similar way to
weather forecasters, who are also required to make frequent risky forecasts (Murphy
and Brown 1984). Arthur Hoerl and Herbert Fallin (1974) also found no signiﬁcant
difference between subjective and objective probabilities in horse races. They argued
that this was due to the high incentives available for successful gambling.
Not only are bettors well calibrated in general, but they are able to constantly adapt
to uncertain and dynamic information. Johnson, Raymond O’Brien, and Ming-Chien
Sung (2010) investigated how bettors respond to changing information. They set out
to test Gerd Gigerenzer’s (2000) assertion that evolution has equipped individuals to
process probabilistic information from frequencies observed in a natural environment.
They investigated the extent to which horse race bettors accounted for post position bias
(an advantage/disadvantage afforded to the horses depending on their position in the
starting stalls for the race), a factor shown to be a particularly important determinate of

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motivation, behavior, and decision-making in betting markets
race outcome at the racetrack examined. Despite the fact that track managers employed
a variety of procedures to change the bias (even between two consecutive races on the
same day and often unannounced) bettors were able to account for most of the dynamic
and changing information through regular outcome feedback, over a period of 6 years.
This important ﬁnding may be accounted for by the fact that (i) bettors have a strong
motivation to make accurate probability judgments, as their own ﬁnancial resources
and often their peer group esteem depend on the outcome of their decisions (Saunders
and Turner 1987), and (ii) those who frequently make probability judgments are often
better calibrated (Ferrell 1994). It has also been shown that bettors’ calibration is
generally improving over time (Smith and Vaughan Williams 2010) and that expert
bettors employ complex mental models encompassing a wide range of variables and
interactions between these variables (Ceci and Liker 1986).
In summary, naturalistic environments, and betting markets in particular, offer rich,
complex settings in which to examine decision-making biases that have been observed
in the laboratory. Due to a number of factors, such as learning, outcome feedback,
and incentives, bettors appear to be more rational, well calibrated, and able to adapt
to dynamic information than participants in laboratory studies. However, there are a
number of ways in which bettors are biased; the ﬁrst, and most widely documented of
these, is the favorite-longshot bias, which is the focus of the next section.
2 Favorite-Longshot Bias
.............................................................................................................................................................................
By far the most widely reported departure from rationality reported in the betting
literature is that of the favorite-longshot bias (FLB). Reported over many decades and
in many jurisdictions around the world, the bias is the phenomenon whereby returns
to bets are such that the chances of low-/high-probability events (long shots/favorites)
are over-/under-estimated.
2.1 Laboratory Evidence of the Bias
Malcolm Preston and Philip Baratta (1948) provided early laboratory evidence of the
bias. They were concerned that “rational” theories of behavior could not universally
explain peculiarities in the way people approached “wagering games” (i.e., games in
which participants are required to bet on an uncertain outcome). They hypothesized
that players might apply a scale of “psychological” probabilities to outcomes that are
not necessarily the same as the mathematically correct probabilities of those outcomes.
In order to investigate this possibility they carried out games with both undergrad-
uate students and faculty members (the latter were more experienced in the ﬁelds
of mathematics, statistics, and psychology). The game required the participants to

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evidence of biased decision-making in betting markets
495
compete against each other, bidding for the chance to win a given prize with a given
probability. They found that the players tended to pay too generously for outcomes
with low probabilities and not high enough for outcomes with high probabilities. This
result was independent of the value of the prizes. The indifference point, where the psy-
chological and mathematical probabilities corresponded, was found to be about 0.20.
Moreover, the faculty members also displayed the bias (though to a lesser extent than
the undergraduates) despite in many cases appearing to actively employ mathematics
when forming their decisions. This suggests that expertise only partially eliminates the
bias. The experimental ﬁndings of Preston and Baratta have since been conﬁrmed in
numerous laboratory experiments (e.g., Yaari 1965; Rosett 1971; Lichtenstein et al.
1974; Piron and Smith 1994).
2.2 Evidence and Explanations for the Bias
The ﬁrst naturalistic evidence of the FLB was from the psychologist R. M. Grifﬁth
(1949). He was inspired by the laboratory evidence of Preston and Baratta (1948)
but keen to test the results in a complex, non-laboratory environment. Employing
U.S. racetrack data, Grifﬁth found that horses with low probabilities of winning were
systematically overvalued while horses with high probabilities of winning were sys-
tematically undervalued. This result was consistent with that of Preston and Baratta,
with a similar indifference point of about 0.20. William McGlothlin (1956) replicated
(and expanded upon) Grifﬁth’s study with a larger dataset. His data also conﬁrmed the
existence of the FLB.
In the decades that followed the original studies a signiﬁcant body of evidence for
the bias emerged in betting markets around the world (e.g., in the United States:
Ali 1977; Asch, Malkiel, and Quandt 1982; Thaler and Ziemba 1988; in the United
Kingdom: Dowie 1976; Vaughan Williams and Paton 1997; in Australia: Tuckwell 1983;
in New Zealand: Gandar, Zuber, and Johnson 2001).4 The emphasis in the research
then shifted toward attempting to explain the origins of the bias. As a result, a broad
range of explanations have been offered, including, for example, the “bragging rights”
associated with holding a winning longshot ticket (Thaler and Ziemba 1988) or the
additional excitement derived from longshot betting (Bruce and Johnson 1992). Robert
Henery (1985) suggested that bettors may discount a ﬁxed proportion of their losing
bets, leading them to believe that longshot bets are more attractive. Alternatively the
bias may arise from particular characteristics of the market itself, such as the cost
of obtaining information and transaction costs (Hurley and McDonough 1995) or the
defensivepricingpoliciesadoptedbybookmakers(Shin1991). Inthischapterwesimply
provide an overview of the signiﬁcant debates concerning the origins of the FLB from
the perspective of bettors’ decision behavior; for more comprehensive explorations
see surveys by Richard Thaler and William Ziemba (1988), Raymond Sauer (1998),
Leighton Vaughan Williams (1999), Bruno Jullien and Bernard Salanié (2008), and
Marco Ottaviani and Peter Sørensen (2008).

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motivation, behavior, and decision-making in betting markets
2.3 Do Bettors Love Risk, or Do They Misestimate
Probabilities? Expected Utility Theory versus
Prospect Theory
One strand of the FLB literature in particular warrants attention because it has led
to an important intellectual debate concerning the relative merits of two prominent
competing theories for explaining decision-making in wider ﬁelds: expected utility
theory and prospect theory. The building block for this debate is the “representative
bettor.” Martin Weitzman (1965) introduced Mr. Avmart, a ﬁctitious person who
represents the “social average” of all bettors. Weitzman’s (1965, 26) innovation was to
infer the preferences of the “most typical” bettor from the population of bettors
instead of concentrating on individuals and trying to derive utility generaliza-
tions from their experimental behavior, more nearly the converse approach was
attempted. A plethora of data concerning the collective risk actions of parimutuel
bettors was employed in investigating utility aspects of the behavior of a hypothetical
member of the group.
Weitzman was concerned primarily with constructing Mr. Avmart’s utility of wealth
curve (the mathematical representation of preferences over various monetary outcomes
and the basis of expected utility theory). He found that the FLB in the data was best
explained by a convex utility of wealth curve, indicating that the average bettor is
locally risk loving (i.e., the average bettor prefers the riskier, low-probability outcomes).
Richard Quandt (1986) extended the analysis by showing that the bias is the natural
result of equilibrium in a market where the average bettor is risk loving. The ﬁndings
of Mukhtar Ali (1977) and Shahid Hamid, Arun Prakash, and Michael Smyser (1996)
also supported this hypothesis.
However, there are alternative scenarios that can explain the biased decisions of
the representative bettor. So, for instance, Joseph Golec and Maurry Tamarkin (1998)
showedthattheFLBcanariseif bettorsareriskaverseingeneralbutwithapreferencefor
skewness of returns. An alternative explanation stems from the motivation behind the
originalPrestonandBaratta(1948)study. Inthisstudyitwassupposedthatthe“psycho-
logical”probabilities assigned to uncertain outcomes were systematically biased in such
a way that small/large probabilities are over-/under-estimated. If this is the case, then
the FLB can be explained solely with reference to bettors’ systematic misestimation of
probabilities (i.e., bettors need not be locally risk loving). This was formalized in Daniel
Kahneman and Amos Tversky’s (1979) prospect theory (later extended and renamed
cumulative prospect theory; see Tversky and Kahneman 1992). The important feature
of prospect theory for this discussion is that objective probabilities are transformed
into subjective decision weights that allow for biases in the estimation of probabilities.
Hence there are now two broadly competing sets of theories regarding the explana-
tions for the bias in terms of the representative bettor: are bettors unbiased in their

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evidence of biased decision-making in betting markets
497
estimation of probabilities but risk loving, or are bettors risk-neutral but biased in
their estimation of probabilities? Unfortunately there is no straightforward answer. As
Menahem Yaari (1965, 278) commented,
at ﬁrst blush it seems as though one cannot, by looking at empirical data, choose
between the two hypotheses (distortion of utility versus distortion of probability)
because utility and probability are two purely theoretical components of an integral
decision process. Thus, the two hypotheses are empirically indistinguishable, and
choosing between them is a matter of taste.
However, some researchers have made progress in this regard. Golec and Tamarkin
(1995) noted that risk love cannot explain the relatively unfair returns for the low-risk,
low-return, side bets offered by some bookmakers. Instead they suggested that over-
conﬁdence (which is consistent with bettors overestimating small probabilities) better
explains the FLB. Jullien and Salanié (2000) found that prospect theory (cf. expected
utility theory) better explains the bias for standard bets, though computational limita-
tions of this approach restricted their analysis. Ian Bradley (2003) adapted the prospect
theory approach of Jullien and Salanié by accounting for bet size and found an even
better ﬁt to the data.
More recently Erik Snowberg and Justin Wolfers (2010) set out to test the com-
peting theories using a novel approach and a large dataset of all the horse races run
in North America from 1992 to 2001 (over 865,000 races). They ﬁrst estimated the
parameters of the two models (the expected utility/risk-love model and the prospect
theory/misestimation of probabilities model) by ﬁtting the models to standard “win”
bets (bets that a horse will ﬁnish in ﬁrst place). They then examined compound exotic
bets, such as the exacta, a bet that two horses will ﬁnish a race in ﬁrst and second place
in a speciﬁc order. Snowberg and Wolfers reasoned that because bettors would bet in
the same manner in the exotic and win betting pools, the same models should apply
for each bet type. Accordingly, they used the ﬁtted models to predict expected market
prices in the exotic betting pools and compared their predictions with the actual prices
on offer. They found that the misestimation of probabilities model predicted exotic
bet prices more accurately than the risk-love model. Snowberg and Wolfers concluded
that, with respect to the representative bettor, prospect theory explained the FLB more
effectively than expected utility theory.
An important issue in this debate is the validity of the assumption that bettors’
decisions can be averaged by the representative bettor. In the third section of this
chapter we show that the distinction between different types of bettors (on the basis
of the quality of the information they hold or how they handle this information) is
crucial to fully understanding some other biases in betting behavior. Russell Sobel
and Travis Raines (2003) demonstrated this by differentiating between “serious” and
“casual” bettors. They identiﬁed serious bettors as those who attend the racetrack on
week nights, bet larger sums, and bet to a greater extent on more complicated types of
bet. Casual bettors, conversely, attend primarily on weekends and bet smaller sums on

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motivation, behavior, and decision-making in betting markets
simpler types of bets. Sobel and Raines found evidence of the FLB, but the bias was
signiﬁcantly reduced in those races that involved a higher proportion of serious bettors.
2.4 The Late-Race Effect
A curious element of the nature of the FLB is its apparent tendency to vary in a
systematic manner over the course of a day’s betting activity. In horse race betting
markets in particular it has been found that the extent of the bias appears to increase
signiﬁcantly in the last race or the last few races of the day. This phenomenon has
become known as the late-race effect. Early evidence of this pattern was uncovered by
McGlothlin (1956), who was investigating the stability of the FLB over the course of the
day. He found that the bias was present in the data as a whole but that bettors did not
underbet favorites in the seventh race of the day (out of eight). McGlothlin argued that
the seventh race was usually the feature race, involving more coverage and scrutiny of
favorites, so it might be expected that bettors would prefer the favorites in these races.
However, he found that, in the eighth and last race of the day, bettors underbet favorites
to a greater extent than in any other race. He suggested that bettors might avoid bets
on favorites in the last race because winning such bets would not recoup earlier losses
(the track take ensured that most bettors would ﬁnish the day out of pocket). Rather,
McGlothlin suggested that they preferred to bet on long shots, hoping for a lucky win
in order to end the day in proﬁt.
Over time, as more evidence of the late-race effect emerged, it was explained in terms
of the risk-loving attitudes of the representative bettor. For example, Ali (1977), who
found a greater degree of the FLB in the last race than in the ﬁrst two races of the day,
posited that this demonstrated that bettors, who were on average risk loving, became
more risk loving as the day progressed. Similarly, Asch, Malkiel, and Quandt (1982)
replicated McGlothlin’s (1956) results, though in their study the extent of the bias was
greater in the last two races of the day. Mary Ann Metzger (1985) also found evidence
of the effect but only if the ﬁrst race of the day was excluded from the analysis. The
late-race effect soon passed into betting lore, with Richard Kopelman and Betsy Minkin
(1991) describing how an avid racing enthusiast known as “Gluck” espoused the rule:
“The best time to bet the favourite is in the last race.” Kopelman and Minkin’s analysis
conﬁrmed that there was a sound economic basis for Gluck’s rule.
More recent evidence has thrown the existence of the late-race effect into question.
Johnson and Bruce (1993) found that bettors in U.K. betting shops tended to place
more bets on favorites in the last race and suggested that this might be due to a “break-
even” effect whereby bettors seek to recover their losses by betting on outcomes that
have at least a moderate success of actually occurring. This hypothesis is supported
by evidence that decision-makers tend to exhibit loss aversion after a series of prior
losses (Thaler and Johnson 1990). Similarly, Lawrence Brown, Rebecca D’Amato, and
Randy Gertner (1994) observed a greater prevalence of the FLB in the last race of the
day than in earlier races, but the difference was not statistically signiﬁcant. Sobel and

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499
Raines (2003) found that (having controlled for the differences in race grade) there was
a slight increase on betting on long shots in the last two races of day (especially the
last race), with no corresponding decrease on betting on favorites. However, they also
found that the general trend over the latter half of the evening (i.e., over the last 7 or
8 races of the 15 in each meeting) is for bettors to begin to prefer favorites and shun
long shots. They note that this could be explained by casual bettors leaving over the
course of the evening (resulting in the remaining more serious bettors betting more on
the favorites). Finally, Snowberg and Wolfers (2010) found no signiﬁcant difference in
the extent of the FLB in the last race of the day (in a dataset of over 850,000 races),
suggesting that the late-race effect has now been eliminated.
From the contrasting evidence discussed above, it appears that bettors’increasing risk
love over a day’s betting cannot fully explain the late-race effect. Johnson and Bruce
(1993) considered that their converse result (a decreasing FLB in the last race) could be
explained by a “break-even” effect. However, a similarly plausible explanation is used
by other authors to explain the opposite effect (an increasing FLB in the last race).
Furthermore, it is not clear that expected utility theory is an adequate explanation. As
Thaler and Ziemba (1988, 171) asked, “why should a reduction in wealth increase the
tendency for risk seeking?” Camerer (2001) pointed out that expected utility theory
cannot explain why the same bettor leaves the racetrack one day, arrives again the
next, and adopts a completely different risk attitude. Thaler and Ziemba proposed
that the effect can be explained by “mental accounting” whereby bettors partition their
wealth into separate accounts and do not attempt to recoup losses in one account with
funds from another. So the late-race effect could be explained by bettors opening a
mental account at the beginning of the day and closing it at the end, with an increasing
desperation to break even as the day progresses (Camerer 2001). Finally, the relative
paucity of evidence for the effect in recent years could be attributed to a learning effect
among bettors, as those who are aware of the effect are able to arbitrage it away should
it reappear.
In summary, the FLB, while proving to be an interesting riddle for researchers,
admirably demonstrates the value of naturalistic environments, betting markets in
particular, in the study of decision-making. While some potentially unrealistic sim-
pliﬁcations (such as the representative bettor) must sometimes be made when seeking
explanations, the quality and quantity of betting market data have enabled the devel-
opment of a large body of research on the nature of preferences and perceptions of risk
under uncertainty.
3 Anchoring and Herding
.............................................................................................................................................................................
Betting market research has largely focused on the FLB, but some studies have inves-
tigated whether bettors make biased decisions in other ways. In particular, anchoring
and herding represent biased behavior whereby decision-makers alter their decisions

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motivation, behavior, and decision-making in betting markets
to account for external stimuli. Thus when employing the anchoring and adjustment
heuristic, decision-makers unnecessarily alter their judgments to reﬂect an initially pro-
vided estimate. Herding arises when decision-makers neglect their own information
and alter their judgments to reﬂect those of others. This section details the ﬁndings of
these studies.
3.1 Anchoring and Adjustment
Laboratory research suggests that when making a numerical estimate individuals, in
an attempt to simplify the decision-making process, tend to start from an initial value
and make “adjustments” upward or downward from it (e.g., Tversky and Kahneman
1974). However, this often results in a bias whereby the decision is “anchored” on the
initial estimate and adjustments are not sufﬁcient. This is known as the anchoring and
adjustment heuristic. For example, Tversky and Kahneman asked participants pairs of
questions, such as:
(a) Is the percentage of African countries in the United Nations higher or lower than
25?
(b) What do you think the exact percentage is?
They found that the ﬁgure given in (a) (i.e., 25 in the above example) signiﬁcantly inﬂu-
enced the participants’ responses to (b), even when the ﬁgure was randomly generated
by spinning a wheel of fortune in the participants’ presence. Higher/lower random
numbers were associated with higher/lower estimates.
Anchoring has mainly been studied in controlled laboratory conditions. The few
studies that have been conducted in naturalistic environments (e.g., among auditors:
Bhattacharjee and Moreno 2002; and among real estate agents: Northcraft and Neale
1987) have generally concluded that anchoring does seem to occur in information-
rich, real-world settings. However, these studies have used questionnaires or artiﬁcial
problems. Consequently the advantages of studying anchoring in betting markets are
that participants are making estimates that matter to them in a familiar, real-world
environment without the use of questionnaires or artiﬁcial problems and that they do
not alter their normal behavior (because they do not know they are being observed).
In the ﬁrst study to investigate whether bettors anchor their judgments excessively,
Shuang Liu and Johnson (2007) were primarily concerned with whether or not partici-
pants in horse race betting markets employed factors relating to previous performance
of horses, jockeys, and trainers as anchors. For example, if a jockey had won his or her
previous race, do bettors overestimate the chance that he or she will also win the current
race? Previous ﬁnishing positions are not anchors in the traditional sense, since bettors
are not speciﬁcally required to make direct comparisons between initial values and
ﬁnal judgment. Rather this study attempted to ﬁnd evidence of basic anchoring, where
decision-makers can be inﬂuenced by anchor values even when not asked to consider

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evidence of biased decision-making in betting markets
501
them directly (Wilson, Houston, and Etling 1996). Liu and Johnson investigated, using
betting market data from Hong Kong, various explanatory variables that represent
possible anchors (such as whether the horse won its previous race). However, the only
signiﬁcant explanatory variable was one that summarized a horse’s ﬁnishing position
over its career; this variable showed that bettors tend to underestimate horses that have
a strong ﬁnishing record. Consequently it appears that bettors tend to ignore some
useful information relating to the horses’ potential (or are unable to effectively employ
such a complicated variable). However, the key ﬁnding was that no other explanatory
variables were signiﬁcant, indicating that bettors do not anchor their judgments on
previous performances.
It is possible that Liu and Johnson’s (2007) results failed to identify the anchoring that
does occur in betting markets since any bias created by the anchoring of most bettors
could be arbitraged away by the remainder of bettors. For instance, it is well known
(e.g., Benter 1994) that large betting syndicates, attracted by the unusually large betting
volumes and strict regulation in Hong Kong (which helps to eliminate malpractice and
insider trading), use sophisticated computer models to make considerable proﬁts in
this market.
Johnson, Adi Schnytzer, and Liu (2009) extended the analysis of Liu and Johnson
(2007) in two ways. First, noting that bettors in Hong Kong often spend considerable
time reviewing race results, they expected that barrier position (the stall position from
which the horse starts the race) would be a signiﬁcant anchor for bettors. Second,
decision-makers with a higher level of expertise tend to be less susceptible to anchor-
ing effects (e.g., Northcraft and Neale 1987), so they expected that more experienced
bettors would be less prone to anchoring. They found that bettors as a whole did not
anchor excessively on barrier position over all their data but that bettors overestimated
the advantage offered by a good barrier position in one of the two racetracks under
investigation. However, they found that expertise signiﬁcantly reduced the extent of
anchoring displayed by bettors (they used early and late betting as a proxy for inexpert
and expert bettors, respectively). In summary, the two anchoring studies conducted
in betting markets indicate that anchoring in real-world environments may be a more
complex phenomenon than has been found in laboratory studies, suggesting that fur-
therresearchmayberequiredtofullyunderstanditsinﬂuenceondecisionsinreal-world
environments.
3.2 Herding
Herding occurs when decision task participants neglect their own information and
adjust their actions to be more representative of the actions of others.
Earlytheoreticalmodelsrationalizedherdingbehaviorasinformationcascadeswhere
decisions are made sequentially by different agents who each hold their own private
information (e.g., Banerjee 1992; Bikhchandani, Hirshleifer, andWelch 1992; Avery and
Zemsky 1998). The validity of the information is inherently uncertain, and as a result,

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motivation, behavior, and decision-making in betting markets
individuals may be rational in disregarding some of their private information when
the information held by other agents appears to conﬂict with their own. Hence strictly
speaking, herding behavior in itself may not be “biased” decision-making. However, a
biased outcome results from the combined effect of herding by multiple participants.
In particular this behavior can lead to expected returns differing signiﬁcantly from their
“rational” value.5
Many empirical herding studies have been conducted in the laboratory. In general
these studies have found that participants display herd behavior but to a lesser extent
than theoretical models predict. However, evidence has generally been inconclusive
(Spiwoks, Bizer and Hein 2008).6
Herding might be expected in betting markets because there is a belief that certain
bettors have access to privileged information. It has been found that betting on a horse
or team that subsequently attracts a high degree of betting interest during the course
of the market (known as a“market mover”or“plunger”) is, on average, proﬁtable (e.g.,
Crafts 1985). The problem, of course, is that it is difﬁcult to identify such opportunities
before the fact, and this is where bettors with access to privileged information can gain
an advantage. Bettors with superior information are often referred to as“insiders”in the
literature because of the presumption that their information is not in the public domain
(e.g., a racehorse owner may have knowledge of secret training programs). However,
there are also some bettors who use only publicly available information but expertly
combine all the information in such as a way as to form highly accurate opinions
of the competitors’ chances; these bettors are often referred to as “informed” bettors.
The presence of insiders and informed bettors in betting markets is widely reported
(e.g., Crafts 1985), and consequently, herding behavior may ensue when “uninformed”
bettors interpret a signiﬁcant price movement as a signal that a competitor is being
backed by insiders or informed bettors and alter their bets accordingly.
The ﬁrst study that investigated whether bettors herd is that of Camerer (1998). He
tested whether bettors might respond to privileged information signals by placing large
early bets in pari-mutuel pools at U.S. racetracks and recording subsequent betting
patterns. The purpose of this ﬁeld test was to investigate whether markets could be
manipulated. However, by observing the reactions of bettors to the temporary bets
(Camerer subsequently canceled the early bets), Camerer was also able to infer the
relative proportions of“opinion bettors”and“full/partial rational expectations bettors.”
Opinion bettors do not take the current odds into account; instead they bet solely based
on their own subjective probabilities of the relative chances of the horses. On the other
hand, full rational expectations bettors believe that current odds fully reﬂect all available
information and so always bet in proportion to the odds. Partial rational expectations
bettors occupy the middle ground, believing that odds do to some extent reﬂect the
information but also that other bettors do not react to this information. Since opinion
bettors completely ignore price movements, they never herd. Full rational expectations
bettors will herd to some extent; if odds move from, say, 20/1 to 12/1 after a “fake”
signal (i.e., following one of Camerer’s early bets), they will bet as if the horse is a
genuine 12/1 shot. Partial rational expectations bettors will herd to the greatest extent;

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evidence of biased decision-making in betting markets
503
they might bet a fake 12/1 down to 10/1. Camerer conducted two studies as part of his
experiment. In the ﬁrst study he placed 50 temporary $500 bets early in the market.
He found that while his bets did temporarily distort the odds, after canceling his bets
the odds returned to their expected levels (based on “control” horses with similar odds
on which he did not bet), indicating that bettors were not responding to the fake
signals. In a second study Camerer increased his bet size to $1,000 and targeted smaller
racetracks and “maiden” races (for horses that had never won a race). He detected a
weakly signiﬁcant herding effect whereby bettors were more likely to respond in the
maiden races. However, overall the results still resolutely showed that bettors did not
display herding behavior. There remains an important caveat: although Camerer’s bets
made up of about 7 percent of the pool in the second study, they still may not have
been large enough to induce herding.
In a later study David Law and David Peel (2002) argued that the apparent lack of
herding in Camerer’s (1998) study probably arose because while the bets were sufﬁ-
ciently large to temporarily distort the markets, there was little incentive for bettors to
herd on the initial price movement since pari-mutuel bettors cannot lock in proﬁts. To
counter this, they conducted an empirical test for herding in U.K. bookmaker markets
for horse racing. They argued that since the returns to a bet with a bookmaker are
known at the time of bet placement, bettors might be more likely to herd in these
markets. They noted that while an initial price movement could be due to informed
trading, a further price movement may result from further informed trading or herd-
ing. Using the Hyun Song Shin (1991) measure of the degree of insider (or informed)
trading, they were able to identify those large price movements that resulted from the
trading of those with access to privileged information (the Shin measure increased
over the duration of the market) or from herding (the Shin measure decreased). Law
and Peel were particularly interested in those horses that opened at shorter odds than
forecasted that then attracted signiﬁcant betting interest. Signiﬁcant positive returns of
10.2 percent could be made by betting on horses with these characteristics whose odds
plunged as a result of informed trading; returns were signiﬁcantly negative otherwise,
at −10.9 percent. Consequently Law and Peel (2002) were able to demonstrate that
herding led to biased prices, with negative/positive returns being reported when price
movements were due to herding/informed betting.
Schnytzer and Avichai Snir (2008) examined herding in bookmaker markets for
horse racing in both the United Kingdom and Australia. They developed a theoretical
model which showed that herding leads to odds that overestimate a horse’s chances of
winning. Speciﬁcally, if a horse that is not attracting bets suddenly attracts a high degree
of betting interest, that horse’s chances are likely to be overestimated due to herding.
However, noting that early plunges in odds suggest trading by bettors with privileged
information, Schnytzer and Snir (2008, 3) hypothesised that, due to the limited budgets
of insiders, “a short time later, when the odds on those runners are lengthened again,
those insiders are either unable or unwilling to place bets of sufﬁcient signiﬁcance to
affect prices, even when the odds on those runners have drifted back to initial levels or
even further.” This may arise because informed traders place most of their bets early

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504
motivation, behavior, and decision-making in betting markets
in the market to secure proﬁts. Schnytzer and Snir considered two possible situations:
either odds increase early in the market and then decrease or odds decrease early in
the market and then increase. In the former, the late betting interest on the horse is
considered to be evidence of herding, since the horse attracted little interest in the early
market, and the ﬁnal odds are expected to overestimate the horse’s chances of winning.
In the latter the early plunge followed by a lack of betting interest in the late market
was considered evidence of cash-constrained informed betting; that is, the ﬁnal odds
are expected to underestimate the winning horse’s chances. The results demonstrated
that for horses attracting early but not late betting interest, positive/negative returns
of 15.3 percent/−10.3 percent were possible from a simple betting strategy for the
Australian/U.K. races (though an 8.5% return was possible for U.K. races if stricter
criteria were applied). On the other hand, only highly negative returns (as low as
−27.2% in the Australian races) were possible for horses that lacked interest in the
early market but were the subject of herding in the late market. These results conﬁrmed
that bettors herd and that this can lead to highly biased outcomes.
In summary, studies of anchoring and herding in betting markets have offered mixed
conclusions. Camerer (1998) was unable to induce herding behavior with his “fake”
signals, but other studies have found evidence of signiﬁcant herding by bettors when
insider trading is prevalent. However, it appears that bettors do not anchor their judg-
ments to the extent that has been reported in the laboratory. This may result from the
fact that bettors are making decisions in an environment with which they are familiar
(cf. naive subjects in unfamiliar laboratory settings) and in which they have learned
(e.g., through repeated trial and improvement) to handle appropriately the redundant
information and decision-relevant cues. Equally, while many bettors may herd to a sig-
niﬁcant extent, the actions of informed bettors, who arbitrage on the herding behavior
of others, may serve to suppress the observable effects of herding.
4 The Gambler’s Fallacy and
the Hot Hand Fallacy
.............................................................................................................................................................................
The gambler’s fallacy and the hot hand fallacy both involve a misunderstanding of the
nature of randomness. The application of these fallacies often results in systematically
biased behavior. The gambler’s fallacy is deﬁned as the belief that an event’s probability
of occurring is reduced after that event has occurred, even if the event is independent
from one trial to the next (Rabin 2002). Pierre Simon Laplace ([1825] 1995, 92) gave
the following examples from lotteries and coin tossing:
when one number has not been drawn in the French lottery, the mob is eager to bet
on it. They fancy that, because the number has not been drawn for a long time, it,
rather than the others, ought to be drawn on the next draw .... It is, for example,

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evidence of biased decision-making in betting markets
505
very unlikely that in a game of heads or tails one will get heads ten times running.
This unlikeliness, which surprises us even when the event has happened nine times,
leads us to believe that tails will occur on the tenth toss.
The gambler’s fallacy is the conviction that the coin, which is known, objectively, to
be fair, is more likely to land heads than tails after the “streak” of nine tails. This
belief is demonstrated in laboratory experiments where participants are asked to invent
a random sequence, such as repeated tosses of a coin. The results show that people
tend to produce sequences containing too many alternations in the outcome relative
to genuine randomness (Falk and Konold 1997). The representativeness heuristic has
been proposed as an explanation: the gambler believes that small samples must be
representative of the population, so if unexpected sequences occur, a correction is
expected (Tversky and Kahneman 1971). As Tversky and Kahneman (1974, 1125)
noted:“chance is commonly viewed as a self-correcting process in which a deviation in
one direction induces a deviation in the opposite direction.” Since nine tails in a row
is an extremely unlikely event, the observer committing the gambler’s fallacy expects
that the next toss should be heads in order to make the sequence of 10 tosses seem less
unusual. A commonly cited example of this phenomenon is that of the Monte Carlo
casino where, during a roulette game in 1913, black occurred 26 times in a row. During
this streak customers bet increasing amounts on red, and the casino proﬁted as a result
(Lehrer 2009).
The hot hand fallacy involves mistaken convictions that run contrary to the gambler’s
fallacy. Inparticular,thisfallacyinvolvesthebelief thatif aplayerorteamisonawinning
(or losing) streak this streak will continue longer than should be expected in a random
sequence. So in a game where the objective is to obtain tails on the toss of a coin, a
gambler who has achieved the unlikely feat of landing tails nine times in a row believes
that he or she is on a “hot streak” and therefore expects that the coin has a greater
probability of showing tails than heads on the next toss.
Thomas Gilovich, Robert Vallone, and Tversky (1985) found that many basketball
players and fans believed that a player would be more likely to score on a shot if he
had scored (cf. missed) on the previous shot. However, they found no evidence to
support this claim in either real games or controlled shooting experiments. The hot
hand has been attributed to the illusion of control, which is the misplaced perception
that gamblers have an element of control over random events (Langer 1975). In fact, it
has been shown that some gamblers believe that luck is separate from chance and that
their good fortune allows them to operate outside the laws of probability while they
are on winning streaks (Wagenaar and Keren 1988). Gilovich, Vallone, and Tversky
(1985) suggested that, as with the gambler’s fallacy, bettors may be employing the
representativeness heuristic. In this case, long runs are deemed too unusual for the
representative sequence, so bettors infer that the sequence generating process is no
longer random (e.g., a basketball player who shoots an usually high run of on-target
shots is said to be “in the zone” or a roulette table or die is assumed to be biased). It
is possible that, while a general belief in the hot hand may be misplaced, an accurate

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506
motivation, behavior, and decision-making in betting markets
belief in the hot hand in speciﬁc instances motivates people to believe in its universality
(see Bar-Eli, Avugos, and Raab 2006 for many examples of genuine hot hand effects).
The remainder of this section details the ﬁndings of studies that have investigated
the two fallacies in naturalistic environments.
4.1 Evidence of the Gambler’s Fallacy in Betting Markets
Charles Clotfelter and Philip Cook (1993) undertook one of the early studies using
real betting data to investigate the gambler’s fallacy. The U.S. state of Maryland runs a
“daily numbers”draw lottery where a three-digit number between 000 and 999 is picked
at random and the bettor wins if he or she selects this number. Clotfelter and Cook
found that betting volumes on a number decreased in the days after the number was
drawn before returning to original levels after 84 days. It was postulated that bettors
could be reducing their bets on numbers that had been drawn previously because they
thought that that number was less likely to appear again. However, Clotfelter and Cook
were unable to eliminate a “wealth effect” from their data: bettors who regularly bet
a particular number might stop betting altogether because they had achieved their
ﬁnancial goals. This could lead to a natural reduction in betting volumes on a winning
number in the days and weeks after its appearance. A more signiﬁcant caveat with
Clotfelter and Cook’s study was noted by Dek Terrell (1994): the Maryland lottery has
ﬁxed payouts (winners are always paid $500 on a $1 bet), so choosing numbers based
on the gambler’s fallacy does not reduce the expected return to the bettor.
Rachel Croson and James Sundali (2005) studied 18 hours of roulette play in a real
casino, during which more than one hundred players placed thousands of bets. They
found evidence of the gambler’s fallacy after streaks of around ﬁve or more similar
outcomes (e.g., ﬁve red numbers in a row). However, Croson and Sundali (2005, 200)
pointed out a similar concern to that existing in the Clotfelter and Cook (1993) study:
“Since the house advantage on (almost) all bets at the wheel is the same, there is no
economic reason to bet one way or another (or for that matter, at all).”7
These studies highlight an important issue: while the gambler’s fallacy is anecdotally
known to be a common belief among gamblers, it does not always result in biased
behavior. For example, in roulette the returns to bets on each outcome are independent
of the bets placed by the customers. Therefore, the decision of which outcome to bet on
is irrelevant. The gamblers in the Monte Carlo casino were not necessarily wrong to bet
on red rather than black (though they might have bet more than they could afford). In
such cases it is plausible that belief in the fallacy only adds to the excitement of the game.
In circumstances where acting on the fallacy results in a systematic bias that leads to
a lower expected return for the bettor, it might be expected that the fallacy would be
eliminated (e.g., by a learning process). However, there are a number of examples of the
gambler’s fallacy resulting in a systematic bias. These studies have necessarily needed
to be creative in order to identify situations where one might expect evidence of the
gambler’s fallacy. For example, Metzger (1985) found evidence that horse race bettors

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evidence of biased decision-making in betting markets
507
tend to believe that streaks of favorites and long shots winning should cancel out. So, if
a series of long shots wins, they bet more on favorites and vice versa. Terrell and Amy
Farmer (1996) thought that bettors at greyhound racing events might believe that the
starting positions of the winning dogs should be more random than it appears. Thus
they might underestimate the winning chances of a dog starting in a given position
from winning if the winner of the previous race also started from that position. Their
calculations revealed that this was the case, with a positive return of $1.09 per dollar
bet for a strategy of betting on dogs starting from the same position as the winner of
the previous race. Terrell (1998) extended the study of Terrell and Farmer (1996) with
a larger dataset but found signiﬁcant evidence of the fallacy only in one of the two years
in their data.
Terrell (1994) conducted a similar investigation to Clotfelter and Cook (1993) but in
a pari-mutuel New Jersey lottery where payouts are shared between all the bettors who
choose the winning number. Hence if many gamblers avoid numbers that have recently
appeared, the expected return to these gamblers is reduced. As expected, the extent of
the gambler’s fallacy was lower in this case. However, there was still a tendency to avoid
numbers that had recently appeared. Terrell also found that if the results of Clotfelter
and Cook were converted to a pari-mutuel system there would be frequent occurrences
when the payout would exceed $500, giving a positive expected return to bettors. This
is not the case in New Jersey, so bettors appear to bet more evenly to avoid forgoing the
increased potential winnings, and this diminishes the potential to exploit the fallacy.
An alternative explanation for the results is that bettors simply prefer not to bet on a
recently seen number in the same way that they prefer certain numbers (such as 777).
Similarly, George Papachristou (2004) found only marginal evidence of the gambler’s
fallacy in the pari-mutuel lottery in the United Kingdom.
4.2 Evidence of the Hot Hand Fallacy in Betting Markets
As indicated above, the hot hand fallacy is also a mistaken perception of randomness.
However, as with the gambler’s fallacy, this mistaken belief does not necessarily impose
economic penalties. Camerer (1989) examined the economic signiﬁcance of the hot
hand fallacy by investigating whether this mistaken belief is represented in gamblers’
betting decisions. He categorized basketball teams based on their current winning or
losing streak (in games) and then compared the actual results with the point spreads
offered by bookmakers.8 If bettors believe in the hot hand, point spreads will over-
estimate the chances of teams currently on winning streaks against the spread while
underestimating the chances of teams on losing streaks. The results showed that the
performance of teams on winning streaks is worse than predicted by point spreads and
that teams on losing streaks perform better than predicted. However, the results were
only marginally statistically signiﬁcant.
William Brown and Sauer (1993, p. 1377), highlighted the importance of the follow-
ing critical assumption in Camerer’s (1989, p. 1257) study: “the hot hand is belief in a

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508
motivation, behavior, and decision-making in betting markets
myth.”Camerer was effectively testing two alternatives: either bettors believe in a myth-
ical hot hand or they do not. However, there is evidence that genuine hot hand effects
exist (Bar-Eli,Avugos, and Raab 2006). Consequently there is a third alternative: bettors
believe in a genuine hot hand.9 In this case, while bettors will move point spreads to
account for the hot hand effect, so teams’ performance levels will also change. Brown
and Sauer considered all three alternatives in basketball point spread markets but found
only mixed results. They could not reject the hypothesis that the hot hand is real and
that bettors correctly account for it, but they could also not reject the hypothesis that
bettors believe in a mythical hot hand.
In a further study on the hot hand in point spread markets for basketball, Dale
Oorlog (1995) found strong evidence against the hypothesis that gamblers believe in
the hot hand. Oorlog devised a number of betting strategies to account for possible hot
hand effects, but none were proﬁtable. Christopher Avery and Judith Chevalier (1999)
investigated U.S. football betting markets and also found a small bias as a result of the
hot hand fallacy, but, again, the magnitude of the effect was small.
Additional mixed evidence for the hot hand fallacy was provided by Gregory
Durham, Michael Hertzel, and J. Spencer Martin (2005). These authors found that
point spreads over-/underestimated U.S. college football teams on short winning/losing
streaks against the spread, which is consistent with the hot hand fallacy. However, the
point spreads suggested that bettors expected longer winning or losing streaks to end
rather than continue. Similarly, Rodney Paul and Andrew Weinbach (2005) reported
that betting against basketball teams on short winning streaks was proﬁtable while bet-
ting against teams on longer winning streaks was not. Moreover, they found no hot
hand effect for teams on losing streaks and suggested that this might be because bettors
derived additional utility from betting on teams on winning streaks.
4.3 The Paradox of the Hot Hand and Gambler’s Fallacies
An important consideration is that the hot hand and gambler’s fallacies appear at ﬁrst to
be opposite effects. While bettors may believe that long runs in the results of players or
teams will continue (the hot hand), they simultaneously believe that long runs should
end (the gambler’s fallacy). This begs the question: how can these two apparently
opposite effects be explained?
One proposed explanation for both fallacies is the representativeness heuristic (Tver-
sky and Kahneman 1971) in which decision-makers believe that sequences should be
representative of the generating process. Decision-makers apply the“law of large num-
bers” too readily; that is, they believe in the “law of small numbers.” In other words,
while the relative frequencies of outcomes approximate the generating process in the
long run, people believe that this should also be the case in the short run. So the gam-
bler’s fallacy is explained because people believe that unusually long streaks are not
representative and so predict an alternation to make the sequence more representative.
The hot hand is explained because people tend to over-infer from short sequences

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evidence of biased decision-making in betting markets
509
in a random process and decide that there is some underlying nonrandom process
generating the sequence (Rabin 2002).
It is potentially problematic to explain opposite phenomena with the same principle.
However, a solution was provided by Peter Ayton and Ilan Fischer (2004; see also
Burns and Corpus 2004), who tested whether the type of random process employed
to generate the result was consequential in whether decision-makers displayed the hot
hand or the gambler’s fallacy. They hypothesized that when outcomes reﬂect human
performance people believe in the hot hand, whereas when outcomes reﬂect inanimate
mechanisms people believe in the gambler’s fallacy. This might explain why winning
streaks of basketball and roulette players are perceived to exhibit long-run tendencies
but outcomes of roulette games and lotteries are not. They conducted an experiment
where they asked participants to play a simulated roulette-style game. Participants
were ﬁrst required to choose between red and blue and second were asked to rate their
conﬁdenceintheirprediction. Theresultsconﬁrmedthatwhilepeoplearemorelikelyto
predictanalternationafteralongrunof eithercolortheyarealsomoreconﬁdentintheir
own ability after a long run of successful predictions. Ayton and Fischer (2004, 1374)
concluded that while the sequences of outcomes (red or blue) and predictions (win or
lose) are each identical independent processes, “the two sequences are psychologically
perceived quite differently; subjects simultaneously exhibited both ... the hot hand
and the gambler’s fallacy.” In a second experiment they found that participants were
more likely to attribute random sequences with low/high alternation rates to human
performance/inanimate mechanisms. This line of experimentation goes some way to
unravel the problematic nature of explaining two apparently opposite effects with the
same heuristic.
In summary, there is evidence from a diversity of naturalistic betting environments
that the decisions of bettors are consistent with the gambler’s fallacy. However, the
extent of the fallacy is reduced when it results in biased decisions, suggesting that
bettors are sensitive to its economic signiﬁcance. Research examining the hot hand
fallacy in betting markets has been inconclusive. None of the above studies found
irrefutable evidence that bettors believe in the hot hand and that market odds are
biased in accordance with this belief. If there is a hot hand effect in markets, it generally
is so small as to be economically insigniﬁcant.
5 Conclusion
.............................................................................................................................................................................
This chapter has shown that while many biases in decision-making have been demon-
strated in laboratory-based studies, there are numerous reasons for suggesting that
these ﬁndings may not translate to the real world. Betting markets provide a valuable
naturalistic setting in which to explore biased decision-making because participants
are making decisions in a situation that is more representative of the environments in

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510
motivation, behavior, and decision-making in betting markets
which day-to-day decisions are made. We have argued that bettors display signiﬁcantly
less biased judgments in their natural domain than do naive participants in labora-
tory experiments. To support this view we have cited a number of examples related to
rationality and calibration of subjective probability judgments. Furthermore, we have
shown that there is only mixed evidence that bettors anchor their judgments on avail-
able information, engage in herding behavior, or believe in the hot hand or gambler’s
fallacies. Even the FLB, which has been the focus of the majority of research in betting
markets, is no longer observable in some markets.
The primary conclusion of this chapter is that while systematic biases reported in the
laboratory have been found in naturalistic betting markets, the extent and generality of
these biases in these real-world environments are often signiﬁcantly less. The context of
the decision task, the incentives offered, the lack of scrutiny involved, and the experience
of the decision-makers all contribute to an explanation for this conclusion. Another
consideration is the importance of aggregation. It is costly and ethically challenging to
obtain betting market datasets from which it is possible to discern individual biases. In a
more typical dataset individual biases may be eliminated by aggregation of the opinions
of a diverse range of bettors. Moreover, even a systematic bias that is attributed to a
large portion of the betting population can be reduced by the unbiased actions of a
wealthy few, as there is always a strong economic motivation to capitalize on the biases
of others.
A drawback of the heuristics and biases approach to decision-making in general is
highlighted by our discussion of the hot hand and gambler’s fallacies. There is the initial
problem of explaining two apparently opposite biases with the same heuristic, though
subsequent research has clariﬁed that there are two separate situations when people
use either of these fallacies. On the other hand, it can be impossible to narrow down
multiple explanations for one bias to the single, most-valid explanation. Thus a wide
range of explanations has been proposed for the FLB. Similarly the hot hand fallacy
could be explained by the illusion of control or by the representativeness heuristic or
by extrapolation of genuine hot hand effects. As Willem Wagenaar (1988, 115–116) has
argued, the heuristics and biases approach
does not specify rules telling us which heuristic will be applied in a given situation.
Even worse, from the individual differences among gamblers, it is obvious that
several heuristics could be chosen in one and the same situation, and that these
heuristics lead to opposite behaviors .... There are so many heuristics, that it will be
virtually impossible to ﬁnd behaviors that cannot be accounted for.
Hence while there is some evidence of biased behavior in betting markets, explaining
its prevalence is another matter altogether.
There are additional issues associated with betting market research that may lead
one to question the generalizability of the conclusions drawn from such studies. For
example, bettors may be unrepresentative of the wider public since they are predomi-
nantly older males (Dipboye and Flanagan 1979), and there may be some self-selection

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evidence of biased decision-making in betting markets
511
effects (indeed, it is not obvious as to why some people gamble and some do not; see
Rachlin 1990). We must also retain some skepticism about generalizability from betting
markets to other economic settings (Levitt and List 2007). Just as laboratory research
should recognize that generalizability of ﬁndings is limited, additional research on
biased decision-making in betting markets should acknowledge that laboratory exper-
imentation is often the ﬁrst available evidence that heuristics are being employed or
biased outcomes are occurring. Without either the theoretical background or the con-
trolled elegance of laboratory research, naturalistic research might be confounded by
the vast array of potential variables involved and the often unintuitive nature of real-
world decision-making. The way forward appears to be a tandem approach with betting
market studies being informed by results from laboratory experiments and the latter
being designed to examine the causes of phenomena that the former highlight. In
this manner the true nature and real-world characteristics of behavioral biases may be
revealed.
Notes
1. As a further example of the importance of context in decision-making, consider the
following problem. There are four cards on the table, each with a letter on one side and
a number on the other. The rule is, “If there is a vowel on one side of a card, then there
is an even number on the other side.” The cards show A, D, 4, and 7. Which cards must
be turned over in order to determine whether the rule is true or false? This is known as
Wason’s four-card selection task (Wason 1968), and usually less than 10 percent of people
respond with the correct answer of A and 7 (most neglect to choose 7 or unnecessarily
include 4). However, when this problem is reframed in terms of certain social contexts,
such as asking subjects to test the rule “If a person is over 18, they can drink alcohol”
and replacing the cards with “16 years old,”“22 years old,”“Coke,” and “beer,” the correct
answer (“16 years old”and“beer”) is given by most respondents even though the problem
is logically identical to the ﬁrst, more abstract, task (e.g., Cox and Griggs 1982).
2. This is a particular advantage of betting markets over other types of ﬁnancial market for
naturalistic research. The payoffs in betting markets are entirely unambiguous, so there
is a time when all uncertainty is resolved. This is not the case in regular ﬁnancial markets,
where prices continuously represent the current expectation of future prices.
3. An exception holds for objective probabilities of less than 0.05, which is the favorite-
longshot bias detailed in the second part of this chapter.
4. Exceptions have been reported in the horse race betting markets in Hong Kong (Busche
and Hall 1988; Busche 1994), the market at one U.S. racetrack (Swidler and Shaw 1995),
and exchange betting markets in the United Kingdom (Smith, Paton, and Vaughan
Williams 2006).
5. In ﬁnancial markets the results can be catastrophic, with herd behavior exacerbating
asset-price bubbles and crashes, and bank runs (Devenow and Welch 1996).
6. Evidence from ﬁnancial markets is similarly inconclusive (Sias 2004).
7. Croson and Sundali also found evidence of the hot hand fallacy: 80 percent of bettors
quit playing after losing a bet while only 20 percent quit after winning. Moreover, bettors
tended to place more bets after winning than after losing.

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512
motivation, behavior, and decision-making in betting markets
8. The point spread market is a betting market in which a bet wins if the home team wins
by a speciﬁed margin of points (the point spread) or, if the point spread is negative, the
home team loses by less than the point spread (this is known as the team winning“against
the spread”).
9. There is a fourth alternative—that bettors are unaware of a genuine hot hand effect—but
this hypothesis is not tested by Brown and Sauer.
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chapter 27
........................................................................................................
BEHAVIORAL FINANCE AND POINT
SPREAD WAGERING MARKETS
........................................................................................................
greg durham
[T]he point-spread betting market may be a fruitful place [in which]
to conduct research about behavioral theories that could apply in
conventional market settings.
— John, Rick, Thomas, and Ben (1988)
1 Introduction
.............................................................................................................................................................................
The objective of this chapter is to review and extend an emerging body of research that
tests theories, models, and general predictions of human behavior—most of which are
rooted in psychology—while using the point spread wagering market as the setting. The
bridge between behavioral psychology and sports betting is provided by the growing
ﬁeld of behavioral ﬁnance, a relatively new subdiscipline of behavioral economics.
Behavioral psychology is a component of behavioral ﬁnance, and ﬁnancial markets
and the point spread market are strikingly similar. As will be explained in section 4,
a clear settling-up point associated with each wager makes the point spread market
a powerful, particularly simple setting in which to test theories of investor behavior.
Furthermore, because of numerous similarities between the point spread market and
ﬁnancial markets, any ﬁndings from the betting market should have useful extensions
for wider ﬁnancial audiences.
This chapter proceeds with discussions of the concept of rational behavior, of the
two general levels of behavioral-ﬁnance research (individual investor level and market
level), and of the conditions that must exist in order for irrational behavior to affect
asset prices. Section 3 documents the evolution from classical ﬁnancial economics to
the current theoretical environment, which is characterized by a much greater openness
to the possibility—or reality—that individuals may not always act in rational manners

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519
and may not always act solely to maximize expected utility of wealth. This section also
summarizes a few select cognitive biases and types of human sentiment that seem to
regularly affect bettor behavior in point spread markets.
Section 4 addresses the mechanics of point spread wagering and touts the usefulness
and advantages of point spread betting markets as research laboratories. Section 5
presents a thorough review of academic studies that have tested for evidence of rational
(or irrational) behavior in point spread wagering markets. This survey is restricted to
point spread betting (as opposed to odds betting or pari-mutuel betting), since point
spread markets are most similar to the more conventional markets wherein ﬁnancial
assets are traded. Section 6 concludes and offers suggested directions for future research.
2 Rationality, Irrationality, and
Behavioral-Finance Research
.............................................................................................................................................................................
Behavioral ﬁnance encompasses traditional ﬁnance, psychology, and perhaps even soci-
ology. Behavioral ﬁnance represents a divergence from the classical assumptions of
traditional ﬁnance in that, unlike the latter discipline, it allows for the legitimate pos-
sibility that various agents in the ﬁnancial marketplace do not always act in rational,
unbiased, utility-maximizing ways (where utility is deﬁned in the traditional terms
of wealth and risk). In the speciﬁc context of investing rational behavior involves
(i) processing new information and updating beliefs in proper Bayesian fashion and
(ii) making decisions that are consistent with the classically presumed investor’s objec-
tive function of maximizing expected utility in mean-variance fashion. Irrationality
is any behavior that is inconsistent with either, or both, of these two complementary
speciﬁcations of rational behavior.
Some studies of investor behavior examine investing activity at the individual level,
either in experimental settings or by using data from individual brokerage accounts.
Robert Bloomﬁeld and Jeffrey Hales (2002), for example, found that human subjects
(MBA students) respond to historical stock-performance sequences in ways consistent
with an investor-behavior model developed by Nicholas Barberis, Andrei Shleifer, and
Robert Vishny (1998).1 In a study that uses proprietary data from household stock-
trading accounts, Brad Barber and Terrance Odean (1999) found evidence of excessive
trading (suggesting that investors are overconﬁdent) and of holding losing stocks too
long (suggesting a desire to avoid the feeling of regret). Examining data from the same
proprietary source, Barber and Odean (2001) also found that men and women both
trade too frequently—men more so—at a cost of lower returns than what would have
been realized using simple buy-and-hold strategies.
However, most studies look at market-level data (stock prices and returns) in test-
ing for evidence consistent with irrational behavior. For example, Werner DeBondt
and Richard Thaler (1985) found long-run reversals in stock returns, suggesting that

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motivation, behavior, and decision-making in betting markets
investors overreact to ﬁrms that perform well, thereby driving these ﬁrms’ stock prices
to artiﬁcially high levels only to have prices drop to normal levels after the long-term
run-ups.2 Narasimhan Jegadeesh and Sheridan Titman (1993) found that stock returns
are positively autocorrelated (i.e., they exhibit momentum) over shorter horizons,
suggesting that investors underreact to information and that information thus slowly
incorporates into prices. As a ﬁnal example, Andrea Frazzini (2006) found positive
post-announcement drift in stock returns following announcements of good news,
suggesting that happily disposed individuals sell their stocks immediately following the
good news, thereby putting instant downward pressure on prices and leading to the
post-announcement drift.
These three noted studies are representative examples among countless others that
utilize market prices in investigations of investor behavior. If investors depart from
rational behavior in predictable, systematic ways and if any pricing errors caused by
these departures are not fully corrected by rational traders, then researchers should
be able to detect the effects that various types of irrational behavior have on asset
prices. The challenge, unfortunately, is that often more than one behavioral bias can
explain an observed pricing anomaly, and, therefore, distinguishing among multiple
explanations is difﬁcult. Even when rationality can be rejected, the source of departure
from rationality may not be immediately apparent.
Implications of irrational behavior will only appear at aggregate price levels if limits
to arbitrage are sufﬁciently large so as to prevent rational traders from fully correcting
any mispricing that emerges due to irrationality. Brad DeLong, Shleifer, Larry Sum-
mers, and Robert Waldmann (1990) explained that arbitrageurs face a short-run risk
that irrational traders might cause prices to deviate further away from fundamental
values instead of the arbitrageurs transacting to eliminate any pricing inefﬁciencies.
If an arbitrageur were forced to liquidate its position before prices are corrected, the
arbitrageur’s round-trip transaction would yield negative proﬁts. Shleifer and Vishny
(1997) proposed the possibility that arbitrageurs may face capital constraints that pre-
vent the arbitrageurs from fully offsetting irrational trading behavior’s effects on prices.
The large body of empirical research showing asset-pricing anomalies strongly implies
that arbitrage is, indeed, limited in many cases.
For at least half a century, psychologists have been documenting human behaviors
that are seemingly irrational; the irrationality is often attributable to predictable biases
that have been shown to systematically impair the human decision-making process.
The list of cognitive biases is long and broad, and includes conservatism, reliance on
the representativeness heuristic, overconﬁdence, the illusion of knowledge, biased self-
attribution, aversion to regret, and aversion to losses, among others. More recently
the more general concept of sentiment has also worked its way into the asset-pricing
and efﬁcient-market literature: many of the types of sentiment that are hypothesized
to affect investors in the ﬁnancial marketplace derive from the cognitive biases just
mentioned. Academicians are attuned to these various psychological impairments and
are examining the ways by which they affect investor behavior as well as the effects that
any irrational behavior has on asset prices and returns.

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3 Behavioral Biases and Irrational
Preferences in Betting
.............................................................................................................................................................................
Asalreadynoted,theﬁeldof behavioralﬁnancepermitshumandecision-makingbehav-
ior that violates the principles of either Bayes’ theorem, the maximization of expected
utility, or both. Behavioral ﬁnance researchers embrace the possibility that an individ-
ual’s ability to behave rationally—in formulating beliefs or in maximizing utility—is
often impaired by behavioral biases or by irrational preferences. This section begins
with a recap of the evolution of alternative utility functions and behavioral models for
a representative investor who might behave normally, where the deﬁnition of normal
has itself evolved over time, perhaps to where it means rational most of the time and
irrational sometimes. The section continues with a brief overview of a handful of cog-
nitive biases that seem to repeatedly affect bettor behavior in point spread wagering
markets and concludes with a discussion of various types of sentiment that have been
hypothesized to exist in point spread markets.
3.1 Departures from the Expected Utility Framework
John Von Neumann and Oskar Morgenstern (1944) (hereafter VNM) developed an
expected-utility-of-wealth function that accurately represents two axioms of rational
preferences and choice (namely, completeness and transitivity) as well as two axioms
of choice under uncertainty (continuity and independence). The VNM expected utility
function relies on an underlying, continuous utility of wealth function that is increas-
ing in wealth and reﬂects diminishing marginal utility of wealth. (This underlying
utility function is often referred to as a Bernoulli utility function.) The concavity of
the Bernoulli function captures the risk aversion of the representative individual who
derives utility of wealth.
The decreasing marginal utility of wealth feature of the Bernoulli function is in
conﬂict with the acceptance of a fair gamble and in even greater conﬂict with acceptance
of a unfair gamble. In response to this limitation of the VNM–Bernoulli model, a
succession of models of expected utility of wealth followed. One prominent model
that emerged is Harry Markowitz’s (1952) utility function that is primarily concave but
locally convex (“locally” meaning at or near an individual’s current wealth level); the
Markowitz model can accurately explain an expected-utility maximizer’s preference
for gambles. Until the late 1970s all of the hypothesized versions of expected utility
continued to adhere to the underlying assumption of rationality, still deﬁned in terms
of the completeness and transitivity axioms.
Prospect theory, developed by Daniel Kahneman and Amos Tversky (1979), repre-
sents the ﬁrst and most enduring diversion away from rationality. This theory posits
a utility function with a reference point relative to which gains and losses are then

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motivation, behavior, and decision-making in betting markets
measured, in contrast to the Bernoulli function which begins at a wealth level of zero.
Furthermore,theprospecttheoryvaluefunctionisS-shaped: itisconcaveovertherange
of gains and convex over the range of losses. The other main departure of prospect the-
ory from VNM utility theory is that the decision-maker is modeled as using decision
weights instead of probabilities in calculating expected value. These decision weights
are increasing in, but do not represent estimates of, corresponding probabilities. Also,
the decision weights are higher (lower) than the true probabilities attached to extreme
outcomes with very low (high) probabilities.
Kahneman and Tversky proposed a two-step decision process. The ﬁrst step is what
they call the“editing phase,” wherein the decision-maker evaluates a set of probabilistic
outcomes (i.e., a gamble) with the goal of organizing and formulating the alternatives
so as to simplify the subsequent comparison across, and eventual choice from among,
the alternatives. The editing phase involves the establishment of the aforementioned
reference point, around which the S-shaped value function will be centered and relative
to which various possible outcomes will be coded as gains and losses. The second
step is the “evaluation stage,” which involves the assignment of the above-mentioned
decision weights as well as subjective values (deﬁned relative to the already established
reference point) to the various possible outcomes. To conclude the evaluation phase,
the decision-maker selects the prospect with the highest expected value.
Human behavior prescribed by prospect theory can often result in departures from
expected-utility theory, including violations of the transitivity property or of the
principle of dominance, but the theory has remained robust in explaining so many
of the empirical and experimental ﬁndings that are in conﬂict with the previous
rationality-based utility functions.
A second theoretical framework that also allows for irrational behavior and is specif-
ically developed with investors in mind is the one advanced by Hersh Shefrin and
Meir Statman (1984). In response to widely observed tendencies of investors to pre-
fer cash dividends, to sell winner stocks too quickly, and to hold “loser” stocks too
long, Shefrin and Statman developed a framework that uses prospect theory as one of
its four fundamental tenets along with the additional behavioral concepts of mental
accounting, aversion to regret (and its converse, desire for pride), and self-control.
Three additional models of investor behavior will be introduced shortly, each within
the respective subsection dedicated to the cognitive biases on which it is based.
Having now established prospect theory as a solid foundation for explaining many
types of irrational behavior, with the Shefrin and Statman framework as a viable off-
shoot, the discussion proceeds to brief overviews of cognitive biases that are rooted in
prospect theory and are particularly relevant to point spread bettors.
3.2 Conservatism and the Representativeness Heuristic
First proposed by Ward Edwards (1968), conservatism is deﬁned as a slowness to fully
revise beliefs in the presence of new information. When individuals are impaired by

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conservatism while updating expectations, they underweigh relevant new information
and over-rely on older data, as compared to how a purely rational Bayesian would
respond. Individuals who exhibit the conservatism bias seem unwilling, or are unable,
to have full faith in the newest information. In a markets context the conservatism bias
is suggestive of investor underreaction.
The representativeness heuristic, developed by Kahneman and Tversky (1972, 430),
is an evaluation mechanism under which an individual assesses the probability of an
uncertain event by the degree to which it “(i) is similar in its essential properties to
the presumed parent population [and] (ii) reﬂects the salient features of the process
by which it is generated.” A person distracted by reliance on the representativeness
heuristic3 will not formulate probability estimates in Bayesian fashion, instead over-
weighting the representative description and underweighting any statistical evidence,
such as sample size.
Barberis, Shleifer, and Vishny (1998) (hereafter BSV) developed a theoretical model
of investor behavior involving a representative agent who believes that, at any instant,
stock price performance is being governed by one of two regimes when in fact it follows
a random process. With each new event (either a continuation or reversal in perfor-
mance), the agent updates beliefs in proper Bayesian fashion about which regime is in
place: a steadily trending regime or a mean-reverting regime. Belief in a continuation
regime generates the same behavior as does the representativeness heuristic; belief in
a reversal regime creates the same effects as those predicted by conservatism. The BSV
model is consistent with two pervasive empirical anomalies that have been the focus
of much research in ﬁnance: short-run momentum and long-run reversals in stock
returns.
3.2.1 Overreaction
Experimental research in psychology shows that individuals react to new information
more excessively than is appropriate, even more so when the new news is striking.
This cognitive error, known as overreaction, follows closely from the representativeness
bias. For the purposes of this survey chapter, overreaction applies speciﬁcally to the
cognitive exercise of updating probability estimates in the face of new information and
given an already existing information set. The mere name of this bias necessitates a
benchmark for deﬁning what an appropriate reaction would be. Whereas the appropri-
ate reaction (or revision in beliefs) would be that which is dictated by Bayes’s rule, an
overreacting decision-maker will overestimate the statistical importance of the piece of
new information.
Dale Grifﬁn and Tversky (1992) (hereafter G&T) hypothesized that in the face
of new evidence about the likelihood of a future event or about the characteris-
tics of an unobservable total population, individuals over-rely on the “strength” (or
saliency) of the evidence and under-rely on the same evidence’s “weight” (or sta-
tistical informativeness). One implication, then, of G&T’s hypothesis is that when
evidence has high strength and low weight, people overreact in a manner consistent

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motivation, behavior, and decision-making in betting markets
with representativeness. A second implication within this same framework is that
conservatism would occur in the presence of low-strength, high-weight evidence.
People are unimpressed by the low strength and react mildly to the evidence, lesser
than what Bayesian updating would suggest.
Manifestations of overreaction are numerous in ﬁnancial markets. Its market-level
effects have emerged in various forms, including excess volatility in stock prices (as
shown by Robert Shiller (1981) or positive cumulative abnormal returns on portfolios
of stocks that were previously losers (as documented by DeBondt and Thaler (1985)).
Another example is the prevalence of unjustiﬁably high stock prices for companies
with recently high sales growth (or with high price-to-earnings ratios) relative to prices
on these stocks’ counterparts, known as value stocks (as documented by Josef Lakon-
ishok, Shleifer, and Vishny (1994)). In another study of investor reactions, Barberis,
Shleifer, and Vishny (1998) found evidence in support of Grifﬁn and Tversky (1992):
investors overreact to high-strength, low-weight earnings surprises and underreact to
low-strength, high-weight surprises.
3.3 Overconﬁdence, the Illusion of Knowledge,
and the Self-Attribution Bias
Overconﬁdence is a belief about a pending outcome that is greater than the underlying
characteristics describing the outcome can justify. Overconﬁdence could emerge in the
form of a person believing that the precision of an information set is greater than it
actually is; people tend to underestimate the amount of uncertainty that truly deﬁnes
the information set. Or, it could be in the form of a person overestimating his or her
ability to successfully complete a task (including the processing of information or, say,
correctly predicting an outcome).
One factor that can contribute to the overconﬁdence bias is the illusion of knowledge.
Individuals tend to assume that their level of knowledge increases with the size of an
information set; however, they fail to realize that any knowledge to be gained from any
extra information is constrained by their general inabilities to properly interpret and
understand information. In addition, overconﬁdence as a personality trait may derive
from the more deeply rooted cognitive bias known as biased self-attribution whereby
individuals tend to attribute successes to their own talents and skills while blaming
failures on random bad luck. An investor’s conﬁdence may rise when an outcome turns
in his or her favor, yet under this bias it will not fall commensurately following an
unfavorable outcome. Hindsight bias—by which an individual, after an outcome is
observed, overestimates his or her ex-ante ability to have predicted the outcome—also
may contribute to overconﬁdence.
As demonstrated by Kent Daniel, David Hirshleifer, and Avanidhar Subrah-
manyam (1998) with a theoretical model, the presence of investors impaired both
by overconﬁdence (about the informativeness of their private information sets) and

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behavioral finance and point spread wagering markets
525
by the self-attribution bias can explain the well-documented empirical anomalies
of momentum and reversals in returns. Another ﬁnancial-market implication of
overconﬁdence is that it can cause investors to trade too frequently, at a cost of realized
returns that fall short of benchmarks, as per Barber and Odean (1999).
3.4 Aversion to Regret
Regret is an unpleasant intellectual and emotional sense that is afﬁliated with the
knowledge that a different past decision would have yielded a current outcome that is
more desirable than the outcome that did emerge from the actual decision taken. As
documented by Kahneman and Tversky (1982), the uneasiness of this feeling will cause
individuals to try to avoid it, even to the point of not taking any action at all out of fear
that in hindsight the action will yield an outcome that is suboptimal. As experimental
evidence, Ilana Ritov (1996) found that when human subjects are faced with a choice,
and if they know that the outcome of the unselected alternative will be made known
after the choice is made, their selection process will result in a different choice than if
the unselected alternative’s outcome will remain unresolved. In other words, when the
probability of knowing the outcome of the unselected option is high (or certain), the
probability of regret is higher. In turn, people will select the options that are less likely
to yield worst outcomes in order to avoid eventual regret.
3.4.1 Aversion to Losses
Closely related to individuals’ aversion to regret is their general aversion to losses. She-
frin and Statman (1985) have shown that—due to this emotional preference—investors
tend to keep stocks of which prices have recently dropped (in contrast to selling stocks
that recently experienced price increases). In other words, investors want to avoid the
feeling of regret that accompanies selling a stock at a loss while they welcome the pride
associated with selling a stock at a gain. Such behavior is in direct conﬂict with the
objective of wealth maximization because of the tax advantages (disadvantages) associ-
ated with negative (positive) capital gains.4 Using proprietary brokerage account data,
Odean (1999) found a strong tendency for investors to hold their losing stocks for too
long, suggesting a desire to avoid the feeling of regret after eliminating other alternate
explanations for not selling “loser” stocks.
3.5 Sentiment
Sentimental investing is a type of irrational behavior in which factors that are uninfor-
mative nonetheless affect investing decisions. Sentiment may be purely emotions-based,
and the investor may even be cognizant of the fact that the bases for such sentiment
are not informative, yet still make investment decisions using these factors. Loyalty and

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motivation, behavior, and decision-making in betting markets
admiration are examples of such factors. Also, such exogenous factors as familiarity
with ﬁrms’ products or services, geographic locations of corporate headquarters, high
visibility within the news media and popular press, or having stocks listed on major
exchanges or having stocks added to major stock indices are all potential sources of
investor sentiment.5 Other sentiment may relate to characteristics of an investment or
pieces of news that are thought to be informative when in actuality they are not, so that
investors trade based on these attributes as if they were informative (as suggested by
Fischer Black (1986)).
4 Point Spread Betting Markets
.............................................................................................................................................................................
With the backdrop of behavioral ﬁnance, potential departures from rationality, and
common cognitive errors and other sources of sentiment in place, the focus of this
chapter now turns to point spread wagering. The goal here is to establish that the point
spread market is a viable research setting. This section will explain how a point spread
market functions and will emphasize the usefulness and advantages of this market as a
laboratory in which to perform tests of rationality.
4.1 Market Conventions and Mechanics
In any point spread wagering market, the asset at stake for a given game is a proposition
that the favored team will defeat the underdog team by an amount greater than the
point spread.6 A bet on the favored team wins if that team wins the game by an amount
greater than the spread while a bet on the underdog wins if the underdog team loses by
an amount less than the spread or wins the game outright. As per the “11-for-10 rule,”
a winning bet pays an amount equal to (1 + 10/11) (the original bet) and a losing bet
pays zero. If the favored team wins the game by an amount exactly equal to the point
spread, all wagers are refunded.7
An important participant in point spread markets is the bookmaker (or sports book),
the entity that facilitates wagers on either team in any given contest. The bookmaker
wants its expected post-game wealth level to be independent of the game’s outcome.8
If equal dollar amounts are wagered on both teams in a game, the sports book is
guaranteed a commission equal to 1/22 of the combined total wagers. In the presence
of this “11-for-10” commission, a winning rate of 52.38 percent is required for a bettor
to break even.9
The point spread is the mechanism that the bookmaker uses to try to satisfy its
objective of balancing the books for a given contest. In the absence of any sentimental
(or irrational) betting, the bookmaker maintains a spread that is equal to the median
of the distribution of possible outcomes, given whatever information set exists at the
time. Such a point spread makes the probability of winning a wager on the favored

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behavioral finance and point spread wagering markets
527
team and the probability of winning a wager on the underdog team both equal to
50 percent, ignoring the small probability associated with a push. On the other hand, if
the bookmaker anticipates or observes a sentimental (or irrational) clientele of bettors
favoring one team, the point spread will be different from the median possible outcome
and the aforementioned probabilities will both deviate from 50 percent. In the presence
of this biased spread, more than half of the rational bettors’ money will be on the sen-
timentally undesirable team, serving to offset the dollars wagered by irrational bettors
on their preferred team and allowing the bookmaker to maintain a balanced book.
The ﬁrst point spread that is posted by the sports book is called the opening spread;
it is the spread at which betting commences. Bets on a game arrive during the betting
period, and a game’s spread should change any time the bookmaker realizes, or even
anticipates, an imbalance in dollars bet on the two contestants.10 The imbalance may
emerge due to the arrival of either new information or a biased clientele of bettors, or
it could emerge due to randomness. Betting continues until the instant when the actual
contest begins; the spread that exists when the betting market closes is called the closing
spread.
The length of time that the point spread market is open for wagering on a particular
game differs across the four most common markets. Betting on almost all National
Football League (NFL) games commences on Monday morning, when opening spreads
are posted at the casinos. Nearly all games are played on Sundays, so that for each NFL
game the market is typically open for about 6.5 days. The market for wagering on college
football games usually opens on Sunday nights and stays open until the respective
kickoffs, a large majority of which occur on Saturday. At the other extreme, the market
for wagering on a basketball game—either professional or college—is typically open for
just half a day, right up until tip-off. The brevity of these markets is due to the higher
number and daily frequency of basketball games.
Besides opening spread, closing spread, and actual outcome, two other key variables
in studies of sports betting markets are forecast error and change in spread. A game’s
forecast error is calculated as the difference between the actual outcome and the point
spread; depending on the desired test it is alternately speciﬁed using either opening
spread or closing spread. The change in spread for a game is straightforward: it is the
difference between the closing and opening spreads.
4.2 Betting Markets as Useful, Advantageous
Laboratories
Point spread wagering markets parallel ﬁnancial markets in numerous ways. Both
markets are characterized by the presence of rational investors, informed agents,
arbitrageurs, irrational traders, and sentimental participants. Like arbitrageurs and
informed traders in ﬁnancial markets, professional bettors stand ready to exploit any
arbitrage opportunities that might arise in sports gambling markets.11 Information
about point spread wagers and information about stocks are both widely disseminated.

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motivation, behavior, and decision-making in betting markets
Sports betting “wise guys” saturate the news services and gambling trade publications
with their “wisdom,” analogously to those expert stock pickers who offer their
predictions for capital markets. The bookmaker for point spread wagers has a near-
perfect analogue in the form of the market maker for stocks and other securities. The
bookmaker uses the point spread to balance wagers on the two teams in a contest, just
as the market maker uses price to manage order ﬂow for a stock. And, just to be clear,
bettors are sports betting’s analogue to investors and traders. Thus, because of these
highlighted similarities, any ﬁndings using point spread markets can be useful for wider
ﬁnancial audiences.
Furthermore, point spread markets possess one key feature that makes them an ideal
setting for empirical studies: every wager reaches its terminal value in a fairly short
period of time. The existence of a clear settling-up point is important for studies of
rationality, since it allows for direct measurement of fundamental value for each wager.
A game’s perfectly observable outcome can be compared with the point spread(s) for
the game so that bettors are easily able to determine which point spread wagers are
winners. The single-payoff feature stands in contrast to stocks, which by deﬁnition
have an inﬁnite stream of possible future payoffs and which thereby create difﬁculty
in connecting changes in prices to revisions of expected future cash ﬂows. Christopher
Avery and Judith Chevalier (1999) emphasized the usefulness of bets’ relatively short
lives. The short life of any given wager reduces the likelihood that new information will
enter the marketplace during trading and cause spreads to change, thereby allowing
researchers to focus more acutely on point spread movements caused by sentiment or
by other behavioral biases.12
Occasionallyacademicsarguethatpointspreadbettingmarketsaretoodifferentfrom
more traditional ﬁnancial markets due to either the negative expected payoff on a wager
or the entertainment value of betting. However, in spite of their expected wealth being
negative, and while likely deriving pleasure and other consumption value from betting,
nearly all bettors are also heavily focused on maximizing their expected utility of wealth,
just as stock market investors are. John Conlisk (1993) presented a model in which
expectedutilityof wealthisthepredominantcomponentof agambler’spreferencefunc-
tion, augmented with a second component that captures a relatively smaller additional
taste for gambling.13 Occasional skeptics notwithstanding, point spread betting mar-
kets are useful laboratories in which to perform tests of investor rationality because of
their numerous parallels to, and advantages relative to, conventional ﬁnancial markets.
5 Empirical Implications of the Various
Biases in Point Spread Markets
.............................................................................................................................................................................
While the implications of the behavioral biases and the alternate speciﬁcations of utility
functions are generally more apparent at the individual level, most of these biases—if

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behavioral finance and point spread wagering markets
529
theycharacterizeasufﬁcientlylargeportionof thebettingpublic—canimpactaggregate
prices (i.e., point spreads). In his late-1990s survey of the economics of wagering mar-
kets, Raymond Sauer (1998, 2031) anticipated such impacts and predicted that “future
papers on wagering markets will certainly be motivated by the behavioral approach.”As
of yet, no studies have tested for evidence of behavioral biases at the level of individual
bettors, largely due to the scarcity of betting data at the individual account level. Instead,
all of the behavioral-focused studies of point spread markets have tested for evidence
only at the market level—these studies are still sparse enough that I can summarize
nearly all of them here.
5.1 Typical Tests for Irrational Behavior
Each study presented in this section employed one or more types of tests for rationality.
One typical test is to formulate betting strategies based on anticipated irrational behav-
ior and then compare the proﬁtability of these strategies against the break-even rate
of 52.38 percent. Another type of test is whether mean forecast errors are statistically
signiﬁcantly different from zero or statistically signiﬁcantly different across groups of
wagers. Another common tool is an ordinary least squares (OLS) regression analysis in
which the dependent variable is actual outcome and the independent variables are any
combination of point spreads (opening or closing), fundamental variables (to proxy
for teams’ skills, abilities, and general performance attributes), and other variables that
reﬂect various potential sources of irrational behavior. Probit analyses are a different
way to test whether the same types of explanatory variables can explain wager outcomes,
with the dependent variable taking a value of +1, 0, or −1, depending on whether a
wager wins, is a push, or loses.
A more recent set of papers test for the effects of irrationality on the spread-formation
process: the dependent variable in an OLS regression analysis is change in spread and
the independent variables are different proxies for the presence of sentiment and other
behavioral biases. Greg Durham and Muku Santhanakrishnan (2012) established that
change in spread is the appropriate analogue to realized return in ﬁnancial markets.
This point is particularly important for any researchers who are interested in testing
ﬁnancial economic theories using a point spread market as the setting yet who may
want to position their studies within the ﬁnance literature as opposed to the sports
economics literature. Tests of investor behavior commonly utilize percentage return
as the variable of interest; tests of bettor behavior can similarly employ change in
spread.
5.2 Informed Bettors and Potential Limits to Arbitrage
One such-positioned study is by John Gandar, Bill Dare, Craig Brown, and Rick
Zuber (1998). While not addressing behavioral aspects of betting, this research is still

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motivation, behavior, and decision-making in betting markets
noteworthy for two reasons: (1) it establishes the presence of informed bettors in at
least one betting market and (2) it is the ﬁrst study to employ the intra-period change in
point spread, albeit as a conditioning variable and not as a dependent variable. Examin-
ing a sample of wagers on National Basketball Association (NBA) games, Gandar et al.
hypothesized that change in spread (from opening spread to closing spread) reﬂects the
betting activity of rational traders who possess better information than what the book-
maker possesses when setting the opening spread. If their hypothesis is true, the degree
of initial mispricing (i.e., the size of the forecast error in the opening spread) should
be positively related to the size of the subsequent change in spread, and the change in
spread should be in the direction of the initially undervalued team. Sorting games into
bins based on intra-day changes in spreads, Gandar et al. found that the proﬁtability
of betting on the initially undervalued teams (i.e., teams in whose directions spreads
subsequently move) at opening spreads14 is a positive function of change in spread,
consistent with rational bettors’ transactions serving to correct errors in bookmakers’
opening forecasts. Information-based trading is an important facet of the NBA point
spread market.
In contrast, an earlier study by Gandar, Zuber, Thomas O’Brien, and Ben Russo
(1988) suggested an insufﬁcient presence of informed bettors. These authors tested for
evidence consistent with rationality in the point spread betting market for NFL games.
While statistical tests do not allow for rejection of rationality, the authors did ﬁnd three
different behavioral-based betting strategies (all implemented at closing spreads) to be
abnormally proﬁtable. These strategies’ proﬁtability suggests that the certain types of
irrational betting are prevalent enough to create biases in spreads that are not fully
offset—or corrected—during the course of betting by rational, informed participants,
perhaps due to the limits to arbitrage discussed in section 2. The role of informed
traders is limited.
5.3 Market Effects of Conservatism
and Representativeness
To date, conservatism and representativeness are the two cognitive biases that appear
most prominently in studies of bettor behavior in point spread wagering markets.
Perhaps the prevalence of these biases is not surprising since both of these biases involve
processing information as it arrives, often in sequential or successive pieces, and then
updating beliefs about an often unobservable parent population, group, or process.
Bettors impaired by conservatism will underreact to the true statistical importance
of the most recent information so that prices (or point spreads) will only gradually
incorporate the new information as bettors gradually respond. Bettors affected by the
representativeness heuristic will overreact to recent information, will tend to want to
detect patterns amid randomness, and will often over-extrapolate past performance
into the future.

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behavioral finance and point spread wagering markets
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5.3.1 Bettor Responses to Strength and Weight
Gandar et al. (1988) examined a strategy of betting against favored NFL teams that, in
their most recently preceding games, covered the point spread by 10 points or more.
The potential proﬁtability of this strategy is consistent with a hypothesis by Grifﬁn and
Tversky (1992) that, upon encountering a new piece of information about an uncertain
future event or parent population, individuals over-rely on the “strength” of a new
piece of evidence and under-rely on the same evidence’s “weight.” One implication
of this hypothesis is that in response to high-strength, low-weight evidence people
overreact in a manner suggestive of representativeness. Gandar et al.’s ﬁnding that
this betting strategy is abnormally proﬁtable suggests that bettors are impaired by
representativeness; bettors do seem to overreact to large lagged forecast errors in spite of
the fact that a wager’s payoff is independent of the amount by which the wagered-upon
team covers the spread.
In a closely related study Durham and Santhanakrishnan (2008) tested predictions
of Grifﬁn and Tversky’s (1992) behavioral hypothesis with an interest in discovering
whether bettors might be impaired with conservatism or representativeness. For a
sample of college football wagers, the authors used length of a team’s current winning
streak15 and the average amount by which the team had covered the spread during the
same streak as measures of weight and strength, respectively. Change in spread was
their measure of bettors’ reaction. Since a wager’s payoff for depends on whether the
wagered-upon team covers the spread, irrespective of the magnitude by which it covers
the spread, the weight of the wager’s outcome is simply whether the bet wins or not.
The amount by which the team covers (or fails to cover) the spread can be thought of as
the strength of the outcome. The authors found that, holding weight constant, bettors
overreact more to high-strength games than to low-strength games. They also found
that bettors underreact more to games involving high weight than to games low weight,
for games of similar strength. Both ﬁndings are consistent with G&T’s predictions
of ways by which individuals impaired by conservatism and representativeness would
affect prices (or point spreads).
5.3.2 Momentum, Streaks, and the Hot Hand
Philip Gray and Stephen Gray (1997) are among the ﬁrst researchers to acknowledge
behavioral ﬁnance research in a study that used betting markets. As part of a thor-
ough examination of market efﬁciency for the point spread wagering market for NFL
games, Gray and Gray accurately drew the analogy of momentum in teams’ perfor-
mances against the spread with momentum in stock prices. They acknowledged the
well-documented behavioral phenomenon whereby individuals perceive runs in ran-
dom series, though they did not mention the representativeness bias by name. They
constructed dummy variables to capture season-long, as well as recent, team perfor-
mance. Using a probit analysis, Gray and Gray found that bettors appear to underreact
to teams’ season-long performance to date (suggestive of conservatism) but that these
same bettors seem to overreact to recent form (i.e., to win–loss records in teams’ most

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motivation, behavior, and decision-making in betting markets
recent four games). These ﬁndings together suggest a proﬁtable (though untested)
betting strategy of betting on teams that have recently performed poorly yet have
performed well across the season overall.
Durham, Michael Hertzel, and Spencer Martin (2005) analyzed data on college foot-
ball wagering to conduct various tests of the BSV model of investor behavior described
insection3. Theauthorsexaminedthenumbersof continuationsandreversalsinteams’
performance histories of various lengths and found that football bettors do not seem to
update beliefs in the same manner as BSV’s representative investor. Durham, Hertzel,
and Martin also found that bettors believe that a team’s performance is more likely to
reverse as the team’s streak (winning or losing) grows longer. This ﬁnding contradicts
the BSV model’s implication that investors become more certain about the presence of
a continuation regime as the number of successive wins (or losses) increases. Durham,
Hertzel and Martin’s two main ﬁndings do not support BSV’s theoretical model of
investor behavior.
One potential outcome from reliance on the representativeness heuristic is that belief
in the phenomenon known as the hot hand will emerge. In the respective realms of
gambling and sports, the belief that a roulette wheel, a craps table, an athlete, or a team
is “hot” is quite common; thus the manifestation of such a belief in sports wagering
markets is not surprising. Bettors will perceive streaks, or patterns in performance,
when performance is, in fact, random. Colin Camerer (1989) and Rodney Paul and
Andrew Weinbach (2005a) found evidence that wagers on NBA teams on current win-
ning streaks tend to lose more frequently than the expected 50 percent, which means
that point spreads are higher than actual outcomes for games involving such streak-
ing teams. These ﬁndings are consistent with bettors’ mistaken belief in the so-called
hot hand: bettors overreact to winning streaks and believe that a winning pattern has
emerged when in fact performances relative to spreads should be random.16 Bettors
overbet on these teams that have been winning recently, causing wagers to be mis-
priced and creating a proﬁtable betting strategy of betting against these recent winners.
Although not speciﬁcally mentioned by either Camerer or Paul and Weinbach, bet-
tors impaired by representativeness is a viable explanation for these ﬁndings. Camerer
makes a more general claim: that a persistent misunderstanding of randomness can lead
to belief in the hot hand (i.e., in winning more frequently than a random process would
suggest).
5.4 Market Effects of Bettor Sentiment
Avery and Chevalier (1999) (hereafter A&C) examined intra-week changes in NFL
point spreads, focusing on possible sources of sentiment that have natural stock mar-
ket analogues. The authors found that bettors do seem to follow “expert” forecasts
despite the general inability of prognosticators to predict which teams will cover
the spreads. NFL bettors also appear to overreact to, and cause spreads to move in
the direction of, teams that perform well in the recent term (i.e., teams exhibiting

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behavioral finance and point spread wagering markets
533
short-run momentum). Also, bettors’ sentiment for teams that are highly visible or
highly recognizable (proxied for by membership in a dominant, large-market football
conference or by appearance at the top of the standings) seems to cause spreads to move
during the week. Overall, A&C’s results suggest that bettors are affected by these vari-
ous types of sentiment and that sentimental wagering does affect price paths or point
spread paths. A&C also found sentiment-based biases in opening spreads, suggesting
that bookmakers attempt to incorporate anticipated sentiment into opening spreads;
this bias is in addition to that caused by the systematic intra-week sentimental bet-
ting. The two biases together lead to a strategy of betting against sentimentally popular
teams at closing spreads, a strategy that is marginally proﬁtable after accounting for
transaction costs.
Following A&C’s lead, Durham and Tod Perry (2008) found evidence that sentiment
also affects the dynamic spread-formation process for college football betting. Their
ﬁndings suggest that bettors naively follow the advice of experts, believe in the hot hand,
prefer to bet on teams that are visible (in terms of major -conference membership or
appearance at the tops of standings), and bet on teams about which they are most
avid (or loyal). The fan-avidity variable marks this study’s novel contribution to the
literature and relies on the premise that college football bettors exhibit strong emotional
commitment and loyalty to particular teams (Wayne Root and Wilbur Cross (1989)).
Durham and Perry constructed a measure of fan avidity for each team by using survey
results from a national market research ﬁrm that asked fans to indicate their favorite
college football teams. As noted, spreads do move in the direction of the teams to which
fans are more loyal. However, betting strategies designed to exploit fan avidity and the
other hypothesized types of sentiment are not proﬁtable except under extreme ﬁltering
rules.
5.5 Other Biased Behavior without Psychological Basis
A general phenomenon—albeit not rooted in any speciﬁc psychological biases—is
that bettors appear to systematically overbet on heavy favorites,17 creating proﬁtable
wagering strategies in all of the markets tested to date. For example,Paul,Weinbach,and
Christopher Weinbach (2003) found that betting on big underdogs in college football is
abnormally proﬁtable (in the absence of bookmaker commissions) and that betting on
big underdogs when they are at home yields abnormal proﬁts in excess of commissions.
Similarly Paul and Weinbach (2005a) showed that betting on big underdogs in the
NBA is abnormally proﬁtable (without commissions) and is abnormally proﬁtable (in
excess of commissions) when the sample is reduced to big-underdog teams playing
at home. And in a study of college basketball wagering, Paul and Weinbach (2005b)
found that a strategy of betting on big underdogs generates a winning percentage that is
statistically signiﬁcantly different from 50.00 percent. However, in contrast to the big-
home-underdog phenomenon in the ﬁrst two markets, abnormal proﬁts come from
betting on heavy-underdog visiting teams.

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534
motivation, behavior, and decision-making in betting markets
While this overarching ﬁnding that people tend to overbet on heavily favored teams is
striking in that it seems to repeat across all point spread markets,only one of the authors’
explanations hints at either a cognitive bias or sentiment as the reason. Paul, Weinbach,
and Weinbach (2003) suggested an asymmetry in information available about the heav-
ily favored teams and information available about their opponents (in college football),
a suggestion that is reminiscent of Robert Merton’s (1987) investor recognition hypoth-
esis. Avery and Chevalier (1999) and Durham and Perry (2008) found that bettors are
attracted to teams that are members of the prominent conferences or that generally
appear at the top of the win–loss standings each year. Avery and Chevalier were the
ﬁrst to propose that these attributes are proxies for teams that bettors may have read
or heard a lot about in the media and that bettors may be sentimentally predisposed to
bet on such teams. The apparent overbetting on heavy favorites seems to support this
notion.
A number of other ad hoc betting rules have been found to be abnormally prof-
itable for different sports across different time periods. However, because the potential
behavioral explanations for any of these ﬁndings are not readily apparent, these rules
are not included in this survey.
6 Conclusion and Directions
for Future Research
.............................................................................................................................................................................
Behavioral ﬁnance has made great strides in recent years in terms of gaining acceptance
in ﬁnance theory, research, and practice. Prospect theory has proven to be robust in
explaining many empirical and experimental ﬁndings in ﬁnancial markets, ﬁndings that
were considered to be anomalies under the assumption of rational behavior. Multiple
theoriesof investorbehaviorcanexplainthewell-documentedphenomenaof short-run
momentum and long-run reversals in returns, though to ﬁnd tests that will distinguish
among the competing theories can be difﬁcult.
The point spread betting market might help to reduce at least some of the difﬁculties
and challenges facing all tests of investor (or bettor) behavior, since the asset-pricing
question is simpliﬁed by a clear settling-up point for each bet and by the absence
of any systematic risk. Many researchers recognize the advantages of this simpler
market and have used it to ﬁnd evidence consistent with bettors being impaired by
representativeness, belief in the hot hand, and various types of sentiment.
Looking ahead, one signiﬁcant development will be if any researchers can gain access
to proprietary betting data at the individual account level. Having such data would
allow for tests that are sports betting’s analogues to all of the work performed by Barber
and Odean (and other coauthors) using stock trading data from household brokerage
accounts. Anyone equipped with such individual-level, point spread betting data could
then test for such sentimental preferences as bettors betting on teams situated in the

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behavioral finance and point spread wagering markets
535
same geographic region as where they live. Or, dollar-volume data could be aggregated
and examined to see whether betting volumes follow patterns similar to those of point
spreads.
Another useful, relatively new type of data are the percentages of dollars wagered on
each team in a point spread wager, data that are currently available from at least two
services: Sports Insights and Sportsbook.com, as per Paul and Weinbach (2011). Paul
and Weinbach are the ﬁrst researchers to successfully employ such data, though thus far
the data have been used primarily to reject the long-believed notion that the objective
function of the bookmaker is to “balance the books” and to reject claims of point
shaving in the sport of college basketball. Perhaps these same betting-proportions data
can be examined to see whether the same sources of sentiment mentioned in this survey
seem to affect the proportions of dollars wagered in games which have net sentiment
for one team.
For researchers who are interested in positioning their sports-betting studies more
squarely amid the behavioral ﬁnance literature, change in point spread should likely
be an important variable of interest. To the extent that bookmakers cannot perfectly
anticipate irrational behavior when setting opening spreads and if the clientele of
arbitrageurs is insufﬁcient to correct all pricing errors, irrationality should affect the
dynamic intra-period spread-formation process. Changes in spreads will reﬂect these
effects.
With the establishment of change in spread as an important new variable of interest,
the emergence of new data types (such as proportions of dollars wagered on the two
teams in each contest and intra-period point spreads besides only opening and closing
spreads), and increasingly easier access to such data, the quote at the beginning of this
chapter from Gandar, Zuber, O’Brien, and Russo (1988) resonates even more soundly
now than when it was written in 1988. An updated version might read like this: The
point spread betting market is likely an even more fruitful place than it has ever been for
conducting research about behavioral theories that could apply in conventional market
settings.
Notes
1. This model is discussed in more detail in subsection 3.2.
2. For ﬁrms that perform poorly, the authors ﬁnd inverse responses: overreaction drives
prices too low and then prices are eventually corrected.
3. For ease of exposition in the remainder of this chapter, either“the representativeness bias”
or simply “representativeness” will be used regularly in place of the more cumbersome—
but correct—phrase “reliance upon the representativeness heuristic.”
4. Furthermore, Odean (1999) has shown that “winner stocks” generally outperform “loser
stocks” across various-length time periods after the winners are sold and the losers are
kept, or held.
5. Christo Pirinsky and Qinghai Wang (2006) found strong evidence suggesting that stock
price formation has a geographic component whereby a region’s residents seem to invest

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motivation, behavior, and decision-making in betting markets
disproportionately in ﬁrms that are headquartered in their own region. Lily Fang and
Joel Peress (2009) showed that the degree of mass media coverage of a company affects
the company’s stock returns. These last two factors (or events) also relate to greater
visibility for a ﬁrm and its stock. Merton’s (1987) investor recognition hypothesis shows
how a ﬁrm’s expected stock returns are affected by investors’degree of familiarity with the
company’sproductsorservices. StephenFoersterandAndrewKarolyi(1999)documented
the negative effects on returns of American Depository Receipts after they list on U.S.
exchanges. Bala Dharan and David Ikenberry (1995) found evidence consistent with the
investor recognition hypothesis following stock listings on the American Stock Exchange
and the New York Stock Exchange. Honghui Chen, Gregory Noronha, and Vijay Singal
(2004) found evidence of increases (decreases) in investor awareness following index
additions (deletions).
6. The point spread can take any value in half-point increments. On rare occasions the point
spread can equal 0, in which case the “favorite” and “underdog” labels are dropped and
the game is labeled as a “pick ’em” game.
7. Introducing some sports betting lingo, the three possible outcomes for a given wager are:
the favorite “covers the spread,” the underdog “covers the spread,” or the bet is a “push.”
8. While the literature provides some evidence in support of the bookmaker’s objective
being different from“balancing the books”(see, for example, Steven Levitt 2004; Paul and
Weinbach 2007; Paul andWeinbach 2011), the more widespread belief (or understanding)
isthatthebookmakerpreferstomaximizeorderﬂowwhileminimizingexposuretogames’
outcomes. Avery and Chevalier (1999) offered a nice explanation with multiple reasons
for why a bookmaker’s goal should be to minimize its exposure to a game’s outcome
against the spread. For additional explanations, please see the literature review by Sauer
(1998).
9. Solving for p in the following equation which sets expected proﬁt equal to $0 yields the
necessary winning percentage to break even: p · $10 + (1 −p) · −$11 = $0.
10. Point spread changes are frequent and nontrivial. For a sample of 7,904 wagers on profes-
sional basketball games, Gandar et al. (1998) found that changes in spread (from opening
spread to closing spread) are different from zero for 79.5 percent of the observations.
For this same sample the mean absolute value of the change in spread is equal to 1.08,
and the standard deviation of change in spread is 0.80. For Avery and Chevalier’s (1999)
sample of 2,366 wagers on professional football games, the change in spread is non-zero
for 70.2 percent of the games. The mean absolute value of the change in spread is 0.68,
and the standard deviation is roughly 0.96. For Durham and Perry’s (2008) sample of
4,584 college football wagers, the spread changes for 84.5 percent of the games. The mean
absolute change in spread is 1.44, and the standard deviation is 2.73.
11. As noted by Paul,Weinbach,andWeinbach (2003),among others,sports books have limits
on the maximum sizes of bets. These limits may prohibit informed bettors from placing
wagers that are large enough to correct many of the mispricings caused by irrational
betting. These limits can perhaps be circumvented if a bettor places a number of bets at
different casinos or offshore.
12. Gandar et al. (1988) reported that only about ﬁve percent of the changes in spreads for
NFL games are caused by the arrival of new information; the ﬁgure is probably similar, if
not lower, for college football games due to privacy rules that prevent the release of certain
types of information about student athletes. For both professional and college basketball
games, this percentage will be even lower because the length of time for which markets

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behavioral finance and point spread wagering markets
537
for wagering on basketball games are open is about one-tenth of that for football game
wagering.
13. The utility-of-wealth function and the taste-for-gambling function are additive. The ﬁrst
function is a classic Von Neumann–Morgenstern expected utility function, where the
underlying utility function is increasing and concave in wealth. The second function is
increasing and concave in the size of the wager and is increasing in the probability of
winning the wager.
14. This betting strategy is obviously not implementable, since it involves placing wagers at
opening spreads, conditional on subsequent changes in spreads.
15. Here and throughout the remainder of this chapter the reader can presume that all
winning streaks, losing streaks, and performance are always deﬁned from a wagering
perspective (i.e., wins and losses relative to spreads), not from the perspective of teams
winning and losing games outright.
16. William Brown and Sauer (1993) veriﬁed that the hot hand is not some fundamentally
grounded improvement in team performance; for Camerer’s sample, the hot hand is,
indeed, a myth.
17. The deﬁnition of heavy favorite depends on the sport. For college football, to be heavily
favored is to be favored by more than 28 points. For college basketball, a heavy favorite is
favored by 20 or more points; for NBA basketball, the threshold is 10 points.
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s e c t i o n vi
........................................................................................................
PREDICTION
MARKETS AND
POLITICAL BETTING
........................................................................................................

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chapter 28
........................................................................................................
A SIMPLE AUTOMATED
MARKET MAKER FOR
PREDICTION MARKETS
........................................................................................................
david johnstone
1 Introduction
.............................................................................................................................................................................
This note describes a simple betting mechanism by which a robot market maker quotes
prices for trades (buy or sell) in a binary security. The security traded has ﬁnite expira-
tion time, at which time it is worth either V = 1 or V = 0. Its value at expiry is a random
(uncertain) variable determined by the occurrence or nonoccurrence of a prespeciﬁed
real-world event (e.g., a stock market increase over a given time interval). In ﬁnance
securities such as this trade fall under the name of “binaries” or “digital options.” In
economics they are known as Arrow securities.
The market maker proposed here is more easily understood than the well-known
Hanson (2003, 2007) market maker and extensions such as Othman et al. (2010). Its
derivation does not involve any mention of a probability scoring rule or utility function.
Its logic is based on an easily understood generalization of a pari-mutuel betting market.
It differs nonetheless from a pari-mutuel market in that traders who bet for or against
V = 1 (or V = 0), by either buying or selling a security that pays out under one of these
outcomes, are aware at the time of trading what payout they will get under each of these
two possible outcomes. Trades are therefore effectively ﬁxed-odds bets; however, unlike
conventional ﬁxed-odds betting, all trades are executed at prices that vary continuously
with trade size. More speciﬁcally, trade prices are worse for larger trades, as is typical
of trading stocks and other ﬁnancial securities.

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prediction markets and political betting
Apart from its straightforward derivation, a notable advantage of this market maker
algorithm is that the opening security price can be set naturally at any point between
0 and 1. This is useful when the market maker’s ex ante probability of a given outcome,
say V = 1, is not the inbuilt Hanson binary asset opening price of 0.5.
1.1 Prediction Markets
The Hanson market maker is widely used in online prediction markets operated by
Inkling Markets, Consensus Point,Yahoo!, and Microsoft. Details are provided by Chen
and Pennock (2010) and Othman et al. (2010). The basic advantage of an automated
market maker in prediction markets is that traders (buyers and sellers) can trade at
any time, unlike a common double auction where there may be no current offers
on the other side of the trade. Automated prediction markets run at low cost and
with minimum human oversight. Helpful and interesting surveys of the literature on
prediction markets are provided by Wolfers and Zitzewitz (2004), Pennock et al. (2001),
Chen et al. 2005, Chen and Pennock (2010) and Agrawal et al. (2011).
The theory and application of prediction markets developed in the ﬁeld of computer
science rather than in ﬁnance or economics, but the theoretical overlap between ﬁelds
is striking and valuable. Note, for example, the connections drawn by Yiling Chen
and David Pennock (2010) between prediction markets, market microstructure, and
efﬁcient markets. Automated prediction markets can also be viewed as a computerized
form of experimental markets with trading conducted on-screen against potentially
unknown individuals rather than across a table.
Automated prediction markets have potentially wide application in behavioral
ﬁnance and behavioral economics. They provide a realistic market trading envi-
ronment in which to test traders’ natural versus rational instincts (in any chosen
judgment or choice problem). Many prediction markets are designed such that the
price of the security traded represents a “market probability” of some well-deﬁned
event. In this way they resemble the over-the-counter markets for binaries that
are now widely traded by “Wall Street” style ﬁnancial market makers, such as IG
Markets.
One of the aims behind the advent of prediction markets was to design a mecha-
nism that would extract and merge probabilistic opinion on important but uncertain
phenomena, such as election results and other business, political, environmental,
medical, and social phenomena. There is a very extensive empirical literature indi-
cating in many contexts that market consensus probabilities are as accurate, and
often more accurate, than such conventional forecasts as those made by experts
or opinion polls (e.g., Berg, Nelson, and Rietz 2008). This is a generalization of
the longer held empirical proposition that bookmakers’ odds are better predictors
of outcomes than those of at least the great majority of individual gamblers. See
Chen and Pennock (2010) and Agrawal et al. (2011) for a partial survey of related
literature.

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a simple automated market maker for prediction markets
545
2 A Generalized Pari-Mutuel
Betting Market
.............................................................................................................................................................................
In a theoretic commission-free pari-mutuel binary betting pool gamblers bet on either
V = 1 or V = 0 and the total pool of money wagered is paid out to those who bet on the
realized event in proportion to the amounts that they bet (the others lose their money).
In a more general form of betting pool, each gambler i bets a pair, (Xi, pi), representing
an amount of cash Xi and a stated probability of pi = Pri(V = 1) = 1 −Pri(V = 0).
Bets are therefore of the form “$200 at probability 0.2.” The payout or return
Xi(pi/q)
if V = 1
Xi(1 −pi)/(1 −q)
if V = 0,
(28.1)
where q = Xipi/Xi is the value-weighted average (pari-mutuel) probability of
V = 1. It is immediately evident that the total money payout under this unusual
market construction is

Xi =
Xi(pi/q)
if V = 1
Xi(1 −pi)/(1 −q)
if V = 0,
(28.2)
as occurs in a common pari-mutuel market. A conventional pari-mutuel betting market
is simply the special case of (1)–(2) in which all gamblers i are constrained to state
pi ∈{0, 1}, implying that when they lose their bet they lose all of it.
Numerical example. Consider four gamblers who bet respectively (Xi,pi) = (600,0.5),
(200,0.9), (150,0), and (50,1), on event V = 1. Note that the third gambler gives event
V = 1 zero probability and, in effect, makes a conventional bet of amount 150 on V = 0.
The total betting pool is 1,000 and the pari-mutuel market probability of V = 1 is
q = 600(0.5) + 200(0.25) + 150(0) + 50(1)
1000
= 0.4.
The respective payouts to each of the four gamblers, in the event of V = 1 or V = 0,
are as shown in table 28.1.
Table 28.1 Payout to Gambler i Given V = 1 and V = 0
i
If V = 1
If V = 0
1
600(0.5/0.4) = 750
600(0.5/0.6)=500
2
200(0.25/0.4) = 125
200(0.75/0.6) = 250
3
150(0/0.4) = 0
150(1/0.6)=250
4
50(1/0.4)=125
50(0/0.6) =0
1,000
1,000

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prediction markets and political betting
3 Market Maker Equations
.............................................................................................................................................................................
There are two securities. The ﬁrst is a binary paying value V = 1 to its owner in the
event of state E (and zero otherwise), and the second is identical except that it pays
value V = 1 in the event of state not-E. The following description deals with pricing the
ﬁrst of these securities. There is no mechanical bond between the two security prices.
Rather they are priced separately using the same MM (market maker) logic, meaning
that the no-arbitrage condition (i.e., prices that sum to one) is satisﬁed only if traders
make that happen via their trading decisions. In many applications there may be no
need for simultaneous trade in both securities. Instead a trader can bet on E (not-E) by
buying (selling, perhaps short-selling) only the E security.
For convenience of expression, one unit of the E security is described as “a share in
E” or simply as a “share.” All trades (buys and sells) in this security are expressed in
terms of buying or selling some given number of shares, and all prices quoted by the
MM are for a given parcel or number of shares. One share in E has value V at expiry.
Suppose that MM initiates the market by lodging a discretionary cash amount
B(B > 0) at given probability p (0 < p < 1). At any time before expiry, MM will
have sold some number of shares and bought some number of shares. Let the sum of
money proceeds (prices) received from buyers (i.e., from selling shares) equal Mb. This
is how much the buyers stand to lose to MM in the event of not-E. Now consider the
traders who have sold shares to MM. They stand to lose money amount Ms in the event
of E. This amount is equal to the number of shares they have sold MM (in total) minus
the sum of the prices of all those previous sales (in the event of E each share is worth
V = 1 and hence its seller loses one minus the price received on its sale). In effect,
the traders who have sold shares to MM have wagered a total of Ms on outcome E at
probability zero (see the numerical example above where trader i = 3 does the same
thing). The assumption here is that amount Ms is deposited with MM as security so
that sellers’ positions (i.e., short positions) are covered for the event they lose.
Under this regime the aggregate betting pool at any moment in the life of the security
is (B + Mb + Ms). The implied market probability of E is
q = B(p) + Mb(1) + Ms(0)
B + Mb + Ms
=
B(p) + Mb
B + Mb + Ms
.
(28.3)
The corresponding market probability of event not-E is
1 −q = 1 −B(p) + Mb
B + Mb + Ms
= B(1 −p) + Ms
B + Mb + Ms
.

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It is important to note that no mention has been made so far in this derivation of
what prices MM buys shares at or sells shares for. Rather the quantities Mb and Ms
are deﬁned as merely the aggregate money amounts collected from buyers and sellers
(respectively). Within these amounts it is typical that no two traders buy at the same
price, or sell at the same price, since the prices quoted by MM change with the level and
direction of preceding trade. The pricing mechanism by which this occurs is explained
below.
3.1 Ask Price for n Shares
If the Ask price for n shares is Askn, then the trader’s return in the case of E(V = 1)
from buying n shares is factor n = Askn. That is, by buying n shares for total price Askn
the trader ends up with share value n in the event of E (each share is worth V = 1)
and, therefore, a return of n = Askn. Note that returns are expressed as factors and that
the trader’s ending cash is the amount wagered or risked (here Askn) multiplied by that
factor.
The MM offers buyers a return of 1 = q in the event of E, where q is the market
probability of E after their trade. If the price paid for n shares is Askn, then the market
probability at that instant is
q =
Bp + (Mb + Askn)
B + Mb + Ms + Askn
.
Note that the price paid by the buyer Askn increases the total money amount received
by MM from selling shares.
Now, setting n/Askn = 1/q, gives
n
Askn
= B + Mb + Ms + Askn
Bp + (Mb + Askn) .
Solving this quadratic equation for Askn gives just one sensible solution,
1
2
+
n −B −Mb −Ms +
3
(n −B −Mb −Ms)2 + 4(Bnp + nMb)
,
.
(28.4)
For example, suppose that there have been no trades to date (implying that Mb =
Ms = 0) and that B = 100 and p = 0.5, then the Ask price for n = 1 [2] {10}(n = 100)
[[n = 1,000]] shares is from (28.4). Askn = 0.5025 [1.01] {5.249}(707.107) [[9524.94]]
or 0.503 [0.505] {0.525}(0.707) [[0.952]] per share.
The problem with these prices is that the trader will notice that to buy a parcel of n
shares it is cheaper to buy them one at a time or better still in tiny fractions of a share.
This can be seen as follows. Suppose the order is for n = 2. The ﬁrst share costs 0.5025.
The price of the second share is found by substituting Mb = 0.5025 in equation (28.4),
since this is how much MM collected from the ﬁrst share sold, and letting n = 1, giving

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prediction markets and political betting
an Ask price for the second single share of 0.5049 (note that Ms = 0 in this calculation,
since no money has been received from short sellers). The sum of these two prices is
1.007, whereas if they were bought in one parcel of n = 2, the price would have been
the higher amount of 1.01.
Suppose that a trader sets out to buy n shares. For each dollar the trader pays to MM
he or she drives up q a little bit more and hence the return factor that she will earn in
the event of E, that is, 1/q, gets smaller for each dollar spent. To encourage a rational
trader to take a larger n, and drive the instantaneous market probability q closer to that
trader’s personal probability of E, the MM allows traders to buy any order of n > 0
shares in arbitrarily small fractions of a share, thus minimizing the price paid for each
inﬁnitesimal fraction of a share and, therefore, maximizing overall expected return.
The MM Ask price for n = N shares is then
N
4
n=0

n −B −Mb −Ms +

(n −B −Mb −Ms)2 + 4(Bnp + nMb)

2n
δn
(28.5)
Hence, for the example immediately above, the theoretical Ask prices for n = 1{10}(n =
100) [n = 1000] shares, calculated by numerical integration, are 0.501 {0.512}(0.613)
{0.867}per share.
3.2 Bid Price for n Shares
If the Bid price for n shares is Bidn, then the trader’s return in the event of not-E (V = 0)
from selling n shares is n/(nBi −dn). By selling n shares (to the MM) for total price
Bidn, the trader risks a loss of (n −Bidn), which occurs in the event of E. To commit
to this transaction the trader deposits the full amount of the potential loss (n −Bidn)
with MM. In the event of not-E, the MM pays this deposit back plus amount n. The
trader is thus left with net gain of n −(n −Bidn) = Bidn, which is the agreed price of
the shares sold by the trader to MM.
The MM offers sellers a return of 1/(1 −q) in the event of not-E, where q is the
market probability of E given that trade
q =
Bp + Mb
B + Mb + Ms + (n −Bidn).
Now, setting n/(n −Bidn) = 1/(1 −q), gives
n −Bidn
n
= 1 −q
= B(1 −p) + Ms + (n −Bidn)
B + Mb + Ms + (n −Bidn) .

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Solving this quadratic equation for Bidn again gives just one sensible solution,
Bidn = 1
2
+
B + Mb + Ms + n −
3
(n + B + Mb + Ms)2 −4(Bnp + nMb)
,
.
The MM Bid price for n = N shares is then
N
4
n=0

B + Mb + Ms + n −

(n + B + Mb + Ms)2 −4(Bnp + nMb)

2n
δn.
(28.6)
Taking the same example as above, the theoretical Bid prices for n = 1 {10}(n =
100) [n = 1,000] shares, calculated from (28.6) by numerical integration are 0.499
{4:875}(38.701) [132.970] or 0.499 {0.488}(0.387) [0.133] per share.
4 Alternative Method of Computation
.............................................................................................................................................................................
Another way to calculate the prices found above proceeds as follows. First consider the
Ask price. The trader who buys shares is charged a “price” per inﬁnitesimal “unit” of
stock
Bp + Mb + M
B + Mb + Ms + M
that increases continuously with the money amount M spent to acquire those shares
(Mb and Ms are as deﬁned above). Note that this“price”function corresponds to (28.3)
and reacts to M in the same way as a conventional pari-mutuel market probability.
The unit average price paid over a total expenditure of amount M = m is then
a = 1
m
m
4
0
Bp + Mb + M
B + Mb + Ms + M δM
= 1
m
$
m −(B(1 −p) + Ms)

log(m + B + Mb + Ms) −log(B + Mb + Ms)
%
.
The number n of shares obtained by the trader who wagers (pays) total amount m is
therefore m/¯a. Thus
n =
m2
m −(B(1 −p) + Ms)

log(m + B + Mb + Ms) −log(B + Mb + Ms)
.
(28.7)
The Ask price m at which the trader can buy some chosen number n of shares is
then found by substituting that number n into (28.7) and then solving this equation
numerically to ﬁnd m. Note that m is the amount that the buyer risks losing by buying
n shares or, in other words, the full amount of his wager.

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prediction markets and political betting
In Mathematica, the best method to solve (28.7) is to use the FindRoot function,
starting the search at m = n/2 (which is a good guess since n shares are always
worth somewhere between 0 and n). This computation method leads to the same
Ask prices as found from (28.5). An advantage of (28.7) over (28.5) is that although
both equations require numerical solution, (28.7) does not involve numerical inte-
gration and is solved extremely quickly and accurately. When calculated from (28.7),
the Ask prices for an order of n = 1{10}(n = 100) [n = 1,000] shares (with B = 100,
p = 0.5, and Mb = Ms = 0 as assumed above) are 0.501 {0:512}(0:610) {0:869} per share.
Note the small discrepancies between the last two of these results and those found by
solving (28.5).
Now consider the matching approach to calculating the Bid price. The trader who
sells shares to MM obtains a “price” per inﬁnitesimal “unit” of stock
Bp + Mb
B + Mb + Ms + M ,
which decreases continuously with the money amount M wagered (risked) by selling
those shares (the terms Mb and Ms are again as deﬁned above).
The unit average price obtained over a total wager of amount M = m is then
b = 1
m
m
4
0
Bp + Mb
B + Mb + Ms + M δM
= 1
m
$
(Bp + Mb)

log(m + B + Mb + Ms) −log(B + Mb + Ms)
%
.
The amount m risked by the trader who sells shares to MM equals n(1 −b), that is
m = n(1 −b). Hence
m = n
+
(1 −1
m
$
(Bp + Mb)

log(m + B + Mb + Ms) −log(B + Mb + Ms)
%,
.
(28.8)
The Bid price (n −m) for some arbitrary number n shares is then found by substituting
that number n into (28.8) and solving this equation numerically for m. In Mathematica
the best method again is to use the FindRoot function initiating the search at m = n/2.
This computation method leads to the same Bid prices as found from (28.6), but as
for (28.7) the computation does not require numerical integration and is quicker and
more accurate. The Bid prices for an order of n = 1{10}(n = 100) [n = 1,000] shares
(with B = 100, p = 0.5, and Mb = Ms = 0 as assumed above), when calculated from
(28.8), are 0:499 {0.488}(0:390) {0.131} per share. Note again the small discrepancies
between the last two of these results and those found using (28.6).

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5 Illustrated Example
.............................................................................................................................................................................
Suppose that MM initiates the market with B = 5 and a probability estimate p = 0 : 3.
Suppose also that the money amounts received so far from traders are Mb = 25 and
Ms = 5. The weight of money received from buyers rather than sellers suggests that
the market believes that the probability of E is higher than p = 0.3. Indeed the current
instantaneous probability of event E is
q =
Bp + Mb
B + Mb + Ms
= 5(0.3) + 25
5 + 25 + 5 = 0.757.
The current bid and ask price schedules offered by the MM for any order size up to n =
200 shares are as shown in ﬁgure 28.1 (cf. ﬁgure 28.2). These prices are found by solving
(28.5) and (28.6) or,alternatively,(28.7) and (28.8). Note that prices behave consistently
with the Glosten and Milgrom (1985) and Easley and O’Hara (1987) explanation of
the bid-ask spread. Speciﬁcally, a buy (sell) order increases (decreases) the market
probability of E, and this price change is more pronounced the larger the order size.
Note also that as the accumulated value Mb +Ms of preceding trade increases the spread
becomes narrower, promoting still further volume and further narrowing of the spread.
For example, in the case of B = 1 and p = 0.3, suppose now that Mb = 250 and Ms = 50.
0
0.0
0.2
0.4
0.6
0.8
1.0
Price Per Share
50
100
150
200
Order Size
Ask
Bid
figure 28.1 Bid and ask prices for orders of given size with B = 5, p = 0 : 3, Mb = 25 and Ms = 5

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prediction markets and political betting
0
0.0
0.2
0.4
0.6
0.8
1.0
Price Per Share
50
100
150
200
Order Size
Ask
Bid
figure 28.2 Bid and ask prices for orders of given size with B = 1, p = 0.3, Mb = 250 and
Ms = 50
The current market probability then is
q =
Bp + Mb
B + Mb + Ms
= 5(0.3) + 250
5 + 250 + 50 = 0.825.
The corresponding bid and ask price schedules are as shown in ﬁgure 28.2.
6 Market Properties
.............................................................................................................................................................................
The MM described here has one main advantage over the Hanson market maker and
one clear disadvantage. Its advantage is that the MM can set the opening share price
at any probability p rather than at 0.5, which is the Hanson requirement for binary
assets. Its most obvious disadvantage is that the potential or worst-case MM loss,
accruing over any future sequence of trade, is not limited to a mathematically known
quantity. By comparison, the Hanson market maker can lose at most, over any arbi-
trary trade sequence, a known factor of B, speciﬁcally B log(2) in the case of a binary
security.
MM allows traders to buy and sell shares at given prices, which in effect allows them
to make ﬁxed-odds bets. For example, if a trader buys n = 10 shares for 5.12, then the
implicit odds are 5.12 to 4.88 in favor of V = 1, since the bet of amount 5.12 will return
a total of 10 if it wins (if V = 1).
Unlike each of the individual traders, MM does not know how much money will be
won or lost by the end of trading when all bets have been made and settled. The amount

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of possible proﬁt or loss to MM can be calculated at any time during trading based on
what bets have been taken already, but not until all trades have taken place can the MM
calculate how much will be won or lost conditional on V . Maximum losses depend,
that is, on the trades that are yet to occur and which cannot be predicted.
Potential losses are generally tempered, however, by the way that prices react to
order size. For example, if there is a strong wave of buying the automated price per
share quickly goes toward one, and hence the possible losses on the recently sold shares
approach zero per share (meaning that the possible gains approach one). The biggest
losses occur on those shares that are bought from MM at prices near zero or sold to
MM for prices near one. These prices can exist only under conditions that in and of
themselves tend to constrain losses. Speciﬁcally, the Ask price might be near zero only
if there is little trade from buyers or if there is much trade with sellers, implying the
possibility of small losses (in the event of V = 1) at worst. Similarly, the Bid price can
be near one only when there is little trade with sellers or when there is much trade
with buyers, implying again only small losses in the event of V = 0, at worst. The other
important limiting factor is that trade volume may not be so disproportionate in either
direction that prices ever get near zero or one, particularly in applications where the
common perception is that E has probability nowhere near zero or one (i.e., there is no
near certainty about whether E will occur or not).
The ultimate MM safeguard is of course to close off trading in one direction if
trading has been too heavily in that direction and potential losses have climbed beyond
a tolerable level. This happens sometimes in betting markets but is far from desirable,
as it defeats the purpose of an automated market maker, namely, to provide liquidity
and allow a trader to either buy or sell at all times. It also prevents full“price discovery,”
since the market probability is not allowed to move to the point that traders want to
take it.
7 Markets with Known Maximum Loss
.............................................................................................................................................................................
The MM described next is a variant MM∗of the one above, modiﬁed to have predictable
maximum possible loss without contemplating any need for a market shut down. To
meet this requirement the modiﬁed MM prices trades so that all trades preceding the
current trade are covered and the market makers’ only exposure is to the last trader.
The method is explained in the following example. Let B = 100 and p = 0.5. Suppose
that the ﬁrst trade executed by MM∗was for x shares at total price C, where negative
x represents a sale of shares by MM giving positive C and positive x represents a
purchase by MM∗giving negative C. The modiﬁed MM∗requires each new trader to
inherit MM∗’s position (x, C) existing after the last trade and then to make whatever
incremental trade is required to reach the desired net inventory purchase or sale.
Assume that the ﬁrst trade is a sale of 30 units, and hence MM∗’s position after this
trade is (x, C) = (−30, 16.0912). The sale price of 16.0912 (0.536 per unit) is found

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prediction markets and political betting
from the ask price equation (28.7) with Mb = Ms = 0. The second trader assumes
a trading account of −30 shares and cash of 16.0912 and hence takes over MM∗’s
position resulting from the previous trade. Suppose that the second trader wants to sell
50 shares. The trader must now sell just 20 shares to MM since he or she starts with −30
(inherited from MM∗). The price for these shares is found by substituting n = 20 in
the bid price equation (28.8). It is important to note that Mb and Ms are again (always)
set at zero, since the net effect of previous trade by MM∗is passed on to the current
trader. The total price received by the second trader is therefore 9.50949 (calculated
from (28.8) with n = 20) plus the cash balance of 16.0912 inherited from MM∗. Thus
the net price received from MM for 50 units is 25:6007 (0.512 per unit).
The MM∗’s position after the second trade is (x, C) = (20, −9.50949). Suppose
now that the third trader arrives and wants to buy 100 units. This trader must ﬁrst
take on the MM∗’s position of (x, C) = (20, −9.50949). To achieve a net inventory
position of 100, this trader must buy just 80 more units. The price of these is 47.2402,
found by solving (28.7) with n = 80 and Mb = Ms = 0. In effect, the trader ends
up paying a total of 47.2402 + 9.50949 = 56.7497 for a net purchase of 100 units
(0.5675 per unit).
In general, the modiﬁed MM logic is as follows. A trader who wants to take a position
of y units (where y can be negative) inherits x units from MM∗and then buys another
y −x units from MM∗. Implicitly, if y −x is negative, then the trader in fact sells
−(y −x) units to MM∗. Upon completion of this trade, the change in the trader’s cash
position is −A + C, where A is the price of the units bought from MM (when units
were in fact sold to MM, A is negative).
The results of the example calculations outlined above are summarized in table 28.2
along with results for a further arbitrary sequence of trades. Table 28.2 gives the unit
price for each trade alongside the corresponding price found using the Hanson market
maker (see Pennock 2006 for details of how to calculate the Hanson prices). The two
automated market maker prices are comparable only because we have assumed that
MM∗sets p = 0.5, as is implicit for Hanson. The two unit prices are quite similar in all
trades, with the proviso that MM∗reacts more slowly than the Hanson price to volume
(albeit in the same direction of course). This presents no clear advantage either way. By
reacting less sharply to orders, MM is “more liquid” than Hanson (with the same B),
and by reacting more quickly the Hanson market maker puts a tighter constraint on
maximum possible losses.
To visualize the difference between the MM∗and Hanson prices, consider the plots
in ﬁgures 28.3 and 28.4 of the bid and ask prices existing at the instant that trade 5
(in table 28.2) takes place. Note that the instantaneous prices (probabilities) at that
moment are slightly different, as a result of different “interpretations” of the preceding
trades, and that the Hanson prices approach zero and one a little more sharply with
order size.
By approaching probability limits less quickly than Hanson, MM∗risks exacerbating
losses, since traders can acquire higher volumes before prices become prohibitive.
MM∗is designed so that all trades executed before the last trade are self-ﬁnancing.

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Table 28.2 Example Unit Prices for Trades in Sequence Assuming B = 100 and
p = 0.5
Trader
MM Price
Hanson Price
(x, C) after Trade
1
Buys 30
0.536
0.537
(−30, 16.0912)
2
Sells 50
0.512
0.512
(20, −9.509)
3
Buys 100
0.568
0.572
(−80, 47.2402)
4
Buys 50
0.708
0.740
(−130, 82.6199)
5
Buys 50
0.768
0.824
(−180, 121.02)
6
Sells 100
0.738
0.782
(−80, 47.2402)
7
Buys 20
0.686
0.711
(−100, 60.9591)
8
Buys 400
0.846
0.923
(−500, 399.325)
9
Buys 1000
0.952
0.999
(−1500, 1351.55)
10
Sells 1500
0.901
0.954
(0, 0)
0
0.0
0.2
0.4
0.6
0.8
1.0
MM Share Price
200
400
600
800
1000
Order Size
Ask
Bid
figure 28.3 MM∗bid and ask prices for orders of given size with B = 100, p = 0.5
0
0.0
0.2
0.4
0.6
0.8
1.0
Hanson Share Price
200
400
600
800
1000
Order Size
Ask
Bid
figure 28.4 Hanson bid and ask prices for orders of given size with B = 100, p = 0.5

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prediction markets and political betting
Speciﬁcally, each new trader takes the position held by MM∗after the preceding trade
and then makes an incremental trade against MM∗to achieve the intended position.
That incremental trade is the only source of possible loss to MM∗.
The incremental trade is priced using (28.7) or (28.8), depending on whether the
trader buys or sells (with Mb = Ms = 0). This ﬁnal trade gives rise to a maximum
possiblelossthatincreaseswithordersize,albeitatadecreasingrateastheinstantaneous
market probability is pushed toward one or zero. Figure 28.5 shows the maximum
possible loss for MM∗under the assumptions of B = 100 and p = 0.3. Mathematically
the possible MM∗loss when the last trader’s incremental trade is a purchase of n shares
at average price ¯a for total amount M = m equals
n(1 −a) = m
a (1 −a)
= m(1/a −1), where a = 1
m
m
4
0
Bp + M
B + M δM
= m2/
$
m −(1 −p)

log(B + m) −log(B)
%
−1.
(28.9)
The instantaneous probability implied by this incremental trade is
q = Bp + m
B + m .
(28.10)
Solving (28.9) and (28.10) so as to eliminate m yields a unique solution for the
maximum possible loss as a function of B, p and q.
B

(p −q)(1 −p)log[(1 −q)/(1 −p)]
(1 −q)(1 −p log[(1 −q)/(1 −p)] −(p −q)

.
(28.11)
Now consider the maximum possible MM∗loss when the last trader’s incremental trade
is a sale of n shares to MM∗at average price ¯b. In this case the amount M = m wagered
(risked) by the trader equals n(1−¯b), implying that n = m/(1−¯b). Hence the amount
that MM∗can possibly lose is
nb = mb/(1 −b), where b = 1
m
m
4
0
Bp + M
B + M δM
=
mBp

log(B + m) −log(B)

m −mBp

log(B + m) −log(B)
.
(28.12)
The associated implicit instantaneous probability is
q =
Bp
B + m.
(28.13)

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Solving (28.12) and (28.13) simultaneously to eliminate m gives the following unique
result for the maximum possible MM∗loss as a function of q:
B

p(q −p)log

p/q

q −p + pq log

p/q


.
(28.14)
Figure 28.5 shows a plot of the maximum possible MM∗loss as a function of q, with
B = 100 and p = 0 : 3. The two segments of this function are (28.11) for q > 0 : 3
(when the trader buys) and (28.14) for q < 0 : 3 (when the trader sells). Here q is the
instantaneous probability implied by the incremental trade made by the last trader.
Note that it is quite possible that MM∗can lose a multiple of B, especially if the
ﬁnal trader’s assessment of the probability of E is very high, encouraging the trader to
buy shares up to a price somewhere near one. Strictly, the feasible MM∗loss is inﬁnite
because there is no limit to how many shares might be bought at prices approaching (but
never reaching) one or sold at prices approaching zero. In most practical applications it
is unlikely if not unthinkable that the incremental trade will be so large that the implied
q is higher than say 0.99 or lower than 0.01 This level of certainty will rarely arise
naturally in any commercial context, and subjective probability assessments close to
theMM’spriorp willoftenbefarmorerealistic. Lossesarelimitedinsuchcircumstances
to a small factor of B. Such losses are possibly warranted economically on the grounds
that traders bring forward opinions and information to the market in exchange for the
MM risking such a loss. In real-money experimental markets the experimenter can x
parameter B so that the maximum plausible loss as a factor of B is not beyond the funds
available for the experiment.
Note that although the possible loss under MM∗is a larger factor of B than under
Hanson, B can be set at a lower amount under MM because the market price under
MM∗is slower in reacting to trades than under Hanson (for a given B). By setting
0.0
0
100
200
300
400
Maximum Loss
0.2
0.4
0.6
0.8
1.0G
figure 28.5 Maximum market maker loss as a function of q assuming B = 100, p = 0.3

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prediction markets and political betting
B lower, this price reaction can be made to closely approximate the Hanson prices
and lead to typically very similar market maker losses (or gains) after a given set of
trades. The problem of how to choose an appropriate value of B has been made very
clear by Chen and Pennock (2010) and is virtually the same problem for MM∗as for
Hanson.
8 Conclusion
.............................................................................................................................................................................
In some market applications the MM may not be prepared to risk accruing losses. There
are two ways to think about this. The ﬁrst is that in most prediction markets contexts
the potential for the MM to lose is justiﬁed by the information obtained from traders
through operating the market. Based on this view, losses are good because they are
repaid with information and tend to attract traders (especially inside traders) to play
and, thus, to impart greater information. The second outlook, applicable in contexts
where a MM wants to proﬁt in aggregate or on average from all the trade attracted, is
that a commission can be charged to all trades, or even just to winning trades, so as to
tip the balance such that the MM is generally (if not always) proﬁtable. Much thought
has been directed toward resolving this issue by those involved in prediction market
design. See, for example, the recent discussions by Othman et al. (2010) and Chen and
Pennock (2010).
References
Agrawal, Shipra, Erick Delage, Mark Peters, Zizhuo Wang, and Yinyu Ye. 2011. A Uniﬁed
framework for prediction market design. Operations Research 59(3):550–568.
Berg, Joyce E., Forrest D. Nelson, and Thomas A. Rietz. 2008. Prediction market accuracy in
the long run. International Journal of Forecasting 24(2):285–300.
Chen, Yiling, and David M. Pennock. 2010. Designing markets for prediction. AI Magazine
31(4):42–52.
Chen, Yiling, Chao-Hsien Chu, Tracy Mullen, and David M. Pennock. 2005. Information
markets vs. opinion pools: An empirical comparison. Proceedings of the 6th ACM Conference
on Electronic Commerce. New York: ACM, 58–67.
Easley, David, and Maureen O’Hara. 1987. Price, trade size, and information in securities
markets. Journal of Financial Economics 19(1):69–90.
Glosten, Lawrence R., and Paul R. Milgrom. 1985. Bid, ask and transaction prices in a
specialist market with heterogeneously informed traders. Journal of Financial Economics
14(1):71–100.
Hanson, Robin. 2003. Combinatorial information market design. Information Systems
Frontiers 5(1):107–119.
——. 2007. Logarithmic market scoring rules for modular combinatorial information
aggregation. Journal of Prediction Markets 1(1):3–15.

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## Page 580

a simple automated market maker for prediction markets
559
Othman, Abraham, Tuomas Sandholm, David M. Pennock, and Daniel M. Reeves. 2010.
A practical liquidity-sensitive automated market maker. In Proceedings of the 11th ACM
Conference on Electronic Commerce. New York: ACM, 377–386.
Pennock,
David M. 2006.
Implementing Hanson’s market maker.
Oddhead blog;
http://blog.oddhead.com/2006/10/30/implementing-hansons-market-maker.
Pennock, David M., Steve Lawrence, C. Lee Giles, and Finn Årup Nielsen. 2001. The real
power of artiﬁcial markets. Science 291(5506):987–988.
Wolfers, Justin, and Eric Zitzewitz. 2004. Prediction markets. Journal of Economic Perspectives
18(2):107–126.

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chapter 29
........................................................................................................
THE LONG HISTORY OF
POLITICAL BETTING MARKETS:
AN INTERNATIONAL PERSPECTIVE
........................................................................................................
paul w. rhode and koleman strumpf
Election betting markets have been growing in popularity. These markets are chieﬂy
an Internet phenomenon, leveraging the ability of a large number of participants to
quickly and cheaply place wagers on the outcome of upcoming elections. The ﬁrst
such market, the Iowa Political Stock Market, was founded in 1988 and involved a few
hundred traders playing for modest stakes. More recent incarnations,most prominently
Intrade and Betfair, have thousands of traders making millions of dollars in wagers.
There is strong evidence that prices in these markets provide accurate forecasts of
election outcomes.1
The prominence of Internet election markets often obscures the long history of such
markets. While it is often claimed that election markets are a recent phenomenon, we
have previously documented that wagering on presidential elections has occurred in
the United States for over a century.2 In this chapter we demonstrate that such markets
are even older and that betting on elections has occurred for hundreds of years in many
Western countries. The twentieth century is distinguished less by the creation of betting
markets than by their absence in the middle of the century.
This chapter discusses the historical evolution of the legality and microstructure
of political betting markets in several countries. The structure, operation, and public
prominence of these markets reﬂect the prevailing culture and electoral institutions.
Betting focused on the most important political outcomes of the time: the choice of
government ofﬁcials in Italian city-states during the sixteenth and seventeenth cen-
turies, papal selection in sixteenth-century Italy, the timing and winning party of
parliamentary elections in eighteenth- and nineteenth-century Britain, the outcomes
of local and national elections in nineteenth-century Canada, and presidential and con-
gressional winners in the nineteenth- and early-twentieth-century United States. There
were also markets on other political events, such as the outcome of no-conﬁdence

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the long history of political betting markets
561
votes, the tenure of leaders and their successors, or the outcome of foreign/military
ventures.3
While there were important differences across countries, several similarities emerge.
First, pivotal elections energized these markets. Not only would important contests
lead to greater betting activity (such as the 1916 U.S. election or the 1948 Italian
race), they could even lead the markets to reemerge from extended dormancies (as
with the 1964 contest in Britain). Alternatively, there was far less betting in peri-
ods of political apathy or one-party rule (such as in the 1930s and 1940s when the
Fianna Fáil party dominated the government of the Irish Free State and the Republic of
Ireland). Second, while newspapers were often uncomfortable reporting on domes-
tic markets, they were less averse to printing stories on political markets abroad.
This likely reﬂects the moral uncertainty surrounding election betting. Third, there
was a general parallel between Britain and the United States in terms of a rapidly
changing but generally unfavorable legal environment, and in both countries public
election betting virtually disappeared around the start of World War II. The conclusion
draws additional parallels and suggests how further research can build on the histories
presented here.
It is important to note a potential limitation. Largely due to language issues our
analysis is centered on Anglophone countries. (It might also be useful to point out
that our analysis is restricted also to countries that have real elections (i.e., unlike the
sham elections in communist/totalitarian countries). This might not be signiﬁcant
problem since political betting markets require at a minimum some form of popular
vote and typically an independent media source to report the resulting prices. In the
pre-twentieth-century period we focus on, these conditions were primarily found in
the English-speaking world. Still we return to this issue in the conclusion.
1 Early Markets: Italian City States
and the Vatican
.............................................................................................................................................................................
In Italy there were historical markets on both civic elections and the papacy. Betting
was common in the Italian city-states in the early modern period, 1500–1700.4 In
addition to voting, selection to public ofﬁce often included intentional randomization,
for example, drawing lots to name the nominators or candidates. In Venice and Genoa
gambling on the outcome of such contests was popular. D. R. Bellhouse has suggested
that the Genoese lottery, one of the ﬁrst modern numbers games, originated with
betting on the drawing of lots—pulling balls associated with speciﬁc candidates from
an urn.5 Political betting continued into Italy’s recent history, including, at times, as
part of its national lotto (established in 1863). As an example, in the pivotal 1948
election the state-run lottery experimented with a betting pool on the composition of
parliament.

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562
prediction markets and political betting
Gamblers have also long wagered on the selection to ofﬁces in the Catholic Church.
Quotes of betting odds on papal succession appear as early as 1503, when such wagering
was already considered “an old practice.”6 During the troubled papal conclave of 1549
the Venetian ambassador Matteo Dandolo observed that the Roman “merchants are
very well informed about the state of the poll, and ... the cardinals’ attendants in
Conclave go partners with them in wagers, which thus causes many tens of thousands
of crowns to change hands.”7 Odds were offered not only on which candidate among
the“papabile”would win but also on when the conclave would end. About two months
into this long and conﬂict-ﬁlled process, the market odds were 10 to 1 (implying a
probability of approximately 9%) that this conclave would never elect a pope. Aversion
to such activities eventually led Pope Gregory XIV, in March 1591, to ban on pain of
excommunication all betting on the outcome of papal elections, the length of the papal
reign, or the creation of cardinals.
Gregory XIV’s threat pushed wagering over papal succession underground, but at
times it resurfaced. As a 1878 New York Times article noted,“The deaths and advents of
the Popes has always given rise to an excessive amount of gambling in the lottery, and
today the people of Italy are in a state of excitement that is indescribable. Figures are
picked out which have some relation with the life or death of Pius IX. Every day large
sums are paid for tickets in the lottery about to be drawn.”8 Betting over the successor
to Leo XIII in 1903 and to Benedict XV in 1922 attracted considerable press attention.9
With the recent rise of Internet betting markets, betting on the new pope could again
occur in public on a large scale.
2 Election Betting in Britain
.............................................................................................................................................................................
2.1 Eighteenth and Nineteenth Centuries
Political betting also has a long history in Great Britain. As one prominent example,
Charles James Fox, the late-eighteenth-century Whig statesman, was known as an
inveterate gambler. His biographer, George Otto Trevelyan, noted that “(f)or ten years,
from 1771 onwards, Charles Fox betted frequently, largely, and judiciously, on the
social and political occurrences of the time.”10 His wagers recorded in the betting book
of the Brooks’ Club included whether the Tea Act would be repealed, how long Lord
North’s minister would last, or on other events related to the coming of the American
Revolution. Newspapers in the 1760s, 1770s, and 1780s are ﬁlled with brief notes about
public betting in London over events in the life of JohnWilkes, the fate of the StampAct,
and the other political outcomes.11 Wagering took place at gentleman’s clubs—such as
Almack’s, Boodle’s, Brooks’, and White’s—and in the colleges of leading Universities—
such as All Souls and Magdalen Colleges at Oxford and Gonville and Caius College at
Cambridge—as well as in less elite public coffeehouses—including Lloyds. Such activity

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the long history of political betting markets
563
was considered in keeping with national tradition: “As far back as the reign of William
the Third, foreigners had observed that, on matters great and small, the only sure test of
English opinions was the state of the odds.”12 A common phrase was“Bet or be silent.”13
Wagering was generally legal under British common law so long as it did not to lead
to immortality or impolity.14 Bets about the outcome of events in war, over the death
of political leaders, over court cases, or between voters over election results were illegal
on these grounds.15 In the Victorian and Edwardian periods the British government
increasingly attempted to limit gambling, especially among the working classes. The
Gaming Act of 1845 made gambling contracts and debts unenforceable in court (but
otherwise liberalized what amounts could be wagered); the Betting Houses Act of 1853
outlawed the operation of betting establishments other than private clubs; the Betting
Houses Act of 1874 cracked down of the advertisement of wagering; and the Street
Betting Act of 1906 made acceptance of wagers in streets and public places illegal.16
Despite legal uncertainty in the late nineteenth and early twentieth centuries, the Fleet
Street press reported on election wagering at the London Stock Exchange and at Lloyd’s
in markets for parliamentary “majorities.”17
2.2 Early Twentieth Century
Election betting grew in popularity with the adoption of spread betting. In this system
bets are based not simply on the winner of the election but the size of the margin (spread
betting is common in political, sports, and ﬁnancial markets in twenty-ﬁrst-century
England).
Laura Beers provides a fascinating account of the evolution of the parliamentary
“majorities” market in the British Stock Exchange between 1910 and 1940 (a small
spread market also existed in 1906).18 The market differed from the American examples
(see below) because wagers were placed not chieﬂy on which party would win but on the
size of their parliamentary majority. That is, the buyer and seller agreed on a threshold
(or “seat price”) for the number of seats won and an amount to be paid for each seat
difference between this threshold and the actual majority. For example, if the threshold
is 15, the actual majority is 20, and the amount per seat is £5, then seller pays the buyer
(20–15)∗£5 = £25. The focus on “majorities” reﬂected the standard vocabulary of
British political analysis.19 No cash was initially fronted, and the “debts of honor” were
settled after election day. Newspapers would report the buying and selling prices—the
gap was commonly 10 seats—but not the names of the participants. Lloyd’s of London
also offered insurance on the election outcome.20
Table 29.1 summarizes the election markets and the actual outcomes between 1910
and 1935. The ﬁrst market to gain substantial attention off the trading ﬂoor occurred
in the run-up to the December 1910 election. Price quotes appeared in the ﬁnancial
press on nearly a daily basis. The starting and ending values of the prices were very
close to the actual outcome, though there was substantial divergence in the middle of
the contest.21 There is little information about the operation of “market for majorities”

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prediction markets and political betting
Table 29.1 Spread Bets on pre-WW2 British Parliamentary Elections
Dec.1910
1922
1923
1924
1929
1931
1935
A. Final Prices
Conservative
272
Liberal
97
Labor
100
182.5
245
Coalition Majority
130
Conservative
Majority
34
(Nat. Gov’t)
Majority
204
169
B. Election
Outcomes
Conservative
271
344
258
412
290
473
386
(Nat. Gov’t)
-556
-430
Liberal
272
62
158
40
59
33
21
Labor
42
142
191
151
287
53
154
Other
85
65
8
12
9
59
55
Actual Majority
122
−99
503
243
Prices: listed values are mid-points in the bid-ask spread; values correspond to seat totals except in
rows where majority is indicated
Election Outcome: Actual Majority corresponds to the party or coalition for which there was a Majority
price listed in the top of the table
for the elections of December 1918 and November 1922,22 but the market on the
December 1923 election was apparently the largest to date, with over £100,000 changing
hands. (This is the equivalent of $6.1 million in 2010 purchasing power as measured
by consumer prices.)23 The market price indicated that the Conservatives would hold a
small majority. But the vote yielded a hung parliament with the Conservatives winning
more seats than any other single party but effectively a minority relative to the whole.
This outcome resulted in large losses for bettors taking the Conservative side and
considerable squabbling over the nature of the betting contract. Speciﬁcally, some who
bought the Tory side of a Conservative majority bet argued that their liability was
limited when the majority reached zero. But they were made to cover the entire deﬁcit.
Over the next two elections brokers shifted to bet on the number of party seats won
and not on the size of majorities.24 Since bettors continue to be able to set the size of
their per-seat wager, seat totals are also a version of spread bets.
The political situation remained unstable, and a new election was called for October
1924. Labour, which was in power, was initially expected to expand its majority. But
the campaign featuring “Red Scare” tactics by the right-wing press led to the shift
against Labour—a decline in support far beyond what the market anticipated—and a
Conservative landslide. The next contest did not occur until May 1929. And for the

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the long history of political betting markets
565
ﬁrst time the popular press covered the election market intensively. Both the Daily
Express and the Daily Mail regularly published stock market spreads. The betting
market generally favored the Conservatives, though price ﬂuctuated signiﬁcantly. One
source of uncertainty was the extension of suffrage to women under the age of 30. In
the popular voting the Conservatives narrowly outpolled Labour; the Liberals ﬁnished
in a strong third position. However, Labour won the most seats in the hung Parliament,
and its leader, Ramsay McDonald, emerged as prime minister.25
Labour’s victory was again short-lived, as splits within the ruling coalition over
responses to the Great Depression led to the call for a new election for October 27, 1931.
(Recall that Britain left the gold standard in late September 1931.) The fragmentation of
the Labour and Liberal parties and the creation of the National Government coalition
with the Conservative party at its core led to the reemergence of a market in majorities.
The market highly favored the prospects of National Government, but it did not go
far enough, as Labour shed over 200 seats. The rise in the price for the National
Government majority was said to help revive British ﬁnancial markets. As examples,
in late October 1931 the ﬁnancial section of the Daily Express carried such headlines
as “Markets More Conﬁdent on Majorities Rise” and “Foreign Money Comes Back as
Majorities Rise.”26 The election betting market was very active, with “Over a Million
(Pounds Sterling) Won and Lost in the City”in 1931 (this is equivalent to $72.9 million
in 2010 dollars). “Nothing like it has been known before.”27
The market’s shortcoming in the 1931 race created signiﬁcant problems. Because the
market signiﬁcantly underestimated the number of seats that the National Government
would win,28 the losses to those who bet against them were great. One prominent
broker, W. A. Bignell, refused to honor his bet with another, Gower W. Elias. This led
to a lawsuit, wherein Justice McCardle voided the contract under the Gaming Act of
1845.29 In response to growing concerns that the now highly visible majorities market
tainted it as a gambling institution, the Stock Exchange formally cracked down on
election betting.30
Betting activity on the next election (November 1935) centered on the large London
bookmakers, such as Ladbrokes and Seaham, rather than on the Stock Exchange. The
prices on majorities continued to appear in the daily press but off the front page. Again
the market favored the National Government but by too little. This did not totally end
such betting in the city. There were still reports of action on the “black bourse,”31 and
in the autumn of 1940, during the battle for Britain, London brokers among others ran
organized betting sweepstakes regarding how many German planes would be shot down
each night. The winnings were used to fund the construction of Spitﬁre ﬁghters.32
As table 29.1 indicates, spread betting was quite accurate in forecasting early elections
but became increasingly less accurate. Beers suggests this has to do with a new set of
factors shaping the vote outcome. While the 1910 contest largely involved only the
Conservatives and Liberals, in the 1920s and 1930s the Fourth and Fifth Reform Acts
substantially expanded suffrage, the Labour Party rose to prominence, and the Liberal
Party began to splinter. The wealthy, male London-based investors who bet on the Stock
Exchange lost touch with an electorate comprised of women and working-class voters.

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prediction markets and political betting
In1929theDailyExpress musedthat“Londonhasneverbeenfamousforknowingmuch
about British politics, and the Stock Exchange has been rather notorious for knowing
even less than the rest of London.”33 While absolute accuracy declined, this seemed
largely due to increasingly difﬁcult political contests in which to forecast. It is important
to note that the markets still outperformed the other available forecasts from pundits,
big bettors,and straw polls (scientiﬁc polls did not yet exist,making the market forecasts
that much more impressive). As Beers writes, the Stock Exchange predictions “appear
to be no worse, and usually slightly better, indicators” than forecasts based on polling
or expert opinion. Spread bets also must forecast a more challenging outcome than
traditional binary wagers: while the seat totals were faulty, the markets still managed to
correctly predict the winning party or coalition in all but one election. In Beers’s words,
“predicting electoral outcomes in three-party ﬁrst-past-the-post political systems is a
notoriously tricky business.”34
2.3 Postwar Twentieth Century: Decline and Rise
In the immediate post–World War II period public election betting in Britain appears
to have slowed to a trickle. Newspapers offer only a handful of quotes regarding the
1945 and 1950 contests.35 And in 1950 the Economist observed: “It is curious that in
a nation devoted to gambling as the British, so little opportunity should nowadays be
taken of a general election, the most sporting of all events.”36 This situation changed
with time.
The modern era of open, large-scale political betting in Britain began in October
1963.37 Following Harold Macmillan’s surprise resignation as prime minister after the
Profumo affair, the gambling house Ladbroke’s overcame the“long-standing reluctance
to make book on political events” by taking bets on his successor as leader of the Con-
servative party.38 Prior to 1963 Ladbroke’s had handled the political betting demands
of its more gentlemanly clientele in a private election book.39 In 1964 William Hill,
the country’s largest bookmaker, also “quickly reversed its earlier policy not to han-
dle election betting.”40 By the end of that year, political betting totaled an estimated
£1,000,000 (the equivalent of about $23 million in 2010 dollars.) About nine-tenths
of this sum was placed on British contests, including the Wilson–Heath general elec-
tion, and about one-tenth was placed on the 1964 American presidential race. Political
markets represented less than 2 percent of national gambling turnover.
Several features of the modern political markets’ microstructure were notable: the
stakes were anonymously wagered; much of the activities focused on party odds rather
than the “majorities” common in the Stock Exchange period;41 house proﬁt rates ini-
tially averaged about 7 percent (taking in £107 for every £100 it paid out);42 and
professional bookmakers set the ﬁxed lines rather than accept bets in the form of pools.
This last feature mattered at times when, for example, Mr. Hill set a line too favorable
to a candidate he supported.43 Odds makers such as Ron Pollard of Ladbrokes became
celebrities, providing color analysis on election night television news.44 In 1965 London

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the long history of political betting markets
567
bookmakers began offering odds on the German election contests. And in early 1966,
with new general elections in Britain, they handled over £2,100,000 (about $44.5 mil-
lion in 2010 dollars). This was purportedly the largest total ever taken on a single
event.45 British markets also opened on American elections, a good 30 years prior
to the return of a legal election market in the United States. It was estimated that
$100 million exchanged hands ($1,540 million in 2010 dollars) following the 1972
presidential election.46 Despite complaints about the immorality of such wagering, the
British betting public never looked back.47
3 Election Betting in Former British
Possessions and Colonies
.............................................................................................................................................................................
Similar bouts of political betting occurred in many of the British offshoots with par-
liamentary forms of government throughout the late nineteenth and early twentieth
centuries. In countries including Australia, New Zealand, Canada, Singapore, South
Africa, and the Republic of Ireland, local bookmakers and members of the stock
exchanges periodically wagered over the outcome of no conﬁdence votes, the tim-
ing of the elections, and the composition of the new majority. In the remainder of the
section the betting markets in several of these countries are discussed in more detail.48
Ireland has had political betting markets as long as the United Kingdom. In the
eighteenth century these were primarily person-to-person bets and formal markets did
not exist. Prior to the Union of Great Britain and Ireland in 1801, the wagers tended to
focusonpoliticaleventsoutsideof Ireland,suchastheoddsontheAmericanRevolution
ending, whether peace would be declared in the Anglo-Dutch War, or the election of
the king of Poland.49 There also were several bets reported on elections for the British
Parliament.50 Similar person-to-person wagers continued in the 30 years following the
Union, with one addition that there were also bets on acts of Parliament related to
Ireland.51 There are no reports of betting markets starting in 1830 and continuing for
the next one hundred years. It is unclear whether this is due to an absence of such bets
or a censoring of newspaper articles due to the conservative mores of the Victorian era.
One exception is that there was some coverage of Canadian elections in the 1890s and
1910s and of U.S. election markets in the late 1890s and early 1900s.52 There were also
nonmonetary wagers at this time, though apparently not at the scale or intensity of
those in the United States, which are discussed later.53 Betting seems to have returned
during the 1920s and 1930s, with both bookmaker and person-to-person wagers on
Irish elections as well as coverage of U.K. parliamentary elections in which insurance
companies played a role in setting odds and offering policies.54 Following the creation
of the State of Ireland in 1937, there was some mention of election betting for both
the ceremonial president as well as Parliament.55 Political bets continued to grow in
prominence with one Member of Parliament even serving as a bookmaker.56 Wagers

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prediction markets and political betting
on both domestic and international elections were deﬁnitely present at the time of their
revival in the United Kingdom in the 1960s.57 The markets have continued to grow, up
to the present day.
Election betting in Australia has existed at least since the 1940s (there were also
occasional mentions of informal person-to-person betting dating back to before after
the establishment of the Commonwealth of Australia in 1901).58 The greatest activity
appeared to be in such major cities as Canberra, Melbourne, and Sydney, where book-
makers as well as sporting clubs posted odds on both state and federal elections.59 Such
betting was reduced, as was newspaper coverage of them, since election wagers were
illegal, with ﬁnes set by the Federal Electoral Act.60 Despite this law, newspaper articles
listed bet amounts and broad descriptions of individual bettors (including an unnamed
senior cabinet minister).61 While most bets involved modest stakes, some bettors in the
1949 federal election had stakes of £4,000 or $151,000 in 2010 dollars (The 1949 election
marked the departure of the Labor Party, which would not return to ofﬁce for more than
20 years). Election betting odds from other countries also were reported as a means of
handicapping their races. There were reports on U.S. presidential betting odds starting
in the late 1890s and continuing through the 1940s and also on U.K. parliamentary
betting odds during the late 1940s and early 1950s.62 This reporting on international
odds was common in other commonwealth countries as the discussion below shows.
Election betting was also prevalent in New Zealand during the late nineteenth
and early twentieth centuries. The island’s newspapers did not publish the local bet-
ting odds—this was apparently illegal—but rather ran frequent admonitions against
betting.63 Freak bets, nonmonetary wagers, were common and considered harmless.
There was a celebrated case involving a former New Zealand premier and future chief
justice, Robert Stout, where his enemies accused him of corruption for using an agent
to buy votes through election bets. That is, the agent agreed to bet with a voter who
received the stake if the principal won the race.64 The newspapers also reported about
election betting in the United States (with odds), the United Kingdom (circa 1910,
including bets over when the next election would be called), and Ireland in the 1930s.65
Several English-language newspapers in colonial Africa and Asia carried articles
about election odds, chieﬂy recapping U.S. presidential races based on wire stories
from Reuters and United Press International.66 Singapore presents one of the more
interesting cases. Under the period of colonial rule, the English-speaking expatriates
used the betting markets to keep track of political events in the Western world. For
example, throughout the 1900–1940 period the Singapore Straits Times reported odds
from Western markets on papal elections, “majorities,” the calling of elections in the
British Parliament, the ﬁrst elections in the Republic of Ireland, presidential and state
elections in the United States, elections in Canada, and the Saar plebiscite.67 News-
paper stories continued to be published on the subdued U.K. betting markets during
the 1950s.68 Following decolonization (Singapore became self-governing in 1959 and
declared independence in 1963), local political betting markets arose that focused on
both Singapore and Malaysian elections.69 The members of the expatriate Chinese
community participated actively in these markets. As was the case in other countries,

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the long history of political betting markets
569
there remained some social distaste for gambling on politics. Politicians warned that
election bets in Malaysia just following independence could “pervert the electoral pro-
cess and dishonestly inﬂuence the results of democratic elections.”70 Such complaints
continued through the 1970s.71
In Canada there were many reports of betting over results in both national and
local elections during the late nineteenth century. For example, the Toronto World had
several reports on betting markets covering the 1882 and 1887 parliamentary elections,
the 1886 West Quebec provincial election, and the 1885 and 1887 Toronto mayoral
elections.72 There was additional coverage of gambling on many of the parliamentary
elections through 1930, with a half a million U.S. dollars bet at Montreal’s markets in
1911 alone ($12 million in 2010 dollars). In addition, there were occasionally active
markets on local elections.73 While many of the bets were one-shot affairs involving
prominent individuals, there were more traditional markets associated with the stock
exchanges in Toronto and Montreal.74 The Toronto Star provided extensive coverage of
election betting in the United States, reporting NewYork City odds right before election
day to bring its readers up to date.75
4 Election Betting in the United States
.............................................................................................................................................................................
In this section we trace the development of American betting markets in the nineteenth
through twentieth centuries. A more formal analysis of the forecasting accuracy and
ﬁnancial efﬁciency of postbellum markets is described in two companion papers.76
4.1 Pre-Civil War
Betting on political events was commonplace in the United States ever since the early
national period.77 Advocates of a candidate frequently offered public bets on his behalf
as a standard part of the election campaign. This became an expected sign of support,
even for races of lesser ofﬁces. As an example, William Cooper of Cooperstown, New
York, enjoyed the strong betting backing of his friends during his race for Congress in
1796.78 Political wagering became especially intense during the partisan conﬂicts of the
Jacksonian era.79 The practice, with its torch-lit parades, chanting partisans, hard cider,
and captive newspapers, ﬁt right into the campaigning spirit of this period, as most
press outlets were closely tied to the political machines of either the Democrats or the
Whigs. Newspapers were at the heart of much of the early betting activity.80 Many of
the election betting articles that appeared in the press were boasts or challenges rather
than reports of actual wagers transacted. As one instance,“to test the sincerity” of local
supporters of Gen. Jackson who “express their entire conﬁdence in the success of their
favorite candidate,” John Leach issued a slate of a dozen bets in his local newspaper
during the 1828 contest.81 The Albany Argus, voice of the New York regency, published

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prediction markets and political betting
its own list of challenges in 1832 and 1836.82 Similar advertisements to wager appear
during most other major elections of the period.83
We know that it was not all bluster; real money was wagered. For example, archival
records show that in late October 1832 John Nevitt of Natchez, Mississippi, placed a
$960 bet on Andrew Jackson’s reelection. This sum was worth the equivalent of $25,000
in 2010 dollars and was more than double what Nevitt annually paid the manager of
his Clermont plantation.84
Such big-stakes wagering was not limited to private citizens. Politicians were often
involved. In 1816 future president James Buchanan lost three tracts of land in northwest
Pennsylvania on an election wager. (Oil was later discovered under these lands.)85
As candidate for governor of New York in 1828, future president Martin Van Buren
wrote to a follow politico: “Bet on Kentucky, Indiana and Illinois jointly if you can,
or any two of them; don’t forget to bet all you can.”86 Battles between the Jackson
forces and the “Bankites” raged during the 1832 contest.87 And in 1834 Van Buren’s
son, John, and friend, Jesse Hoyt, recorded making over one hundred election bets,
amounting to $12,000 to $15,000 ($315,000–$394,000 in 2010 money). At this time
John Van Buren was New York attorney general and Martin Van Buren was the nation’s
vice president.88 As another indication of the involvement of elected ofﬁcials, the
Washington D.C. correspondent for the North American reported in early 1840: “Some
heavy bets were made between members of the House, to-day, on the approaching
Presidential Election.”89 Election betting in 1840 was carried on as never before.90 The
1844 contest between Henry Clay and James K. Polk witnessed an even greater ﬂurry
of betting.91 Press reports indicate that more than $6 million ($180 million in 2010
dollars) changed hands in New York in the 1844 contest between Clay and Polk.92
A debate over the information value of polls versus betting odds arose during the
antebellum era. The 1824 election was an open race, with no party nomination process,
several potential candidates, and more democratic electorate. Politicians and journalists
were eager to gauge support for leading candidates, including John Quincy Adams,
Henry Clay, and Andrew Jackson, among others. They explored different measures,
such as the number of endorsements, favorable editorials, and toasts at Fourth of
July celebrations. Using the magnitude and direction of betting on elections was also
explicitly considered. But such wagering was judged immoral and too closely tied to
electioneering propaganda to be a reliable source of information. Instead conducting
and reporting on (unscientiﬁc) straw polls of potential votes became common.93
4.2 The Ebb and Flow of Election Betting
in the Pre-Civil War Period
To provide a better sense of the ebb and ﬂow of election betting in the antebel-
lum period, we surveyed the historical newspapers and periodicals available in the
leading online sources—African American newspapers of the nineteenth century, the

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571
Cengage–Gale nineteenth-century U.S. newspapers, PaperofRecord.com, the Proquest
American Periodical Survey and Historical Newspapers, and the Readex EarlyAmerican
Newspapers—for relevant articles over the 1800 to 1860 period. Our tabulation
excluded articles concerning legislative action to outlaw election betting as well as
those discussing nonﬁnancial bets and included roughly 150 articles. The cumulative
distribution of this sample is displayed in ﬁgure 29.1. The sample contains a small
number of articles in the ﬁrst decade of the nineteenth century, but observations drop
off during the so-called Era of Good Feelings (1815–1823) period. The number of
articles picks up in the mid-1820s with the beginning of the Jacksonian movement and
Whig reaction. The peak of activity occurs in 1840 and 1844 and then falls off again.
Activity falls in the 1850s before rising during the 1860 election season.94
Wagering on elections became highly controversial. In 1840 Van Buren supporters
charged that British gold was being invested in “bragging bets” and “buying votes” in
favor of Harrison.95 In turn, in the aftermath of the 1844 contest, the Whigs protested
that a combination of gamblers favoring Polk had committed voting fraud using the
winnings from election bets to defray their expenses.96 New York governor Silas Wright
complained vigorously in his 1845 message to the state legislature of “the extensive
and rapidly increasing practice of betting upon elections, and the interested and self-
ish, and corrupting tendencies which it exerts upon the election itself.” Wright urged
the legislature to make election betting a criminal offense.97 The evangelical reform
movements associated with the Second Great Awakening also preached long and hard
against election betting.98 And the Illinois Supreme Court did invalidate one bet as
“against public policy and the best interests of the whole country.”99 Election betting
was commonly considered a form of vote buying.100
1800
180
160
140
120
Cumulative Number of Article
100
80
60
40
20
0
1810
1820
1830
Year
1840
1850
1860
figure 29.1 Cumulative distribution of articles on election betting, 1800–1860

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prediction markets and political betting
With the collapse of the Second Party system and the ongoing Democratic–Whig
rivalry, election betting appears to have slowed.101 We can only speculate why. By the
late 1840s a large number of states had made election betting illegal. The reorientation
of the parties and the development of intense sectional conﬂicts may have reduced the
sphere of personal contact leading to wagering as well as trust that the losing stake
would actually be paid. Political wagering did not disappear, however, as the career
of Abraham Lincoln makes clear. In 1857 his law ﬁrm handled a case involving a bet
over the 1856 presidential election.102 During the 1864 election Lincoln also apparently
employed agents to entice Democrats in swing states into wagering on the election in
order to disqualify their votes come election day.103
Much of the activity in the period surrounding the Civil War took the form of public
challenges for propaganda purposes. In 1864 August Belmont, a wealthy New York
Democrat and representative of the Rothschilds’ interests in America, boasted that he
would “bet heavily” on George B. McClellan being elected president. Belmont’s terms,
however, represented a conditional wager, stating that a victory for Lincoln’s former
general would bring peace while Lincoln’s reelection would result in continued war
and eventual disunion.104 Other proposals were offered for bragging rights and were
not serious wagers. An extreme example of this purportedly occurred in 1868 when
New York drugstore owner H. T. Helmbold offered to bet $1 million cash at even
odds to take the Democratic side on a slate of election propositions. J. Kinsey Taylor
of Philadelphia, meanwhile, offered to take the Republican side headed by Ulysses S.
Grant.105 It is unclear whether both sides actually staked this wager. Such even-money
boasts do not provide a meaningful set of odds concerning which candidate would win
the election. But markets generating such odds would soon come.
4.3 Post–Civil War Wall Street Betting Market
Election betting involving real ﬁnancial stakes occurred in almost every city, but
increasingly over the postbellum period such wagering became organized in markets
centralized in New York City. In the late 1860s and early 1870s activity was focused in
pool halls such as Johnson’s and Morrissey’s. Betting in this period took the recently
developed pari-mutuel form. That is, participants would buy ﬁxed-dollar shares in the
ﬁnal pot and the odds would be determined at the end of all betting (a candidate’s ﬁnal
odds of winning were determined by the proportion of the total bet volume wagered
on him). The New York dailies reported substantial activity in the national and state
contests of the 1870s, but the form of betting made the odds difﬁcult to translate
into subjective probabilities. In addition, problems arose with the 1876 Rutherford B.
Hayes–Samuel J. Tilden presidential contest. This election was essentially a draw, with
the political parties charging each other with fraudulently manufacturing votes. The
House of Representative eventually decided this highly contested election. The acri-
mony spilled over into the betting market, where $4 million was wagered ($84 million
in 2010 terms).106 John Morrissey, the leading New York pool seller and an active

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the long history of political betting markets
573
Democrat, opted to cancel the pools, returning the stakes minus his commission. This
solution left many unsatisﬁed, a situation contributing to the push during the next
session of the New York legislature to outlaw pool selling.
After a brief lull in the late 1870s and early 1880s, election betting revived in the
mid-1880s and began to ﬂourish in the 1890s. Activity moved out of pool rooms and
onto the Curb Exchange in the ﬁnancial district and to the major Broadway hotels. The
politically connected hotels included the Republican-oriented Fifth Avenue Hotel and
the neighboring Democratic/Tammany–oriented Hoffman House.107 The Metropol
and Waldorf Astoria also were locations for betting on elections. The leading bet com-
missioner, or stakeholder, in the public eye was Charles Mahoney, who held sway at the
Hoffman House until 1910.108 Over most of this period the standard betting and com-
mission structure was for the betting commissioner to hold the stakes of both parties
and charge a 5 percent commission on the winnings. If the commissioner trusted the
creditworthiness of the bettors, it was not necessary to actually place the stakes, and
instead the signed memorandum or letter of obligation sufﬁced.109
Figure 29.2 graphs the cumulative number of articles returned from online searches
for“election bet”in the NewYorkTimes from 1851 to 1950 and theWashington Post from
1880 to 1950. It is clear from this ﬁgure that the heyday of election betting extended
from the 1890s through the mid-1910s.110 During the late 1890s and early 1900s the
names and four-ﬁgure stakes of bettors ﬁlled the pages of New York’s daily newspapers.
The environment for election bets became less favorable starting around 1910. The
key developments were changes in tax laws,NewYork state antigambling legislation,and
public attitudes toward organized ﬁnancial markets. The Hart–Agnew Act outlawing
professional bookmaking that employed written bets was passed by the New York
1000
New York Times and Washington Post
New York Times
900
800
700
600
Cumulative Number of Articles
500
400
300
200
100
0
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
figure 29.2 Cumulative “Election Bet” articles in the New York Times and Washington Post,
1851–1950

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prediction markets and political betting
legislature in 1908 (and was extended to cover oral bets in 1910). The prohibition was
directed primarily against horse racing and the Tammany-linked Metropolitan Turf
Association, but the law’s passage also reduced betting on elections for several years.
In 1912 the New York Curb Association publicly reminded its members that placing
bets was contrary to NewYork laws.“Any member found betting,placing bets,or report-
ing alleged bets to the press will be charged with action detrimental to the interest of the
association, which may lead to his suspension.”111 The betting commissioners in the
ﬁnancial district initially responded by revising their contract form—creating a memo-
randumbetween“friends”totransfermoneyconditionalontheelectionoutcome—and
by raising the commission rates to reﬂect their increased legal exposure. There was some
talk of moving operations to New Jersey, and many commissioners reduced or stopped
keeping book.112 When the heat was reduced after a few years, election betting revived.
Ironically, in the 1916 contest between President Woodrow Wilson and Charles Evans
Hughes, who as New York governor had signed the Hart–Agnew act into law, election
betting on Wall Street reached its peak: $10 million (or $205 million in 2010 dollars)
was wagered on the national election.
By the late 1910s newspapers more commonly published stories centering on bet
commissioners and bucket shops within the ﬁnancial district. (Bucketing was the prac-
tice of a broker accepting an order to buy a stock without actually executing it. The
broker was essentially betting with the client about the changes in the stock’s price, a
bet catered to low-stakes investors.) In the early 1920s three so-called brokerages domi-
nated election betting in the Wall Street ﬁnancial district: W. L. Darnell & Co., 44 Broad
Street; J. S. Fried & Co., 20 Broad Street; and G. B. de Chadenedes & Co., also of 20
Broad Street.113 Other prominent New York bookmakers of the period included John
Doyle, owner of a Broadway billiard academy, who principally handled wagers on sport-
ing events, such as prize ﬁghts and the World Series, and Fred Schumm, a politically
connected café owner in Brooklyn, who dealt in both election and sports bets.
The organized ﬁnancial markets continued to attempt to limit involvement of their
members. For example, in May 1924 both the New York Stock Exchange and the
Curb Market passed rules/resolutions against election gambling. The exchanges liked
to distinguish between their risk-sharing and risk-taking functions, which were deemed
socially productive, and gambling on sporting events, such as horse races or prize
ﬁghts, which were viewed as zero-sum entertainment activities with outcomes that
did not affect the broader world. But unlike with sporting events, betting on elections
potentially belonged in the risk-insurance category, and the information it provided
had real-world value. One could readily imagine a risk averse owner of an investment
project betting for a candidate unfavorable to the project in order to hedge against
a “bad” election outcome. However, in practice it appears that bets were partisan
in the sense that bettors took the side of their preferred candidates. Reﬂecting their
growing marginalization, election bets became anonymous. In contrast to the earlier
period, newspapers in the 1920s and 1930s no longer reported the names of those
making wagers. Instead, bets were reported to involve six-ﬁgure amounts advanced by
unnamed leaders in the business or entertainment worlds.

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the long history of political betting markets
575
4.4 Demise of the Wall Street Election Betting Markets
The formal political betting markets appear to have largely disappeared by 1944, though
informal bets continued to take place right up to the current period of Internet-based
markets. There are several explanations for the demise of the Wall Street markets:
(1) the rise of scientiﬁc polling, (2) the passing of several of the leading election betting
commissioners, (3) the active suppression of the New York illegal gambling scene,
(4) the contraction, during the early 1940s, of key sources of betting dollars, and (5) the
legalization of horse race betting.
The press attention devoted to the Wall Street betting odds was due in part to the
absence of creditable alternatives. In the early years of the twentieth century the only
other information available concerning future election outcomes came from the results
from early-season barometer contests (such as the mid-September contest in Maine),
overtly partisan canvasses, and unrepresentative straw polls.114 Over the 1894–1918
period the New York Herald published the results of its massive straw polls in the weeks
leading up to election day. In November 1916, for example, it reported its tabulations of
nearly one-quarter of a million straw ballots collected from across the country.115 In the
1920s and 1930s Literary Digest issued the best-known nonrepresentative poll based on
mass-mailing postcard ballots to millions of names listed in telephone directories and
automobile registries. After predicting every presidential elections correctly from 1916
to 1932, the Digest famously called the 1936 contest for Alfred Landon, the Republican
candidate, in the election that Franklin Roosevelt won by the largest Electoral College
landslide ever.
The early polls based on scientiﬁc samples correctly predicted Roosevelt’s victory.
George Gallup, who had left academia and the advertising industry and in 1935 formed
the American Institute of Public Opinion, was often credited with a singular gift of
prophesy.116 However,thepollsof theotherpioneersof publicopinionresearch,includ-
ing Elmo Roper, who began the Fortune Survey in 1935, and Archibald Crossley, also
called the 1936 race correctly (as did the Wall Street betting odds). The numbers from
scientiﬁc polls were available on a relatively frequent basis and were not subject to the
moral objections against election betting. Newspapers, including the Washington Post,
began to subscribe to the Gallup polling service and to tout its weekly results in its
pages. At the same time, the paper reduced its coverage of betting markets. Such trends
are displayed in ﬁgure 29.3, which reports the cumulative number of articles published
in presidential election years in the New York Times and Washington Post returned from
an online search of selected “poll” and “election betting” terms from 1916 to 1944.
Other factors also contributed to the demise of theWall Street betting market. Several
of the preeminent betting commissioners active in election wagering left the trade either
due to death by natural causes (John Doyle) or to gang-land slayings (Sam Boston).117
NewYork mayor Fiorello La Guardia’s general crackdown on illegal gambling, including
“raids on brokers’ ofﬁces,” also made it “difﬁcult to ﬁnd betting commissioners in the
ﬁnancial district” by 1944.118 Tammany Hall, which had often taken the Democratic
side of wagers during the heyday of New York election betting, also fell on hard times.

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prediction markets and political betting
Gallup Poll
400
350
300
250
200
150
100
50
0
1916 1920 1924 1928 1932 1936 1940 1944 1948
1916 1920 1924 1928 1932 1936 1940 1944 1948
1916 1920 1924 1928 1932 1936 1940 1944 1948
1916 1920 1924 1928 1932 1936 1940 1944 1948
350
300
250
200
150
100
50
0
100
125
75
50
25
0
0
10
20
30
40
50
60
70
Literary Digest
Election Betting
Wall Street Betting Odds
New York Times
Washington Post
figure 29.3 Cumulative number of articles returned from selected“Poll”and“Election Betting”
search terms, 1916–1948
La Guardia’s repeated reelection as mayor cut off much of Tammany’s patronage,
driving the organization to declare bankruptcy in 1943. In addition, wartime taxes
were purportedly crimping the pockets on Wall Street.119 A ﬁnal factor was the legal-
ization of horse race betting in New York in 1939. The possibility of betting several
times each day at the track, rather than once or twice a year on elections, siphoned the
dollars of bettors and bookmakers.
5 Conclusion
.............................................................................................................................................................................
Election betting has a long history that is often characterized by higher stakes and
greater emotion than what is exhibited in the Internet markets of today. Wagering
was such a central cultural feature of the premodern era that even those who lacked
the money to place a wager got involved. In the United States during the eighteenth
and nineteenth centuries, nonﬁnancial bets—where losers had to roll peanuts with a
toothpick down a street, climb up a greased pole, shave their hair or make other public
gestures—were wildly popular. In 1900 at least half a million such “freak bets” were
made.120 Although it is sometimes claimed that political betting markets are a recent
invention, our research shows that clearly they are not. Rather it is the absence of such
markets during the mid and late twentieth century which is the exception.

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the long history of political betting markets
577
A further comparison of the experience in different countries during this period
may shed light on the factors that promoted or suppressed betting markets. For exam-
ple, one could look at variations in terms of when scientiﬁc polls were introduced in
different countries to see if this was a key factor in the displacement of the markets.
An alternative approach would be to explain why the Internet was needed to spawn
modern markets in the United States, whereas far more low-tech markets emerged a
quarter century earlier in Britain. Finally, study of the rapid creation of political betting
markets in previously colonized countries such as Singapore might uncover evidence
of the role played by social norms inherited from the period of British rule. By gaining
a better understanding of the historical dynamics of political betting markets we can
begin to analyze how current developments are likely to shape and alter their current
incarnations.
We are conﬁdent that future research will build on this chapter in terms of both depth
(greater precision on the genesis of the markets described here) and breadth (adding
discussion of other countries). One reason is technological. This work has beneﬁted
from the relatively new creation of online newspaper archives that contain coverage
of historical political betting markets. As more newspaper corpora become available,
a more reﬁned and broader timeline will be possible. A second reason is the possibil-
ity of crowdsourcing. This work has been hindered by the authors’ limited language
proﬁciency. For example, we know from English-language sources that election betting
periodically occurred during French elections but are unable to track its prevalence
in French sources.121 Future research involving researchers with a variety of linguistic
backgrounds can expand our perspective on when and where bets have been placed on
elections.
As a postscript, we note that in March 2013 the highly visible online political betting
market, Intrade, closed due to unspeciﬁed “ﬁnancial irregularities.” The most active
Intrade market at the time involved forecasting the next Pope. (FN. John Cassidy,
“What Killed Intrade?” New Yorker, 11 March 2013.) Among the problems facing the
site were the recent death of its founder and a crackdown by the US Commodity Futures
Trading Commission on participation by American citizens. Despite this, several other
online sites such as Betfair continue to provide platforms which have thick markets on
political elections and other topics. Given the long history reviewed above, we anticipate
that betting markets on the US Presidential race will be as active as ever in 2016. Policy-
makers can stand in the way of their efﬁcient operation; they cannot push them out of
existence.
Notes
1. Justin Wolfers and Eric Zitzewitz,“Prediction Markets,” Journal of Economic Perspectives
18 (2004): 107–126; Paul W. Rhode and Koleman Strumpf,“Historical Presidential Bet-
ting Markets,”Journal of Economic Perspectives 18, no. 2 (2004): 127–142; Paul W. Rhode
and Koleman Strumpf,“Manipulating Political Stock Markets: A Field Experiment and a
Century of Observational Data,”working paper, June 2008; http://people.ku.edu/~cigar.

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prediction markets and political betting
2. Rhode and Strumpf,“Historical Presidential Betting Markets.”
3. There also were markets that indirectly captured election outcomes. Insurance premia,
exchange rates, and security prices of politically connected assets often reﬂect (or span)
the same fundamentals that would drive political stock market prices.
4. Jonathan Walker,“Gambling and the Venetian Noblemen, c. 1500–1700,” Past & Present
162, no. 1 (1999): 28–69, esp. 31 on the practices of scommetter, betting on elections.
5. D. R. Bellhouse, “The Genoese Lottery,” Statistical Science 6, no. 2 (1991): 141–148;
Nicole Martinelli,“Online Gaming, Italian Style,”Wired, Dec. 18, 2006.
6. Frederic J. Baumgartner, Behind Locked Doors: A History of Papal Elections (New York:
Palgrave, 2003), 88, 250. See also Renaud Villard, “Le Conclave des Parieurs: Paris,
Opinion Publique et Continuité du Pouvoir Pontiﬁcal à Rome au XVIe Siècle,”Annales
64, no 2 (2009): 375–403.
7. Frederic J. Baumgartner, “Henry II and the Papal Conclave of 1549,” Sixteenth Century
Journal 16 no. 3 (1985): 301–314; quote on p. 305.
8. New York Times, 2 March 1878, 2.
9. New York Times, 11 July 1903, 2; Atlanta Constitution, 11 July 1903, 3; Chicago Tribune,
27 July 1903, 4; Los Angeles Times, 18 Aug. 1903, 5; Scotsman, 24 Jan. 1922, 4, and 7 Feb.
1922, 5. See also Manchester Guardian, 9 Aug. 1978, 2, which notes the role of clergymen
placing bets.
10. George Otto Trevelyan, The Early History of Charles James Fox (New York: Harper &
Brothers, 1880), 416; and New York Times, Nov. 7, 1880, 4.
11. Freeman’s Journal, 3 Jan. 1763, 3; 31 Jan. 1763, 2; 11 Feb. 1763, 3; 25 Oct. 1763, 2; 23 July
1765, 2; 21 Dec. 1765, 2; 15 Feb. 1766, 2; 8 March 1766, 2; 4 Aug. 1767, 2; 19 March 1768,
2; 28 May 1768, 2; 20 Sept. 1768, 3; 18 Feb. 1769, 2; 19 Feb. 1769, 2; 21 March 1769, 2; 4
July 1769, 2; 18 Dec. 1781, 4; 20 June 1789, 4; Finns Leinster Journal, 14 Oct. 1772, 2; 10
April 1776, 2. Translated into percentage terms, the odds reported in Freeman’s Journal,
8 March 1766, 2, in favor of the repeal of the Stamp Act varied between 59–64 percent in
March 1766. Freeman’s Journal, 20 Sept. 1768, 3, also reports betting in the “Court End”
of Dublin.
12. Trevelyan, Fox, 414. For an account of partisan betting behavior in the 1837 parliamen-
tary contest see Charles Greville and Henry Reeve, The Greville Memoirs: A Journal of the
Reigns of King George IV and KingWilliam IV,vol. 2 (NewYork: Appleton, 1883), 510. See
also Algernon Bourke, The History of White’s, 2 vols. (London: Waterlow & Sons, 1892).
Bourke (1:101) noted that among the British elite during the eighteenth and nineteenth
centuries the“custom of deciding everything by wager is so universal”that polite conver-
sation is ﬁll“with little more than bet after bet,or now and then a calculation of the odds.”
13. John Robinson, The Last Earls of Barrymore, 1769–1824 (London: S. Low-Marston,
1894), 113–114.
14. Among the court cases decided on gaming were Foster v. Thackery, 1 Term Reports 57
(1781) regarding the outbreak of war between England and France; Allen v. Maur, 1 Term
Reports 56 (1786), regarding an election wager between two voters; Atherfold v. Beard, 2
Term Reports 610 (1788), regarding the level of the duty on hops; Lacaussade v. White,
7 Term. Reports 535 (1798), regarding the date when England and France would sign
articles of peace. British Parliament, House of Lords, The Three Reports from the Select
Committee on the Lords Appointed to Inquire into the Laws Respecting Gaming (London,
1844), 41–42. For the legal standing of wagers see T. Starkie, “Appendix I: Substance of
the Common and Statute Law Relating to Gaming,” 223–231, in House of Commons,

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the long history of political betting markets
579
Report from the Select Committee on Gaming; Together with the Minutes of Evidence,
appendix and index (London, 1844).
15. Joseph Chitty, A Treatise on the Laws of Commerce and Manufactures and the Contracts
Related Thereto: With an Appendix of Precedents, vol. 3 (London: A. Strahan, 1824),
82–83. In a widely publicized article, Sir Frederick Milner charged that he lost a recent
parliamentary race due to effects of election betting. “Betting as a Force in Politics,” Pall
Mall Gazette (London), 6 Aug. 1886, 1.
16. David Dixon, From Prohibition to Regulation: Bookmaking, Anti-Gambling, and the Law
(Oxford: Clarendon, 1991), 38–81; Mark Clapson, A Bit of a Flutter: Popular Gambling
and English Society (Manchester: Manchester University Press, 1992), 18–38; Jim Orford,
Kerry Sproston, Bob Erens, Clarissa White, and Laura Mitchell, Gambling and Problem
Gambling in Britain (Hove, U.K.: Brunner-Routledge, 2003), 3.
17. “Latest Parliamentary Betting,” Punch, 21 July 1894 (which may be meant ironically);
Times of London, 5 Dec. 1910, 6, and 7 Dec. 1910, 12 (which are not). Annual Register:
A Review of Public Events at Home and Abroad for the Year 1910 (London: Longsmans-
Green, 1911), 256–257. Wire stories about election betting were also carried in papers
throughout the British Empire. As one example, Liverpool betting odds on Gladstone’s
1892 prospects appear in New Zealand papers including the Manawatu Herald, 7 July
1892, 2; Feilding Star, 5 July 1892, 2; Bush Advocate, 5 July 1892, 3, Poverty Bay Herald, 5
July 1892, 2, Hawke’s Bay Herald, 6 July 1892, 3, and others.
18. Laura D. Beers, “Punting on the Thames: Electoral Betting in Interwar Britain,” Journal
of Contemporary History 45, no. 2 (2010): 282–314.
19. Pundit commentary and newspaper election contests were commonly framed in terms
of majorities. Examples of newspaper prediction contests based on majorities include
London Daily Mirror, 11 Jan. 1906, 6; 4 Dec. 1923, 2; 9 Oct. 1924, 2; and London Daily
Express, 8 Nov. 1922, 10; and 29 Nov. 1923, 8.
20. Beers,“Punting,” 282; London Daily Express, 28 May 1929, 1. The London Times, 3 Dec.
1910, 12; London Daily Mirror, 2 Dec. 1910, 17, and Irish Times, 22 Dec. 1910, 9, provide
good ﬁrsthand descriptions of the early market; the Irish Times, 18 Oct. 1924, 3; London
Daily Express, 13 March 1929, 13; and Manchester Guardian, 22 April 1929, 14, cover the
later period.
21. Beers, “Punting,” 285. Examples of prices in 1910 appear in the London Daily Mirror, 3
Dec. 1910, 17; 5 Dec. 17; 6 Dec. 13; 8 Dec., 13; 9 Dec., 13; London Times, 5 Dec. 1910, 6.
TheactivityattractedattentionintheUnitedStates; seeNewYorkTimes,11Dec. 1910,C2.
22. Dublin’s Sunday Independent, 25 Sept. 1921, 5, provides quotes from London insurance
ﬁrms over losses resulting from the dissolution of the British Parliament in 1921.
23. Exchange values calculated on MeasuringWorth.com, www.measuringworth.com/
exchange.
24. Beers,“Punting,” 287–288, 291.
25. Beers,“Punting,” 296.
26. London Daily Express, 17 Oct. 1931, 12, and 20 Oct. 1931, 12. Similar claims appear in
the next contest: “Election ‘Majorities’ Set Market Tone,” London Daily Express, 6 Nov.
1935, 14.
27. London Daily Express, 29 Oct, 1931, 1. London Daily Mirror, 21 Oct. 1932, 18, estimated
that “three-quarters of million changed hands” in the 1931 contest.
28. New York Times, 27 Oct. 1931, 1.
29. London Daily Express, 21 Jan. 1932, 3; London Daily Mirror, 21 Oct. 1932, 18.

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prediction markets and political betting
30. London Daily Mirror, 19 Oct. 1933, 7, 21;
Beers, “Punting,” 301. Summarizing the
prewar situation, “Election Gambling,” Economist, 4 Feb. 1950, 252 noted: “There was a
much publicized lawsuit when a trader, unable to honour his debts, pleaded the provi-
sions of the Gaming Act. The sequel was a ban by the Council of the Stock Exchange on
all such dealings, which has been reafﬁrmed at each subsequent election.”
31. London Daily Express, 31 Oct. 1935, 10; 5 Nov. 1935, 2.
32. Toronto Star, 26 Oct. 1940. Mike Smithson, The Political Punter: How to Make Money
Betting on Politics (London: Harriman House, 2007), 4–5, writes of the record in the
betting book of Magdalen College, Oxford, of the gentlemen’s wagers between physicists
James Grifﬁths (one of the developers of radar) and (Bernard) Rollin in August 1940
regarding the number of German planes downed each evening. Brian Howard Harrison,
in “College Life, 1918–1939,” writes: “All Souls SCR (Senior Common Room) regularly
conducted sweepstakes on general elections between the wars”; in Brian Howard Harri-
son, ed., The History of the University of Oxford, vol. 8, The Twentieth Century (Oxford:
Oxford University Press, 1994), 87.
33. London Daily Express, 19 March 1929, 12.
34. Beers,“Punting,” 307, 309.
35. Quotes for the 1945 election appear on the front page of the Sydney, Australia, Morning
Herald, 23 July 1945; the odds come from the insurance brokers or Lloyds and heavily
favor the Conservatives. Odds for the 1950 contest are given in London Daily Express,
11 Jan. 1950, 1, with the provisos that “Only a few members in the Stock Exchange are
doing business on the Election, Very unofﬁcially” and that such election betting was
banned.
36. “Election Gambling,” Economist, 4 Feb. 1950, 252.
37. Two years earlier the 1961 Betting and Gaming Act substantially liberalized wagering
on sporting events in Britain. Graham Rock, “Gambling a-gogo,” London Observer, 29
April 2001.
38. “Odds-On Politics,” Economist, 21 Aug. 1965, 715–716.
39. New York Times, 10 May 1964.
40. “Whirl in the Pools,” Economist, 17 Oct. 1964, 273; Manchester Guardian, 2 Oct. 1964;
Observer, 10 Oct. 1964; FinancialTimes, 8 Oct. 1964, 14; Smithson, Political Punter, 9–11.
41. In 1966, as an example, 72.5 percent of the total parliamentary betting at Ladbrokes was
on general election results; 9.0 percent was on “majorities”; and 18.5 percent was on the
results in speciﬁc constituencies. Irish Times, 22 March 1966, 8.
42. Through taxes on wagering the British Chancellor of the Exchequer earned about
6 percent on the volume of activity. Irish Times, 2 March 1974, 8.
43. “Odds-On Politics,” Economist, 21 Aug. 1965, 715–716.
44. See Manchester Guardian, 4 Nov. 1969, for Pollard’s election night appearance. The
Guardian, 15 March 1966, 10, noted Pollard saying that “the weight of money is more
accurate an indication of public opinion than anything the polls can produce. He casts
a cold eye on some of the wilder swings forecast by other methods.”
45. Martin Rosenbaum, “Betting and the 1997 British General Election,” Politics 19, no. 1
(1999): 9–14.
46. “Betting on the White House race a big business,” The Singapore Straits Times, 30 July
1972.
47. “Election Betting Scored in Britain; Wager Affect Voters and Results, Opponents Say,”
New York Times, 5 April 1966, 5; Manchester Guardian, 5 April.1966, 3.

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the long history of political betting markets
581
48. There was some betting on local elections in South Asia in the pre-1947 era. See Ceylon
Observer (Colombo, Sri Lanka), 14 Dec. 1911, 15. We have seen little evidence of elec-
tion betting in India before the mid-1980s, but we know that “poll betting” has become
commonplace. See Times of India, 7 Jan. 1985, 3; 23 Nov. 1989, 3; 21 May 1991, 5; 8
Nov. 1993, 9; 7 May 1996, A1; 3 Oct. 1999, 8; and “Betting: Fluctuating Fortunes,” India
Today, 31 May 1991, 58–59.
49. Finns Leinster Journal, 10 April 1776, 2; Freemans Journal, 18 Dec. 1781, 4; 5 Oct. 1763, 2.
50. Freemans Journal, 19 March 1768, 2;
14 Oct. 1772, 2; 25 March 1784, 4.
51. There were bets on the timing of elections in the French Chamber of Peers (Freemans
Journal, 5 March 1819, 2), the military success of Admiral Horatio Nelson (Freemans
Journal, 23 April 1801, 2), and Parliamentary acts that would grant greater rights for
Catholics (Freemans Journal, 26 April 1828, 2).
52. The Canadian market covered included bets on both the winner and the number of
seats in the Parliament of Canada: Irish Times, 6 March 1891, 5; 5 Sept. 1911, 7. The
U.S. markets are reported in Irish Times, 22 Dec. 1865, 3; 30 July 1904, 10; 8 Nov. 1904,
5; 7 Nov. 1905, 1; 3 Nov. 1906, 8; 3 Nov. 1908, 8; 6 Nov. 1916, 5; 4 Nov. 1924, 5; Irish
Independent, 7 Nov 1905, 5.
53. Irish Times, 27 Jan. 1906, 12.
54. Irish election bets on the Dáil Éireann, the lower house of the Irish Parliament, are
discussed in Scotsman, 5 Jan. 1933, 9; Irish elections odds from Irish bookies are in Irish
Independent, 4 Sept. 1925, 12; Irish person-to-person bets are in Connacht Sentinel, 26
Jan. 1932, 2. Coverage of U.K. parliamentary elections include those on the winning
party (Irish Independent, 10 Oct. 1924, 12; Sunday Independent, 12 Oct. 1924, 7) and
majorities bets (Freeman Journal, 11 Dec. 1923, 2). The role of insurance companies on
the U.K. bets is in Sunday Independent, 25 Sept. 1921, 5.
55. Irish Times, 15 July 1945, 1; Southern Star, 14 Feb. 1948, 3.
56. Irish Times, 15 Feb. 1964, 10.
57. Irish election coverage includes odds on individual seats, Irish Independent, 7 March
1966, 10; the governing party in Dáil Éireann, Irish Independent, 4 Feb. 1968, 6, and, 17
June 1969, 14; and local elections in Northern Ireland, Irish Independent, 24 Feb. 1969,
6. Coverage of the U.K. markets included odds from U.K. books like Ladbrokes, Corals,
and William Hill (Sunday Independent, 16 Aug. 1964, 6; Irish Independent, 4 Oct. 1974,
1) as well as Irish books (Irish Independent, 5 Feb. 1974, 1). In addition to early coverage
of U.S. markets in the 1940s (Irish Times, 20 Sept. 1940, 6), Irish books also set odds for
American elections (Irish Independent, Apr. 1967). There was even coverage of British
books’ odds on Australian elections (Sunday Independent, 16 Nov. 1975, 1).
58. The Melbourne Argus, 17 Jan. 1868, 5; 13 Sept. 1917, 8.
59. The Hobart, Tasmania, Mercury, 7 Aug. 1948, 8; the Canberra Times, 26 May 1954, 1.
60. The aim of the law is to avoid voting based on the wager rather than preferences. The
Hobart, Mercury, 29 May 1913, 6.
61. The Melbourne Argus, 12 Dec. 1949, 6; 13 Dec. 1949, 8.
62. For the United States seethe Hobart Mercury, 29 Jan. 1897, 3; the Sydney Morning Herald,
13 Nov. 1916, 8; the Hobart Mercury, 1 Nov. 1944, 2. For the United Kingdom see the
Sydney Morning Herald, 23 July 1945, 1; the Melbourne Argus, 27 Sept. 1951, 3.
63. Wanganui Chronicle, 22 June 1875, 2; Ashburton Guardian, 31 Oct. 1893, 2; see the
Wellington Evening Post, 4 Nov. 1873, 2 and 10 May 1884, 2; Poverty Bay Herald,

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prediction markets and political betting
14 Dec. 1889, 2, Nelson Evening Mail, 30 Nov. 1899, 3; and the Grey River Argus,
5 Aug. 1920, 3.
64. Nelson Evening Mail, 28 Nov. 1893, 1; 4 Jan. 1894, 1; Marlborough Express, 3 Jan. 1894, 2
65. Wellington Evening Post, 17 Jan. 1933, 8.
66. See the Mombasa, Kenya, East African Standard, 12 Nov. 1910, 2; Rhodesia Herald, 7
Jan. 1910, 10; Buluwayo (Zimbabwe) Chronicle, 12 March 1914, 12. For examples of
local election betting in South Africa see Scotsman, 13 June 1929, 9; Tribune (Lahore,
Pakistan), 11 Nov. 1910, 4.
67. The Singapore Straits Times, 8 Sept. 1903; 25 March 1929 and 26 Feb. 1929; 10 Jan. 1933;
4 Nov. 1920 and 6 Nov. 1906; 29 July 1930; 15 Jan. 1935.
68. The Singapore Straits Times, 28 Jan. 1950, 24 Feb. 1950, 19 Oct. 1951, 20 May 1955, and
8 Oct. 1959.
69. The Singapore Straits Times, 18 Aug. 1959 and 10 May 1969.
70. The Singapore Straits Times, 27 June 1963. Other newspaper articles in which election
betting is criticized appear on 20 March 1961 and 28 June 1963.
71. The Singapore Straits Times, 1 July 1978.
72. The issues of the Toronto World are: 8 June 1882 for the 1882 parliamentary election; 22
and 25 Feb. 1887 for the 1887 parliamentary elections; 1 Oct. 1886 for the West Quebec
election; 6 Jan. 1885 for the 1885 Toronto mayoral election; 3, 4, and 5 Jan. 1887 for the
1887 Toronto mayoral election.
73. Canadian Parliamentary elections are discussed in Manitoba Daily Free Press, 5 March
1891; New York Times, 30 Oct. 1904, and Toronto Star, 1 Nov. 1904; New York Times, 22
Sept. 1911; Scotsman, 28 July 1930. There were also markets on a by-election in London
Ontario; see Toronto World, 20 Nov. 1920; for a market on Quebec provincial election
see Winnipeg Free Press, 19 Oct. 1939.
74. The Montreal markets are discussed in New York Times, 22 Sept. 1911.
75. As examples see Toronto Star, 2 Nov. 1896, 2 Nov. 1908, 5 Nov. 1912, 4 Nov. 1916, 4 Nov.
1924.
76. Paul W. Rhode and Koleman Strumpf, “Historical Presidential Betting Markets,”
Journal of Economic Perspectives 18, no. 2 (2004): 127–142, and “Historical Predic-
tion Markets: Wagering on Presidential Elections,” working paper, November 2003;
www.unc.edu/~cigar/papers/BettingPaper_10Nov2003_long2.pdf.
77. As early examples see Connecticut Gazette, 17 Dec. 1800, 2; and the Democrat, 10 Nov.
1804, 2.
78. Alan Taylor,“‘The Art of Hook & Snivey’: Political Culture in Upstate New York during
the 1790s,” Journal of American History 79, no. 4 (1993): 1371–1396, 1386. Taylor con-
sidered “bets between the friends of candidates” one of four main instruments in early
electioneering (1380). He noted that “rival interests strove to intimidate one another
and to impress voters with bets. A bet between the supported of rival interests was an
exercise in competitive self-assertion. A public bet on a candidate was an investment of
reputation and honor as well as of money.”
79. As examples at the beginning of this era see Baltimore Patriot, 9 Nov. 1824, 2; and New-
Hampshire Patriot & State Gazette 1, Dec. 1828, 2. Glenn C. Altschuler and Stuart M.
Blumin, Rude Republic: Americans and Their Politics in the Nineteenth Century (Prince-
ton, N.J.: Princeton University Press, 2000), 73, hold that while political parties were
not directly responsible for most election betting in the period, they did encourage the
practice among their partisans.

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the long history of political betting markets
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Several noteworthy recent surveys of political history in the early national and Jack-
sonian period, including Sean Wilentz, The Rise of American Democracy: Jefferson to
Lincoln (New York: W. W. Norton, 2005), and Michael F. Holt, The Rise and Fall of
the American Whig Party: Jacksonian Politics and the Onset of the Civil War (New York:
Oxford University Press, 1999), are remarkably silent about election betting.
80. Regarding the political scene in New York in the 1790s, Taylor, “The Art of Hook &
Snivey,” 1386, writes that “the newspaper ofﬁce became a kind of brokerage house for
wagers. There a gentleman could leave a note or bond indicating what he would bet on a
candidate; there a rival gentleman could agree to take up that note or bond or leave one
of their own. The curious could call to inquire about who had bet and how the wagers
stood. Like the accumulation of nomination notices in the papers, reports of the ebb
and ﬂow of bets served as public opinion polls.”
81. New-Hampshire Statesman and Concord Register, 20 Sept. 1828.
82. Essex Gazette, 25 Oct. 1828, 2; New-Hampshire Patriot & State Gazette, 10 Sept. 1832;
and Connecticut Courant, 29 Aug. 1836
83. As examples see the Spirits of the Times, 8 Sept. and 20 Oct. 1832; the Globe (Washington,
D.C.),
6 Oct. 1836; Barre Gazette, 30 Oct. 1840, 2.
84. Entriesdated27Oct. and12Dec. 1832intheJohnNevittDiary#543,SouthernHistorical
Collection, Wilson Library, University of North Carolina at Chapel Hill.
85. Philip S. Klein, President James Buchanan: A Biography (University Park: Pennsylvania
State University Press, 1962), 29, 434. For Buchanan’s activities see also the Salisbury
(N.C.) Carolina Watchman, 2 Nov. 1848.
86. Edward M. Shepard, American Statesman: Martin Van Buren (Boston: Houghton-
Mifﬂin, 1900), 453. Calendar of the papers of Martin Van Buren, prepared from the
originalmanuscriptsintheLibraryof Congress(Washington,D.C.: GPO,1910),includes
references to election bets in his correspondence in 1813 (p. 21), 1826 (p. 78), 1828 (p.
93), 1834 (p. 220), 1835 (p. 245), 1836 (pp. 272, 274).
87. Augustus C. Buell, History of Andrew Jackson: Pioneer, Patriot, Soldier, Politician,
President. 2 vols. (New York: Charles Scribner, 1904), 2:270–272.
88. William L. MacKenzie, The Life and Times of Martin Van Buren (Boston: Cooke, 1846),
255–256; New-Hampshire Patriot and State Gazette, 10 Sept. 1832, 3; Vermont Gazette, 6
Oct. 1832, 2; Eastern Argus Semi-Weekly, 22 Oct. 1832, 2; and the Pittsﬁeld Sun, 25 Oct.
1832, 3.
89. North American and Daily Advertiser (Philadelphia), 26 Feb. 1840.
90. The Farmers’ Cabinet (Philadelphia), 13 Nov. 1840, 2.
91. New York Herald, 15 Sept. 1844; Daily National Intelligencer (Washington, D.C.), 5 Sept.
1844; Boston Daily Atlas, 25 Sept. 1844; Scioto Gazette (Chillicothe, Ohio), 31 Oct. 1844.
92. New-Hampshire Patriot (Concord, N.H.), 5 Dec. 1844, [4].
93. Daily National Intelligencer,6Aug. 1824,3; JamesW. Tankard Jr.,“Public Opinion Polling
by Newspapers in the Presidential Election Campaign of 1824,”Journalism Quarterly 49,
no. 2 (1972): 361–365; Tom W. Smith, “The First Straw? A Study of the Origins of
Election Polls,” Public Opinion Quarterly 54, no. 1 (1990): 21–36.
94. The number of newspapers covered in the online sources generally expands over time.
This makes interpreting these trends somewhat problematic. The decline in the number
of observations on election betting articles after 1844 is even more signiﬁcant once the
expansion in overall coverage is taken into consideration.

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prediction markets and political betting
95. See New-Hampshire Patriot, 7 Sept. 1840, for these speciﬁc charges and 14 Sept. 1840 for
a more general criticism of corrupting inﬂuences of election betting from the Demo-
cratic side. See Pittsﬁeld Sun, 22 Oct. 1840, 2, for the slate of bets allegedly offered by
agents of the “British Whigs.”
96. David Bacon, “The Mystery of Iniquity: A Passage in the Secret History of American
Politics, Illustrated by a View of Metropolitan Society,”pt. 2, American Whig Review, July
1845; Calvin Colton, The Life and Times of Henry Clay, 2 vols.
(NewYork: A. S. Barnes,
1846), 2:443. The alleged frauds against Clay echoed in Republican charges against the
Tilden campaign in 1876. See Republican Campaign Textbook for 1880 (Washington,
D.C.: Republican Congressional Committee, 1880), 57.
97. MacKenzie, Life and Times, 205. Such messages were often mixed. In December 1838
Pennsylvania governor Joseph Ritner (Anti-Masonic party) had railed against the vogue
for election betting,“the very worst and most pernicious species of gambling ... a people
is preparing for despotism when it turns the elective franchise of its highest ofﬁces into
a mere subject of pecuniary speculation.” Atkinson’s Saturday Evening Post, 5 Jan. 1839,
2. But earlier in the election season the pro-Ritner Philadelphia newspaper the Penn-
sylvania Inquirer and Daily Courier, 20 Aug. 1838, offered to bet $10,000 in his favor in
the race for governor against David Porter. (For a counteroffer see Harrisburg Reporter
and State Journal, 21 Sept. 1838.) In this hotly contested election, which ended in the
so-called Buckshot War, the sum wagered purportedly totaled more than half a million
dollars. Colored American, 28 Nov. 1838.
98. New York Evangelist, 6 July 1839, 106; Christian Register and Boston Observer, 12 Dec.
1840, 200; Christian Reﬂector, 8 Aug. 1844, 125; Christian Inquirer, 27 Nov. 1858, 2.
99. The case involved a wager on the 1864 presidential contest. Cleveland Morning Herald,
8 Aug. 1871.
100. Altschuler and Blumin, Rude Republic, 71–72; North American and Daily Advertiser
(Philadelphia), 23 June 1840. In criticizing the “ridiculous, immoral, and pernicious
custom” of betting on elections, the Middlesex Gazette, 8 Oct. 1828, 2, noted that the
practice was “quite prevalent in many States, but it is unfashionable in New England,”
adding “long may it remain so.”
101. For examples of election betting in the 1850s see Mississippian and State Gazette
(Jackson), 25 June 1852; Vermont Watchman and State Journal (Montpelier), 21 Oct.
1852; the Pittsﬁeld Sun, 24 July 1856, and Bangor Daily Whig and Courier, 10 Nov.
1856.
102. Jesse W. Weik, The Real Lincoln: A Portrait (Boston, Houghton-Mifﬂin, 1923), 174–176.
103. Irish Times, 10 Oct. 1864, 4.
104. New York Times, 26 Oct. 1864, 4, 31 Oct. 1864, 43 Nov. 1864, 4, 5 Nov.1864, 4, 7 Nov.
1864, 4.
105. Charleston Tri-Weekly Courier, 31 Oct. 1868; North American and United States Gazette
(Philadelphia), 30 Oct. 1868.
106. The Teller (Lewiston, Idaho), 2 Dec. 1876.
107. Downtown hotels, including the Fifth Avenue Hotel on Fifth Avenue at Twenty-third
Street and the Windsor on Forty-six Street near where Jay Gould lived, were secondary
locations for trading stocks and bonds in the mid-1890s. New York Curb Market,
Committee of Publicity, 1929, 9.

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585
108. New York Times, 26 March 1910, 16.
109. New York Times, 10 Nov. 1906, 1; 29 May 1924, 21; 4 Nov. 1924, 2; Wall Street Journal, 29
Sept. 1924, 13. New York Times, 9 Nov. 1916, 3. For the long tradition of election betting
see New York Herald Tribune, 2 Nov. 1940, 23.
110. One indication of the predominance of election betting in the United States during
this period comes from across the Atlantic. In response to the appearance of a news
item about the betting odds on a 1908 by-election involving Winston Churchill, the
Manchester Guardian (8 May 1908, 8) complained “we have deﬁnitely adopted the
bad American custom of studying the betting as a guide to a forecast of election
results.”
111. Wall Street Journal, 8 June 1912, 5. In May 1924 both the New York Stock Exchange and
the Curb Market passed resolutions barring their members from engaging in election
gambling. Again, in late 1927, both exchanges blocked the use of“when issued”contracts
to discourage gambling. Wall Street Journal, 23 Dec. 1927, 11.
112. New York Tribune, 30 Oct. 1908, 1. See also New York Times, 22 Oct. 1909, 1; 11 July 1912,
10; 18 July 1912, 1. Regarding changes in commission rates see the New York Tribune, 30
Oct. 1908, 1.
113. Two of the three (Fried and Darnell) in fact were owned jointly by Samuel Solomon
(aka Sam Boston) and the Silinsky brothers (Abraham, Frank, William). Although the
newspapersoftenreferredtotheoddsasquotationsfromtheCurb,thelinkswiththeNew
YorkCurbExchangewereinformalatbest. FrankSilinskydidhaveaseatontheExchange,
and Richard C. Fabb, an early publicist for the market, also worked for the Fried ﬁrm
over the mid-1920s. “Bets to Exceed $5,000,000,” New York Times, 31 Aug. 1924, 3.
114. Claude Everett Robinson, Straw Votes: A Study of Political Prediction (New York:
Columbia University Press, 1932); Louis Bean, How to Predict Elections (New York:
Knopf, 1948); Susan Herbst, Numbered Voices: How Opinion Polling Shaped American
Politics (Chicago: University of Chicago Press, 1993), 69–88; Thomas B. Littlewood,
Calling Elections: The History of Horse-Race Journalism (Notre Dame, Ind.; University of
Notre Dame Press, 1998), esp. 42–45, 85–10, and 113–119.
115. New York Herald, 5 Nov. 1916, 1.
116. Polling the Nations, “A Brief History of Polling,” presents a “potted” history of these
events; http://poll.orspub.com/static.php?type=about&page=briefhistory.
117. New York Times, 8 Nov. 1940 14; 4 Aug. 1942 1; New York World-Telegraph, 11 Oct. 1944.
Doyle retired and then died; Boston left the business after a close associate was killed as
a result of a double-cross.
118. New York World-Telegraph, 11 Oct. 1944, which includes an analysis of why wager-
ing in New York City on the 1944 Dewey–Roosevelt election contest “was extremely
quiet.” For coverage of La Guardia’s intensiﬁed wartime campaign against gambling
and vice see New York Times, 18 Jan. 1943, 17; 21 June 1943, 1; 4 Dec. 1943, 16; 18
Dec. 1943, 17.
119. Warren Moscow, The Last of the Big-Time Bosses: The Life and Times of Carmine De Sapio
and the Rise and Fall of Tammany Hall (New York: Stein & Day, 1971), 24; New York
Journal American, 18 Aug. 1944; New York News, 1 Nov. 1944.
120. E. Leslie Gilliams, “Election Bets in America,” Strand Magazine, February 1901, 185–
191. For an examination of freak bets as rituals see Mark Brewin, “The Freak Bet and

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prediction markets and political betting
the Performance of the Democratic Paradox,” Communication Review 9, no. 1 (2006):
37–62. Irish Times, 9 Feb. 1901, 9.
121. London Daily News, 5 July 1871. See also New York Times, 3 Dec. 1887, 1; 28 June 1894,
1; 18 Jan. 1895, 1. The 1887 article highlighted “the large number of betting agencies
started in the streets near the Chamber” of Deputies in Paris.

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## Page 608

s e c t i o n vii
........................................................................................................
LOTTERIES AND
GAMBLING
MACHINES
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chapter 30
........................................................................................................
THE EFFICIENCY OF
LOTTERY MARKETS
........................................................................................................
david forrest and o. david gulley
Introduction
.............................................................................................................................................................................
Each day millions of people around the world spend the equivalent of millions of
dollars on various lottery games. In many jurisdictions, a clear majority of adults buy
tickets (59% in the United Kingdom, according to Wardle et al. 2011). So many people
purchase such tickets that, in 2010, worldwide sales of lottery games reached about
$245 billion.1
Why do so many people play lottery games? At ﬁrst glance it does not seem rational to
buy a ticket to a game which nearly always features an expected value of much less than
the price of the ticket, where the odds of winning the large prizes are extremely long,
and where the vast majority of players in a given drawing do not win any type of prize.
Other forms of gambling, such as horse racing and casino games, offer a much higher
expected value, relative to the price of playing, far higher odds of winning prizes, and
a larger proportion of bettors winning at least a small prize. Above and beyond these
advantages, other forms of gambling usually offer obvious non-pecuniary beneﬁts to
the players, such as the fun and excitement of watching a race or competing against
other players or the attraction of a convivial venue.
So why do so many people play? A possible reason is for investment purposes. Lottery
games offer generally poor payouts in that takeout rates are around 50% as compared to
casino-type games, which offer payouts of around 90 percent or even higher. Moreover,
the vast majority of bettors win nothing. The investment motive for play thus does
not appear very attractive at ﬁrst glance. Yet one type of lottery game—lotto—offers a
potential return of millions of dollars on an investment of pocket change and is the only
route to vastly higher wealth for most people. Paying such high grand prizes generally
implies a high degree of skewness in the returns. As discussed below, skewness is often
a desired feature of a variety of gambling opportunities.

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lotteries and gambling machines
Another reason people play lottery games is for the fun and entertainment involved.
While it is not as obvious as with other forms of gambling (consider the exciting
atmosphere of a racetrack, for example), lottery games do offer their own form of
non-pecuniary beneﬁts. As noted by Jonathan Simon (1998b), when players buy lotto
tickets to a game with a massive jackpot, they are buying a dream. Thus for up to
a few days players can daydream about how they would spend the winnings, what
they would tell their boss at work, and so forth. Lotto tickets are also quite cheap and
convenient to buy. In the United States, for example, there are around 150,000 sales
outlets that sell state lottery tickets (Matheson and Grote 2005). These outlets are in
grocery stores, convenience stores, gasoline stations, and other similar outlets. Further,
proceeds of lottery games are often designated for spending on such things as education,
recreation, arts, and so on Players may value supporting these endeavors.
A third explanation for lottery play, irrationality on the part of bettors, will be dis-
cussed below. Appealing to player irrationality to explain the existence of a $245 billion
industry is, well, unappealing. We contend there is sufﬁcient evidence for the behavior
of lottery players being consistent with rationality that there is no necessity to resort to
the story that they must just be “stupid.” In short, there must be some good reasons
why people spend so much money on lottery games.
Assuming that players are rational utility maximizers, the combined utility from the
investment and entertainment components are enough to induce many people to play
lottery games. This chapter is concerned with how players use information relevant
to lottery games. As detailed below, such information includes the odds of winning a
particular game, the value of prizes, how prizes are distributed across winning tickets,
howotherplayersbehave,andthealternativegamblingoptionsthatcompeteforplayers’
money.
Why is it important to understand bettor behavior with regard to lotteries? First,
state-sponsored lottery games continue to expand both in terms of the number of
games offered by each state and by the number of states offering games. Expansion of
lottery games is driven by the revenue generated from lottery games. Second, lotteries
have been heavily criticized on moral, ethical, and policy grounds for taking advantage
of ill-informed consumers who do not understand the true odds of winning and how
little money (relative to other forms of gambling) is returned to players as prizes.
Finally, the nature of lottery games offers economists an excellent opportunity to study
decision-making under uncertainty and how consumers process relevant information
in making playing decisions. Our focus will be on the extent to which lotto games are
efﬁcient because, as discussed below, lotto games offer several particularly interesting
features.
An Example of a Typical Lotto Game
To win the grand prize in a typical lotto game a player buys a $1 ticket (or the local
equivalent of a modest, round sum of money). To win the grand prize jackpot players

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the efficiency of lottery markets
591
must correctly match 6 numbers drawn randomly without replacement from, say,
49 numbers. This is called a 6/49 game. Smaller prizes are awarded for matching fewer
than six numbers and, sometimes, a bonus number. Lottery operators retain around
ﬁfty percent of each dollar bet (give or take 10%), some of which covers operating costs
and the rest of which is turned over to the state.2
Lotto games are a pari-mutuel game,which means that there can be multiple winners.
Winning ticket holders share equally in the grand prize. If the jackpot is not won on
a given draw, the jackpot is rolled over into the jackpot of the next drawing. Multiple
rollovers over several draws can create very large jackpots. Smaller prizes are also
(usually) pari-mutuel, but there is almost never a rollover for smaller prizes because
the odds are low enough so that smaller prizes are nearly always paid out.
In deciding whether to purchase a lotto ticket for a given drawing, a potential bettor
is confronted with a complex probability problem. To evaluate whether or not the bet
is utility maximizing, the bettor must evaluate the characteristics of the ticket. These
include the cost and convenience of buying the ticket along with the expected value,
risk, and skewness of the returns to the gamble.
Although betters in general may not know how to calculate the expected value of a
ticket, they are aware that, as the jackpot grows, a larger payout is available with no
change in the relevant probabilities. Thus they perceive that the value for money (i.e.,
the expected value) of a wager has been increased. In fact, demand modeling exercises
track drawing-by-drawing sales closely when they model sales as a function of expected
value, so it seems reasonable to assume that potential players behave as if they make
decisions based on expected value where expected value is serving as a proxy for buyer
perception of value for money.
The expected value of a $1 lotto ticket depends on several factors: the structure of the
game, the amount of the previous jackpots (if any) rolled over into the current jackpot,
and the number of tickets purchased in the current drawing. Generally, the expected
value is:
EV = [p]∗[JACKPOT]∗[SHARE] + EVs,
(30.1)
where p is the probability of winning the jackpot, JACKPOT is the value of the jackpot,3
SHARE is the expected proportion of the jackpot a winner will keep, and EV s is the
expected value of smaller prizes.
As can be seen from the equation above, to calculate the expected return on a ticket
bettors must understand (or at least act as if they do) the probabilities of winning the
various prizes, how sharing the jackpot might affect the expected value, and how the
smaller prizes contribute to the expected value.
From equation (30.1), we can see why lotto games are conducive to testing for efﬁ-
ciency. First, the structure of the game is such that bettors have a lot of the information
required to compute the expected value. The probabilities of winning the various prizes
are known. The size of the jackpot is not known perfectly because it depends on how
many tickets are purchased. However, bettors do know whether the previous jackpot

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lotteries and gambling machines
has been won or not. If it has not been won, then they know the value of the rollover
amount. Players have previous draws from which to infer the implications of a given
rollover for the size of the jackpot, and in any case, many lottery operators also pro-
vide an estimate of the size of the jackpot.4 Second, rollovers can cause jackpots to
skyrocket into the hundreds of millions of dollars. As shown below, large jackpots
raise the expected value of the typical lotto ticket, but the entry fee remains the same.
The variation in expected value caused by rollovers allows economists to examine how
players change their behavior in response to new information. Third, lotto games are
pari-mutuel in that players share the grand prize and most of the smaller prizes. This
feature requires bettors to use information about, and forecast the behavior of, other
players. Fourth, the value of the asset (the ticket) has a known value once the drawing
takes place—many ﬁnancial assets do not have known terminal values, which makes it
more difﬁcult to assess the ﬁnal outcome of participants’ decisions. Finally, data from
many lotto games around the world are available so that researchers can examine the
behavior of players in many settings.
Victor Matheson (2001), among others, has developed a more formal equation for
the expected value of a single ticket for a given drawing:
EV =
i wiVi +

AV j

1 −e−Bwj
B

(1 −θ) +
i wi + wj

θτ
(30.2)
where wi and wj are the probabilities of winning non-jackpot prizes and the jackpot
prize,respectively; V is the various values of the non-jackpot prizes; AV is the advertised
jackpot prize; B is the number of other ticket buyers for the drawing; θ is the marginal
tax rate on any winnings; and τ is the price of the ticket.
If players are risk neutral the expected value would be enough to inform the play-
ing decision. Risk neutrality for a population of gamblers does not seem a plausible
assumption, however. Players also will likely consider the risk of the gamble, loosely
deﬁned as the chance of winning nothing. If lotto players were strictly risk averse and
cared only about the expected value and risk, then explaining why otherwise rational
people play lotto games would be rather difﬁcult. Players could have Friedman–Savage
utility functions and be risk loving for increases in wealth offered by lotto games. This
would imply a preference for positive skewness, such as would be associated with high
jackpots. The attraction of skewness, referring to how the expected value is distributed
across various levels of prizes, potentially outweighs the negatives of low expected value
and high risk. Lotto games feature a very high level of skewness compared to other lot-
tery games and to other gambling opportunities in that a disproportionate share of the
prizes is very large and paid out to a very few grand prize winners. While we will not
write them down here, the equations for these expressions are also complex. Do players
use appropriate information and act as if they understand how the expected value, risk,
and skewness of lotto games are determined?
Overall, lotto games offer one of the cleanest available avenues to test for efﬁciency
in the processing of information by economic agents in the market for a ﬁnancial asset.

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the efficiency of lottery markets
593
If lotto players can process relevant information efﬁciently, then, since most other
ﬁnancial markets are conducted among investment specialists, there is at least a chance
that participants there can do likewise.
Do Players Behave Rationally?
Efﬁcient processing of information will result in efﬁcient functioning of markets only
if the behavior of economic agents, lottery players in this case, is underpinned by
rationality.5 By rationality we mean that players act in generally predictable ways that
are consistent with economic theory and behavior in other markets. The demand for
lottery games is examined later in this section (see “The Economics of Lotteries: A
Survey of the Literature,” by Kent Grote and Victor A. Matheson). Some of the results
from lottery demand studies are relevant here, though, because they demonstrate ratio-
nality in various dimensions of behavior. First, demand curves for lotto games slope
downward. That is, as the effective price of a ticket declines the quantity demanded
increases. Effective price, deﬁned as the price of a ticket less the expected value, declines
when jackpots rise. Thus bettors bet more given a larger jackpot. While the estimates of
price elasticity vary somewhat, the results are overwhelming consistent with a down-
ward sloping demand curve. Levi Pérez (2011) has provided a thorough review of
the literature. Second, demand is positively correlated with income—lotteries may be
said to be weakly regressive from the viewpoint of assessing impact on income dis-
tribution, yet ceteris paribus measures of income elasticity tend to be positive. Third,
the introduction of alternative gambling opportunities tends to affect betting on lot-
tery games. Fourth, lottery players substitute away from other betting opportunities
when the relative effective price of a lotto ticket falls.6 Fifth, people buy more lottery
tickets if transaction costs decrease.7 Finally, bettors seem to have stable preferences
in that they prefer less risk (i.e., are risk averse) and greater skewness (to a point,
at least).8
In sum, a large literature shows that lottery players act in ways consistent with ratio-
nal behavior and in ways that are consistent with other consumer goods. Such behavior
indicates that players process available information and change their behavior in pre-
dictable ways when new information becomes known. We now turn to the main focus
of the chapter: are lottery markets efﬁcient? Efﬁciency is one step beyond rationality
and requires even more sophisticated behavior on the part of players. For example,
rational players will increase lotto play in response to a larger expected value. Efﬁciency
requires bettors to act as if they understand equation (30.2) above.9
Do Players Use Information Efﬁciently?
It is crucial for properly functioning markets that available and relevant information be
correctly evaluated and used by market participants when making buying and selling

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lotteries and gambling machines
decisions. Markets usually contain incentives for participants to exploit information.
Markets do not work well in allocating scarce resources with, for example, asymmetric
information, little or no information available, or when participants do not act cor-
rectly on relevant information. Moreover, as pointed out by Ian Walker (1998) and
David Forrest, O. David Gulley, and Robert Simmons (2000), studies of demand for
lottery products implicitly assume that lottery markets are efﬁcient. Financial markets
are said to be efﬁcient when relevant information is incorporated into the price of
the asset. Not surprisingly, most of the academic literature on market efﬁciency uses
ﬁnancial markets as testing grounds. Financial markets offer easily available data (trad-
ing volume, high-frequency bid/ask prices, news that may affect asset prices, etc.) and
incentives for market participants to exploit available information (the ability to earn
abnormal proﬁts above and beyond a normal risk-adjusted rate of return). The general
ﬁnding is that ﬁnancial markets are weak form efﬁcient (asset prices fully reﬂect all
past price data), mostly semi-strong form efﬁcient (asset prices fully reﬂect all publicly
available information), and usually not strong form efﬁcient (asset prices fully reﬂect
all information, including inside information). Many anomalies to efﬁciency are found
but often are difﬁcult to exploit.10
How can these notions of ﬁnancial market efﬁciency be applied to lotto markets?
RichardThalerandWilliamZiemba(1988)haveprovidedastartingpointforanswering
this question. Weak form efﬁciency is deﬁned by the average ticket not having a positive
net expected value (i.e., the price of the ticket is greater than the expected value from
equation (30.2)). Strong form efﬁciency is deﬁned as all bets having an expected value
of 1−t, where t is the takeout rate. Lotto games are overwhelmingly found to be weak
form efﬁcient. Grote and Matheson (2006) studied over 18,000 lotto drawings in the
United States and found very few instances where the average ticket had a positive net
expected value. In other words, lotto players, when faced with large jackpots due to
rollovers, tend to increase betting to beyond the point at which the expected value of
the average ticket is driven below the price of the ticket.11 Equation (30.2) shows that
the reason for this result is that, while the increase in sales will increase the size of the
jackpot, the likelihood of more winners sharing the jackpot also increases. The latter
effect becomes more dominant as sales increase.
However, lotto games are not strong form efﬁcient by Thaler and Ziemba’s deﬁnition.
There are two reasons for this ﬁnding. First, as discussed in detail below, players
often do not play randomly chosen combinations; some combinations are heavily
played and others are lightly played or not played at all in a given drawing. Tickets
for the former combinations will have relatively low expected values, whereas tickets
for the latter combinations will have higher expected values. Thus different bets in
the same draw have different expected returns, a violation of strong form efﬁciency.
Second, across different drawings, by equation (30.2), the expected value of a lotto
ticket approaches 1−t as sales rise. “Approaches” is the key word. As equation (30.2)
shows, rollovers will increase the expected value at a normal level of sales, typically
to higher than 1−t, but then the resulting increase in sales will work to reduce the
expected value back toward 1−t. However, expected value will not fall all the way

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the efficiency of lottery markets
595
back to 1−t (i.e., sales will not increase enough) since, as expected value closes in on
1−t, marginal players would decline to play because the lotto would offer a relatively
unattractive bet.12
In one sense therefore, lotto markets cannot be fully “efﬁcient” since some draws
(rollover draws) offer higher expected rates of return than others (non-rollover draws).
But Frank Scott and Gulley (1995) developed a method to test for a form of efﬁciency
using the concept of a rational expectations equilibrium. In markets where participants
must forecast the future (and/or some other unknown(s)) the market is said to be in
rational expectations equilibrium when the expectations of market participants match,
on average, the actual outcomes. Rational expectations equilibrium of course does not
imply perfect forecasts but, rather, that the forecasts are unbiased and that any forecast
errors are not serially correlated.
Scott and Gulley examined four lotto games in three states (Kentucky, Massachusetts,
and Ohio) and proceeded in two stages. In the ﬁrst stage they calculated the expected
value of tickets in each drawing using the equivalent of equation (30.2) and then
regressed this expected value on all data available to bettors at the time bets are placed.
The data included the value of the rollover (and in the case of the two Massachusetts
lotto games the estimated value of the jackpots), a time trend, and assorted control
variables.
In the second stage the difference between the actual and ﬁtted expected values from
stage one were regressed against actual ticket sales. If bettors correctly forecast sales
using available information, then ticket sales should be uncorrelated with the forecast
errors. The authors found that bettors, on average, correctly forecast sales and that a
rational expectations equilibrium exists.
In studies of ﬁnancial market efﬁciency trading volume (of shares, contracts, cur-
rency units, etc.) is often used as a proxy for information ﬂow in the market. A higher
volume of trading indicates more information ﬂow, as indicated by buying and selling
orders. Each of these orders represents a buyer’s or seller’s views about whether or not
the asset is appropriately priced. In lotto markets, trading volume would be represented
by ticket sales. More sales would of course indicate the view that the particular drawing
was a good deal in terms of an investment and/or entertainment. In ﬁnancial markets
noise traders are those who trade on little or no information. A sufﬁcient number of
noise traders can cause ﬁnancial asset prices to deviate from efﬁcient values. Is there
an equivalent problem with rollover drawings? Are those who buy extra tickets sold
in a rollover noise traders, caught up in the excitement, who act without really under-
standing the nature of the bet and the expected value of the ticket? Thus we may see
deviations from efﬁciency in rollover drawings. Scott and Gulley’s ﬁndings suggest that
this is not the case.
It is also possible that inefﬁciencies could be observed early in the history of a new
lotto game, as players have not yet had much experience with the game. Forrest, Gulley,
and Simmons (2000) replicated Scott and Gulley’s (1995) ﬁndings for the U.K. National
Lottery and showed that the U.K. National Lottery market is efﬁcient in the sense of
conformity with rational expectations. They also examined how quickly bettors learn

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lotteries and gambling machines
the rules of the game, ﬁnding that efﬁciency is achieved with the ﬁrst 30 weekly draws
of the lotto game. Thus they found little evidence that inexperienced players cause the
lotto market to be inefﬁcient.
Consider one last test of the efﬁciency of lotto markets. U.S. state lotteries pay out
jackpot winnings in annuities and advertise the undiscounted sum of the annuity pay-
ments. Advertised jackpots are therefore larger than the present value of the jackpot.13
Are buyers fooled by this behavior? That is, by manipulating the nature of the annuity
to increase its nominal value do players react by increasing their purchases of tickets?
Matheson and Grote (2003) found that players are not fooled. They analyzed ﬁve states
(California, Florida, Georgia, Virginia, and Washington) that lengthened the annuities
associated with jackpot. This of course allows the lottery operators to advertise larger
jackpots. The authors used Scott and Gulley’s concept of rational expectations equi-
librium in lotto markets to examine the periods before and after the annuity change.
By doing so, Matheson and Grote tested whether or not bettors adjust their forecasts
of expected value to account for the lengthened annuity period. They found that in all
ﬁve states the residuals from the expected value equation were uncorrelated with actual
sales after the annuity period change, indicating that players acted as if they were able
to adjust their expected value forecasts. Such behavior is strong evidence of efﬁcient
use of information on the part of players.
Efﬁciency in Other Lotto Games and Other
Forms of Gambling
For the reasons discussed above, this chapter focuses on lotto games. Other lottery
games can also provide insight into player rationality and market efﬁciency. Daily num-
bers games offer prizes for correctly matching a randomly drawn four-digit (usually)
number. Prizes may either be ﬁxed or pari-mutuel. For ﬁxed-prize games, daily lottery
game players have no incentive to choose unpopular numbers, and as a consequence
they tend to concentrate their number choices as shown by Herman Chernoff (1981)
and Charles Clotfelter and Philip Cook (1989). Clotfelter and Cook compared the dis-
tributions of numbers played in the Maryland and New Jersey daily numbers games.
Maryland’s game features ﬁxed prizes while New Jersey’s game is pari-mutuel. They
found that the distribution of numbers played by New Jersey players is much more
uniform than that of Maryland players. This is strong evidence that at least some play-
ers in New Jersey understand the costs of playing popular numbers. Players of daily
games also demonstrate the gambler’s fallacy. Clotfelter and Cook (1989) noted that in
the Maryland daily numbers game the winning number for the most recent draw sees
a steep drop-off in the number of players choosing it. Play of that number does not
return to normal levels for several months. However, the behavior of Maryland players
is not irrational because avoiding recent winning numbers does not cost them anything
because the prizes are ﬁxed, not pari-mutuel.

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the efficiency of lottery markets
597
Instant games offer payouts for correctly matching a certain number of images that
are revealed after a player scrapes away the opaque covering on a playing card (thus they
are also called scratch-off games). Lottery operators offer a variety of instant games at
any one time. In these games a ﬁxed number of tickets are printed and distributed to
lottery retailers. Prizes are randomly distributed throughout the printed tickets. Grand
prizes may be quite large—one U.K. instants game offered a top prize of £1 million
a year for the rest of the winner’s life. Given the structure of the game, the odds of
winning the grand prize can change over the life of the game as winning tickets are
purchased. If the large prizes are won quickly, then the odds of winning those prizes
of course fall to zero. But if the large prizes are not won quickly, the odds of winning
improve as more tickets are sold. Some states do not publish how many winning tickets
have been claimed. This behavior has led to a least one lawsuit.14 In a technical sense,
efﬁciency is certain to be violated in this case because the expected value of a ticket
varies according to when in the life of the game the ticket is purchased.
We end this section with a brief discussion of the efﬁciency of non-lottery gambling
markets. There is a large literature on the efﬁciency of other gambling markets. See
Vaughan Williams (2005) and Hausch and Ziemba (2008) and the citations therein.
While it is somewhat difﬁcult to draw conclusions from the large and disparate litera-
ture, the general ﬁndings seem to be that participants in non-lottery gambling markets
do tend to process information rationally, and often efﬁciently, even though the nature
of the bets is more complex than for lotto games. There are, though, a number of
exceptions to the general conclusion of efﬁciency. For example, one of the best docu-
mented anomalies is the favorite-long shot bias, where bettors overbet long shots and
underbet favorites. This behavior could of course be interpreted as evidence that at least
some bettors are acting irrationally. However, consistent with our discussion above, the
act of betting on a long shot (even when bettors know perfectly well it almost surely
will not pay off) could bring sufﬁcient utility to bettors to warrant being described as
rational behavior. Consider the years of stories that a successful long shot bet would
allow the winner to tell friends. Love of skewness might also make such bets attractive
for ﬁnancially oriented bettors. Further, once transaction costs are accounted for, many
of the reported inefﬁciencies and the implied trading rules offer little or no potential
proﬁt.
These ﬁndings are important in our context because they are broadly in line with
the results for lottery games, indicating consistent behavior across various types of
gambling opportunities.
Deviations from Efﬁciency
The literature on ﬁnancial market efﬁciency documents deviations from efﬁcient out-
comes. The common feature of these deviations is the potential to earn abnormal
proﬁts (proﬁts above those expected for a given level of risk) using a trading rule. For
example, the trading rule for the January effect, which holds that stock prices have a net

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lotteries and gambling machines
tendency to increase in January, would be to buy stocks in December and then sell at
the end of January. Repetition of this rule could conceivably generate abnormal returns
over time. For our purposes, are there trading rules (i.e., consistent actions on the part
of players) that could be employed to earn abnormal proﬁts in lotto games?
First, consider the ﬁndings above related to positive expected values of lotto tickets.
The point of the discussion is that such occurrences are very rare, hard to predict
based on available information, and becoming less frequent. Moreover, even if positive
expected value drawings could be identiﬁed, it would take a large initial stake and
perhaps millennia to have a realistic hope of making a proﬁt. See Haigh (2008) for a
detailed example. As we pointed out above, the risk and skewness of returns also are
important. Efﬁciency conditions are not violated if players decline a bet with a positive
net expected value if they dislike risk and the skewness is too extreme. Consider the
case of the Lotto Extra game offered by the U.K. National Lottery from 2000 to 2006. It
was a standard 6/49 game that offered only one prize—the jackpot. Moreover, to enter
the game, players had to ﬁrst buy a ticket to the main lotto game. Despite the fact that
the Lotto Extra game held many positive net expected value drawings (several times
offering expected returns of more than 50%), sales dwindled as week after week no one
won anything. But this is not evidence of inefﬁciency since players looked at risk as
well. (See Forrest and Alagic 2007 for a discussion.)
Second, consider lotto mania as examined by Michael Beenstock and Yoel Haitovsky
(2001). Lotto mania is said to occur when rollovers have their own impact on lotto
sales, even when controlling for the size of the announced jackpot. Using the Israeli
lotto game (the structure of which has undergone a number of changes), the authors
found that lotto mania tends to occur after three consecutive rollovers. Such behavior
would seem inconsistent with efﬁciency because the authors control for the size of
the jackpot such that the rollover should contain no new information for players to
exploit. The trading rule here would be to avoid drawings that seemed manic because
the potential is for the mania to drive down the expected value of a ticket. Yet by buying
a ticket a player has secured a very cheap entry pass into“part of the excitement.”In such
circumstances the value of the entertainment (dream) component of the lotto ticket
may be enhanced, making ticket purchases more likely. Matheson and Grote (2004)
also investigated the related idea of “Lotto fever” whereby the increase in sales caused
by a rollover actually reduces the expected value of a ticket (i.e., players overbet). The
authors examined nearly 18,000 lotto drawings in the United States and found only
11 examples of such behavior, all involving relatively large jackpots. Matheson and
Grote also found that lotto fever examples became less common over time. So while
lotto mania may exist, players generally do not seem to overreact to the point that the
resulting bet is a relatively poor one in terms of expected value.
Third, “jackpot fatigue,” also discussed by Beenstock and Haitovsky (2001). Jackpot
fatigue is thought to be a possible consequence of lotto mania: over time it takes ever
larger jackpots to induce a given level of sales. Such behavior may be due to bettors
becoming accustomed to particular levels of prizes, and so it takes ever larger prizes
for them to increase purchases. Beenstock and Haitovsky found evidence for jackpot

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the efficiency of lottery markets
599
fatigue but also showed that it wears off (i.e., bettors return to their old levels of
responsiveness) after several months. Matheson and Grote (2004) also found evidence
of jackpot fatigue for U.S. state lotteries.
Fourth, the halo effect, as examined in Matheson and Grote (2007), occurs when
sales rise for the drawing after a large rollover-induced jackpot is won. Other things
being equal, the expectation would be that after a large jackpot is won sales will return to
pre-rollover levels. One explanation for the halo effect is that publicity surrounding the
large jackpot make people more aware of the lotto game and thus generates an increase
in sales even though the expected value is now relatively low. Another explanation is that
new players, drawn in by the large jackpot, continue to play once the jackpot is won. The
authors used the U.S. Powerball lotto and found evidence of a halo effect. They found
that past jackpots did not offer any improvement to forecasts of sales, which rebuts the
publicity explanation. They did ﬁnd that past sales help forecasts of sales but that the
effect fades quite rapidly. This suggests that new players have not become addicted to
the lotto game. The authors offered a third, and more likely, explanation of the halo
effect. Smaller prizes can be claimed from lottery retailers. Since sales of a rollover-
induced jackpot are relatively high, when the jackpot is won many more than the usual
number of small prizes also are won. These players cash in their winning tickets and
reinvest a portion of their winnings in tickets for the next lotto drawing. Such behavior
is rational because transaction costs are low (players are already at the retail outlet).
Also, as long as players do not overbet as previously described, the behavior is consistent
with efﬁcient behavior.
Fifth, do players really care most about the expected value of a ticket when making
playing decisions? Indeed, we have pointed out the difﬁculties presented for the average
player to work out equation (30.2). Do players really use expected value when making
decisions, or do they use some other, simpler method to make playing decisions? Cook
and Clotfelter (1993) and Forrest, Simmons and Neil Chesters (2002) argued that
expected value does not drive player decision as much as the size of the jackpot. This is
an appealing idea for several reasons. First, the jackpot is a well-known value that does
not require players to even attempt to estimate the expected value (or risk or skewness)
of a ticket. Second, very few people are motivated to play a lotto game just because
of the smaller prizes—everyone plays for the grand prize.15 Forrest, Simmons, and
Chesters (2002) estimated a two-stage demand model for the U.K. National Lottery
game in the spirit of Gulley and Scott (1993), and others, and found that using the
jackpot rather than expected value did a better job of ﬁtting the sales data. These results
suggest that it is the entertainment (dream) component of the utility function that is
relatively more important to players. If the investment component was very important,
then the expected value of smaller prizes would help explain lotto game sales. Beenstock
and Haitovsky (2001) discuss, but do not show, ﬁndings that suggest that Israeli lotto
players are not affected by changes in the odds of winning the grand prize. These
ﬁndings are consistent with Cook and Clotfelter’s (1993) and Forrest, Simmons, and
Chesters’s (2002) results. This begs the question: if jackpots matter and odds do not,
why do lottery operators around the world pay out smaller prizes—and lots of smaller

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lotteries and gambling machines
prizes at that? In the U.K. National Lottery, for example, the bottom prize (£10 for
matching three of six numbers) payout is higher than the jackpot payout. The Spanish
lotto pays out 10 percent of sales in the form of the smallest prizes, which are equal to
the entry fee; 10 percent of tickets are in fact randomly assigned this refund.
Finally, do lottery players choose their own numbers, or are they more apt to let the
computer choose random numbers for them? The answer to this question is not clear.
Lotto games universally allow players to let the lottery computer generate numbers for
them. But many players select their own numbers that may have personal signiﬁcance
and can easily be remembered and played over and over. Because players’ choices
of numbers are positively correlated with each other, this behavior can dramatically
reduce the expected value of a ticket with a popular combination relative to other
tickets. If at least some bettors choose numbers nonrandomly, then other bettors can
potentially improve their expected returns by playing unpopular combinations. Thus
perhaps the most interesting, and potentially compelling, deviation from efﬁciency
is the well-documented phenomenon of “conscious selection” whereby the selection
of numbers becomes correlated across players. Clotfelter and Cook (1989) provided
evidence that players of daily numbers games and lotto games do not pick their numbers
(and combinations) at random. Hal Stern and Thomas Cover (1989) examined the
Lotto 6/49 game in Canada, where the most popular numbers are 3, 7, 9, 11, 25, and 27
while the least popular are 20, 30, 38, 39, 40, 41, 42, 46, 48, and 49. George Papachristou
and Dimitri Karamanis (1998) studied number choice in the Greek 6/49 lotto, where
24, 13, 25, 9, 16, 36, and 3 are the most popular numbers and 47, 1, 43, 31, 21, 42, and 39
are the least popular. However, they concluded that playing even these numbers does
not offer a realistic hope of earning an abnormal proﬁt when such behavior leads to
positive net expected value wagers. Patrick Roger and Hélène Broihanne (2007) found
that the most popular numbers for the French 6/49 lotto are 7, 12, 9, 13, 11, 10, 8, 24,
and 25 and that the least popular numbers are 32, 41, 39, 40, 38, and 43.
Why do people pick numbers (and, by implication, combinations) that many other
people also play? Clotfelter and Cook (1989) offers a helpful starting point. The authors
cite “events and dates,” “personal lucky numbers,” and “numbers of convenience” as
methods people use to choose numbers that a lot of other people also end up choosing.
“Numbersof convenience”referstochoosingnumbersthatformapatternonthebetting
slip. They note the fact that the most popular combination in one of the Massachusetts
lotto games is formed by the left-to-right diagonal of the playing slip. Another reason
for nonrandom choice may be that players are unaware that others are also choosing
numbers nonrandomly, thus making it more likely that many people may end up
choosing the same combinations. Lottery players surely know that others are also using
birthdays and other such numbers as part of their combinations, though they may well
underestimate the actual number of people playing a particular combination. Players
may also think they are picking numbers at random but actually are not. For example,
Simon (1998a) noted the case when 133 people won the U.K. National Lottery jackpot.
He mapped the winning combination on to the playing slip for the game and found
that there was actually a pattern of play on the slip. People also may pick combinations

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601
that for them provide some level of utility—a combination of relatives’ birthdays or, as
Clotfelter and Cook (1989) put it, their own “personal lucky numbers.” These may be
easy-to-remember, rather than lucky, numbers—PINs used to access cash machines are
probably correlated across individuals even among the nonsuperstitious. Finally, there
could be underlying psychological reasons why people pick particular combinations.
This last reason opens the door for a brief discussion of the psychology literature related
to gambling and lotteries in particular. The reason for delving into the psychological
motivations for lottery gambling is that it is crucial to understand people’s motives for
playing the lottery, as these motives are in turn helpful in understanding how people
might react to available information that may inﬂuence the decision to participate and
also their level of play.
Simon (1998a) provides a detailed discussion of nonrandom number choice by
lotto players. He analyzed the combinations chosen for a single draw of the U.K. lotto
game. The U.K. National Lottery provided him with summary information about the
combinations played for the drawing held on October 19, 1996. Thus he has data on the
number of times each combination was played but not the numbers that make up the
combinations. In the lotto drawing that Simon exploits, about 87 percent of tickets sold
were to players choosing their own numbers. In contrast, Grote and Matheson (2006)
pointed out that about 70 percent of U.S. lotto players opt for random generation.16
Expanding on Clotfelter and Cook (1989), Simon discusses Ellen Langer’s “illusion
of control,”17 which, if accurate, would imply that bettors believe they have at least
a little control over their chances of winning if they pick their own numbers. Note
that even perceived control can generate player utility. Simon also discusses various
heuristics that people may use to help them make decisions under uncertainty. These
heuristics cause people to overestimate the likelihood of rare events, such as winning a
lotto jackpot. This behavior is consistent with prospect theory, as Cook and Clotfelter
(1993), among others, have noted.
As discussed above, we assume that people are rational, utility maximizers. Another
possible explanation is that people who play lottery games are acting irrationally, in
the sense that they don’t understand the odds of winning and are throwing money
away. Paul Rogers (1998) has provided a thorough examination of the psychological
underpinnings of lottery play. He noted several reasons why people may choose combi-
nations that many others choose as well. Indeed, Rogers discusses a large psychological
literature which argues that gambling (and maybe especially lottery gambling) is the
result of irrational beliefs on the part of players, citing in his argument many of the
motivations discussed by Simon (1998a). Rogers (1998, 115) argues that“... normative
accounts [such as utility from the gamble] provide a far from adequate explanation of
gambling habits, and in particular, that of lottery gambling.” He goes on to note that
“cognitive theories of gambling assume that the core beliefs of the regular gambler are
in some way ﬂawed.” An example of such behavior is the gambler’s fallacy, in which
events that are actually independent of one another are believed to be correlated. As
applied to lottery games this fallacy argues that players think that numbers (or com-
binations) that have been recently drawn are not likely to be drawn again for some

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lotteries and gambling machines
time. Conversely, numbers that have not been drawn in some time are “due.”18 Rogers
also argues that people generally do not have a good grasp of the objective probabil-
ities of winning various prizes, especially the jackpot. Reasonably, he points out that
for all intents and purposes people have no experience with one-in-fourteen-million
probability events and so have no real understanding of how truly unlikely it is to
win the jackpot. However, many players now have years, or even decades, of experi-
ence playing lottery and lotto games, so it is highly likely that they have learned over
time that it is really hard to win large lotto prizes even if they still do not understand
what a one-in-fourteen-million event truly is. This learning is one possible reason
why sales of most lotto games, controlling for other factors, tend to trend downward
over time.19
In effect, Rogers argues that gamblers often, or even usually, do not process rele-
vant information correctly. Rogers (and many others, of course) notes that lottery play
is most heavily concentrated among groups with relatively little education and those
employed in middle status occupations. Lottery play has a relatively low prevalence
among professionals. His arguments are consistent with the idea that those who tend
to play the lottery (or even gamble at all) are those unable to appreciate the nature
of the wagers they are placing.20 However, this conclusion is at odds with a great
deal of the observed behavior of lottery players as detailed above. Indeed, in situa-
tions where most players choose numbers randomly, many of Rogers’ arguments are
weakened.
The general conclusion is that some players choose their own numbers, and thus
combinations, that are not random but are somewhat predictable. Player choices seem
to be guided by a variety of factors, ranging from the design of the playing slip to false
beliefs about the nature of random numbers. If it was the case that such nonrandom
selection of numbers had little or no impact on expected values of tickets or any
other effect, then this behavior would not be very interesting. But it does in fact have
several effects. First, the nonrandom selection of numbers reduces the probability that
a jackpot is won and is instead rolled over to the next drawing.21 More importantly, if
players concentrate their bets on a relatively few combinations, those combinations will
have lowered expected values, and other, lightly played combinations will have higher
expected values. The magnitude of the impact on expected value can be very high.
Consider Simon’s (1998a) example that for the U.K. National Lottery “over 10,000”
tickets play the combination of 1, 2, 3, 4, 5, 6. Assume for the sake of convenience
that exactly 10,000 tickets choose this combination and, combining this ﬁgure with
the actual jackpot of about £11 million, that each player would win only £1,100 if that
combination is chosen. Given the probability of winning the jackpot of 1 in 13,983,816,
the expected value of the jackpot portion of the ticket is nearly zero, which, given the
prize structure of smaller prizes, leaves the expected value of the ticket at about 31 cents.
This compares to an expected value of well over one pound for a combination that only
one person (maybe at random) has chosen. In fact, 1, 2, 3, 4, 5, 6 is not even the most
popular combination for the U.K. National Lottery. That is 7, 14, 21, 28, 35, 42, and 49.
It is chosen “tens of thousands of times” per drawing (Simon 1998a).

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the efficiency of lottery markets
603
Note that in the literature on ﬁnancial markets deviations from market efﬁciency
generally do not hold up once taxes and transaction costs are accounted for. Moreover,
once information about the deviation comes to light, the potential for abnormal proﬁt
is generally eliminated, or at least greatly reduced, as market participants attempt
to exploit the inefﬁciency. In lotto markets deviations from efﬁciency are extremely
difﬁcult, and thus costly, to exploit. As discussed above, the ability of players to exploit
positive expected value situations is limited—players would need a very large initial
stake and millennia to have a reasonable chance at a positive payoff from the strategy
before suffering the fate of a gambler’s ruin.
Despite the costs that players incur when choosing numbers nonrandomly, as long
as the choice and/or the numbers themselves have sufﬁcient utility, then such behavior
is rational. It is not efﬁcient because relevant information is not being exploited.
Conclusion
.............................................................................................................................................................................
We examined the degree to which lotto markets are efﬁcient in processing informa-
tion available to market participants. While there are examples of inefﬁciencies to be
found, the ability to exploit these to earn abnormal returns is either severely limited
or nonexistent. Our conclusions are consistent with Matheson and Grote (2005, 2008)
and Ziemba (2008), who also discuss the degree of rationality and efﬁciency in lottery
markets. We conclude that lotto market participants act as if they understand the odds
of winning, the risk of losing, the skewness of the returns, and how the behavior of other
bettors inﬂuences the expected price of a ticket. We began this chapter by asking why
and how people play lottery games and argued these questions are closely related: why
people play affects how they play. Our ﬁndings are consistent with the notion that at
least some players are motivated, at least in part, by the investment component. Other
players are clearly motivated by the entertainment/dream component. Our ﬁndings
have implications for players, lottery operators, and public policy.
What are the implications of our ﬁndings for players? First, players can materially
improve the expected value of their tickets by choosing combinations that are not
popular with other players. Simon (1998a) and many others have shown that it is
possible for players to do better, in terms of expected value, by making sure that a
randomly selected combination contains unpopular numbers. A randomly selected
combination that happens to have popular numbers still may have a relatively large
number of other players. So while they cannot affect the probability of a win, they
can improve their payout if they do win. All the same, it is still quite difﬁcult to earn
abnormal proﬁts. Second, players should be aware of the behaviors of lottery operators
in terms of advertising and changing the structure of lotto games.
What are the implications of our ﬁndings for game operators? First, since lottery
players seem to act as if they understand the rules of the game, operators may be

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604
lotteries and gambling machines
insulated somewhat against the claim that they exploit unknowing and ill-informed
customers. Second, therefore, lottery operators cannot fool players with maneuvers
like changing the length of the annuity payment, so should not try to do so. Third,
because lottery operators have the incentive to not publish the actual combinations
that bettors play, and because some bettors themselves seem to have preferences for
particular numbers/combinations, there is a material risk that at some point a very
popular combination is going to win a major lotto game somewhere in the world.
Having hundreds, or even thousands, of winners, each expecting a large prize, could
be a public relations problem.22 To minimize the chance of this happening, it might be
worthwhile for lottery operators to consider publishing popular combinations. Lottery
operators, not surprisingly, are likely to resist this idea because doing so may lead
to fewer rollovers. In fact, Clotfelter and Cook (1989, 88–90) and Simon (1998a)
have pointed out that lottery operators actively encourage their customers to choose
numbers that are not random. Moreover, bettors may not be inclined to give up“their”
combinations, leading to entrapment. Entrapment occurs over time as players spend
more and more money on a particular combination fearing that if they stop playing it
that particular combination will be a winner. See Simon (1998a). On the other hand,
it is unlikely that bettors realize exactly how many other people play the most popular
combinations and thus how little they will actually pocket in the event they do win the
jackpot. Finally, our results suggest that the options for operators to increase sales are
somewhat limited. From above, tricks like changing the annuity length will not work.
Other, more feasible options include changing the face price of a ticket,23 decreasing the
takeout rate (increase the expected value), changing the odds of winning the jackpot,
or changing the odds/payouts of smaller prizes (alter the skewness of the game). There
are a variety of risks and limitations to pursuing these strategies. Walker and Juliet
Young (2001) discuss lotto design issues with an eye to how to maximize revenue. One
last option might be for a state to join a consortium of states in offering a long odds–
large jackpot game. Cook and Clotfelter (1993) found a positive correlation between
population and sales, implying room in the marketplace for such games. Indeed, these
games (Powerball, Mega Millions, and EuroMillions, for example) feature at times
massive jackpots that receive quite a bit of media attention. In relatively small market
areas, multistate games outsell the local lotto game.
What are the implications for public policy? Lottery operators, at the behest of
the state, usually act in ways that maximize revenue to the state. To what extent should
lottery operators (i.e., the state) act to maximize net revenues accruing from the lottery?
The focus on revenue maximization drives states to pursue behaviors that would not be
acceptable in the private sector or other forms of state activity. The proﬁt motive leads
states to encourage nonrandom number selection, play down the true odds of winning
large prizes, and aggressively advertise lottery games. This behavior can put states in
an awkward ethical position. For example, some U.S. states run liquor monopolies,
and they do not glamorize alcohol and exhort citizens to drink more, as is done in
the marketing of lottery products. Clotfelter and Cook (1990, 103) suggest several
alternatives to the revenue-maximizing lottery. One approach would “accommodate

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the efficiency of lottery markets
605
the widespread interest in betting on long shots without encouraging that interest.”
The other would “serve the interests of players as the players themselves deﬁne them.”
Either way removes the revenue imperative currently imposed on most lottery agencies.
Pursuing these objectives, rather than revenue maximization, and providing more
information to bettors in the form of greater disclosure of odds and combination
choice would work to insulate lottery operators from much of the criticism leveled
against lotteries.
Notes
1. See eLottery.com, www.elottery.com/markets.html.
2. Some lotteries are operated directly by the state, and others are run by private entities
under contract from the state.
3. Historically U.S. state lotto games have paid out the jackpot in an annuity and the lottery
operator has advertised the undiscounted value of the annuity as the jackpot. Thus in
examining U.S. lotto games the present value of the annuity must be calculated.
4. There has been no study of how well lotto operators forecast jackpots and, by impli-
cation, sales. Operators would have a short-term incentive to overestimate jackpots
in an attempt to increase sales. However, doing so can be damaging in the long
run. See “Texas lottery considers changing jackpot calculation,” LotteryPost.com;
www.lotterypost.com/news/114498.
5. In most markets researchers are interested in how well both buyers and sellers process
information. In lotto markets the seller (the operator) provides a perfectly elastic supply
of tickets regardless of the size of the jackpot. Thus the behavior of buyers will be
our focus. It is interesting to note, however, that lottery operators also seem to act in a
rational manner. As a rule, operators are required to maximize revenue to the state. There
are a number of game parameters that operators can choose (odds of winning various
prizes, how payouts are distributed across different prizes structures, etc.). They can
also choose the portfolio of lottery games offered (lotto games, daily numbers, instants,
etc.). In general the ﬁndings in the literature indicate that lottery operators act in a way
that is consistent with revenue maximization in that they structure the lotto game to
maximize revenue to the state and that the various games offered are not cannibalizing
one another, except for when multistate games are introduced into states with existing
lotto games. Levi Pérez and Forrest (2010) showed that Spanish lottery game cross-
price elasticities are fairly low, indicating limited cannibalization across games. Forrest,
Gulley, and Simmons (2004) found similar results for the U.K. National Lottery. Grote
and Matheson (2006) found that there is both a displacement effect (the introduction
of a new game causes players to reduce play on existing games) and a substitution effect
(the relative prices of games change, causing players to play games with the relatively
higher expected value) when multistate lotto games are introduced in states with existing
lotto games.
6. One strand of literature examines the displacement effects when a new form of gambling
is introduced to compete with an existing form of gambling. Donald Elliott and John
Navin (2002) and Stephen Fink and Jonathan Rork (2003) found that lottery revenue
for U.S. states has been cannibalized by riverboat and commercial (non-tribal) casinos,

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606
lotteries and gambling machines
respectively. Mehmet Tosun and Mark Skidmore (2004) concluded that lottery sales
in border counties typically fell substantially after neighboring states introduced large-
scale slot machine gaming facilities at racetracks. Note that the reverse is also true: the
introduction of lotteries can impact sales of other forms of gambling. Gulley and Scott
(1989) and Richard Thalheimer and Mukhtar Ali (1995) showed that the introduction
of state lotteries reduced betting on horse racing. Forrest (1999) reported a substantial
decline in the football pools following the introduction of the U.K. National Lottery.
Melissa Kearney (2005), though, found no effect of the introduction of state lotteries
on participation rates in betting and bingo. Another strand of the literature examines
substitution effects, when the price of one form or gambling changes relative to another.
Using monthly data from the U.K. tax authorities, David Paton, Donald Siegel, and
Leighton Vaughan Williams (2001) showed that aggregate betting tends to be lower in
months when the lotto game features high prize levels. Forrest, Gulley, and Simmons
(2010) found that large lotto jackpots had negative, albeit modest, impacts on horse
and football betting. Collectively these ﬁndings strongly suggest that gamblers do not
robotically participate in one or another form of gambling but rather actively and
consciously make playing decisions that are affected by relevant information.
7. It has been documented that lottery players reinvest some of the proceeds from winning
tickets. Small prizes can be claimed at lottery retailers so that transaction costs are
reduced(theplayerisalreadyattheretailer). SeeMathesonandGrote(2005)forevidence
of reinvestment of winnings. However, Forrest and Gulley (2009) found no evidence of
reinvestment of small prizes in the U.K. lotto game. This is also discussed further below.
8. See Walker and Young (2001). Bettor preference for skewness extends to other wagering
markets. See Golec and Tamarkin (1998).
9. Throughout this chapter we abstract from the question of the playing behavior of prob-
lem and addicted lotto players. Lotteries“do not tend to be addictive for adults”(Grifﬁths
1999).
10. Over the past several decades many challenges have been made to the efﬁcient markets
hypothesis, most notably arising from the relatively new ﬁeld of behavioral ﬁnance. See
Malkiel (2003) and Shiller (2003) for a discussion. Behavioral ﬁnance uses cognitive
theories in attempting to explain market inefﬁciencies.
11. When the expected value is greater than the price of a ticket there is incentive to“buy the
pot,”thatis,foraperson,orusuallyasyndicateof people,tobuyticketswithallof thepos-
sible combinations so as to ensure at least a share of the jackpot. Small-scale syndicates
are quite common among lotto players. The Internet allows for easy creation of larger
syndicates (see, e.g., www.global-lottery-syndicates.com/category/youplayweplay). A
syndicate attempted to buy up tickets to a May 1992 drawing of the Irish Lottery. For-
tunately, the syndicate did have a winning ticket but had to share the jackpot with two
other winners. Syndicates must buy each ticket separately—lottery operators do not
allow anyone to simply write a check to cover the purchase of all combinations. For
the July 12, 2011, drawing of the EuroMillions game, a rumor had a Russian syndicate
working to buy a large number of tickets. Matheson (2001) Grote and Matheson (2006)
discuss the possibility of buying a “trump ticket” (representing all combinations) in the
situation where the expected value is greater than the cost of a ticket.
12. It is not clear that Thaler and Ziemba’s concept of strong form efﬁciency is applicable
here because the expected value of a rollover drawing is greater than the expected value
of a non-rollover drawing for any ﬁnite level of sales. In a rollover drawing, expected

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the efficiency of lottery markets
607
value approaches 1−t from above, while in a non-rollover drawing it approaches from
below.
13. Winners do generally have the option to receive the present value of the jackpot in a
lump sum. European lotto games, on the other hand, pay out the jackpot prize as a lump
sum and therefore advertise this value as the jackpot.
14. See “Canada Lotto 6/49 faces lawsuit,” www.worldlottery.net/news/canada-lotto-649-
faces-lawsuit.asp. As information about the rate at which prizes in instants games are
being won is potential useful to bettors, websites have sprung up to help players keep
track of prizes won in instants games. See, for example, LottoCrawler.com.
15. This is not to imply that smaller prizes are irrelevant. See the discussion below.
16. Reasons for this difference in behavior are unclear. Perhaps relatively more U.S. players
are casual players who are more likely to choose numbers randomly. It also may be
the case that U.K. players have more gambling experience in general—the U.K. gam-
bling market offers far more betting opportunities than are available in the United
States. This experience yields a preference among players for choosing their own
numbers. Finally, the opportunity to choose their own numbers was not introduced
until March 1996, so most U.K. players had grown accustomed to choosing their own
numbers.
17. See Langer (1982).
18. Jonathan Guryan and Kearney (2008) investigated a variant of the gambler’s fallacy—the
“lucky store effect.”Using data from the Texas lottery they found that ticket outlets where
winning tickets for large prizes have been sold experience subsequent increases in ticket
sales that are far higher than for nearby stores. Guryan and Kearney speculated on why
players expect negative serial correlation in winning numbers and positive correlation in
the location of winning stores and came up with a number of possibilities, all involving
choicesmadebyhumans(wheretopurchaseaticket,astoreclerk“withgoodkarma,”and
others). The point is that bettors are potentially incurring higher costs (transportation,
etc.) without improving their chances of winning. Such behavior is at odds with rational
behavior.
19. For an amusing discussion of probabilities surrounding the July 12, 2011, drawing of
the EuroMillions game, which featured a £166 million jackpot with odds of 175 million
to one, see www.williamhillmedia.com/index_template.asp?ﬁle=10859.
20. Consistent with Roger’s views, the Internet is, to use the most appropriate descrip-
tion, littered with “how to win big on the lottery” sites. Many are in the business of
selling software that purportedly helps people win lotto games. Others perpetuate vari-
ous falsehoods regarding lotto games. See howtowinlotto.blogspot.com for examples of
gambler’s fallacy and other misconceptions regarding lotto games.
21. Farrell et al. (2000) found this to be true of the U.K. National Lottery game. They
estimated a demand function that accounts for nonrandom play and found that the
results with respect to the price elasticity of demand were not much different from
studies that have not accounted for non-random play.
22. In a 1990 interview, the director of the Massachusetts State Lottery said that having a
combination like 1, 2, 3, 4, 5, 6 win a lotto drawing would be a “nightmare.”
23. Pérez and Forrest (2011) discuss how sales of the Spanish lotto game were affected by
several changes in the nominal price of a ticket. It is quite infrequent, however, for lotto
games to change the price of a ticket.

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lotteries and gambling machines
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chapter 31
........................................................................................................
THE NATIONAL LOTTERY
........................................................................................................
john lepper and stephen creigh-tyte
Historical Background
.............................................................................................................................................................................
The ﬁrst National Lottery draw of the modern era took place on November 19, 1994.
However, since the time of Queen Elizabeth I, running a state-sponsored lottery has
been commonplace. Between 1566 and 1826, with a break between 1699 and 1710,
state-sponsored lotteries were held in England either under a separate act of Parliament
or by means of license from the sovereign.
The earliest state lottery in the United Kingdom was established in order to pay for
improvements in facilities at the Cinque Ports or for “... reparation of the havens and
strength of the Realme, and towards such other public good workes” (Ashton [1898]
2011, 223). This ﬁrst Lotterie Generall consisted of 400,000 lots priced at 10 shillings
each (the equivalent of £1,580 in 2009 currency) (Ofﬁcer and Williamson n.d.).1 The
lottery was advertised as having no blanks; that is, every ticket was to be paid a sum of
2 shillings and 6 pence (2s 6d) and have the chance to win a prize. In addition, those
purchasing 30 or more tickets would receive pensions in yearly amounts for the rest of
their lives (Ewen [1932] 1972). However, only about one-twelfth of the lots were sold
after more than two years. Thereupon, the conditions for the lottery were changed.
Only one-twelfth of the tickets drawn had prizes on them, and those that did were
one-twelfth of their originally designated value.2 The draw of all 400,000 tickets lasted
from January 11 until May 6, 1569. Prizes were generally of plate or precious objects.
The Lotterie Generall was thus a method of borrowing by the state and differentially
rewarding lenders by lot. The failure of the Lotterie Generall was such that the exercise
was not repeated by the government until 1694.3
These early lotteries had a ﬁxed number of tickets announced before the draw, and
the prize draw did not take place until all tickets had been sold. Drawing of prizes took
place in a public place, such as by the West Door of St. Paul’s Cathedral. There were
two variants on this general theme. In one type, called loan lotteries, there were no

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lotteries and gambling machines
losing tickets (blanks) and the draw determined the return (whether high or low) that
the subscriber to the debt obtained (Cohen 1953; Raven 1991). In the other type the
draw acted like modern-day rafﬂe in which there are winners and losers.
The demand for war ﬁnancing led to the resurrection of the State Lottery in 1694
(Cohen 1953; Williams 1956; Woodhall 1964). In the Million Adventure game, sub-
scribers (adventurers) bought a tontine annuity so that as each subscriber died his or
her annuity was divided among the survivors. Annuities paid 10 percent over 16 years
and were ﬁnanced by duties on beer and salt. In addition, there were 2,500 prizes total-
ing £40,000. Large prizes were given for the ﬁrst and last ticket drawn. £1 million was
raised by selling 100,000 tickets at £10 each (the equivalent of £15,300 in 2009 terms)
(Ofﬁcer and Williamson n.d.).
Tickets were sold in books and consisted of three perforated sections. One was
retained by the adventurer, one was kept in the book as a check, and the last was
rolled up, secured with a silk thread and placed in a box labeled A. A second set of
tickets (197,250 blank and 2,500 with prizes) was placed in another box marked B.4
On the day of the draw the boxes were taken to Guildhall in London, and two “dis-
interested and ﬁt” persons drew tickets from each box in turn (Williams 1956). In
1699, after the failure of the 1697 lottery in which only 1,763 of the 140,000 tickets
were sold, Parliament made lotteries illegal. Queen Anne restarted the State Lottery,
authorized by annual statute, in 1710. From then, until 1826 when it was abolished,
the general features of the State Lottery remained in place. Nevertheless, during
that period there many changes in the detail of the rules by which the lottery was
conducted.
The State Lottery was run by the Commissioners of the Lottery appointed by the
Treasury. As before, a loan of ﬁxed amount was raised by selling annuities issued by
the Treasury through the Lottery Ofﬁce. After 1726 lottery tickets were called Joint
Stock Lottery Annuities because the bearer of a ticket was entitled to cash the ticket for
the original share of the total proceeds less the annuity interest plus any other prize
(Ewen [1932] 1972, 144). This had the effect of removing the tontine element from
the annuities. Jacob Cohen (1953) showed that the yield on lottery annuities varied
between 1694 and 1784, when they were last issued, but for much of the eighteenth
century yields were around 3 percent. Subscriptions were invited through lottery ofﬁces,
the keepers of which were licensed after 1782. The prizes were of varying sizes and
were in addition to the annuity payments. An adventurer was, therefore, gambling
both on the size of the prize but also on his or her life expectancy (Cohen 1953).
Sometime in the eighteenth century it became the custom to employ a roster of pupils
from the Christ’s Hospital Bluecoat School as the “disinterested and ﬁt” persons who
undertook the drawings. A number was drawn from one drum by one boy, and the
associated prize or blank was drawn from the other drum by another boy. Results
were announced and noted by clerks who sat between the drums and subsequently
published.
In 1765 and 1769 and from 1785 lotteries reverted to the pure revenue-raising raf-
ﬂe type (Raven 1991). Tickets were no longer annuities, and prizes offered the only

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613
prospect of gain to adventurers. Moreover, after 1788 the agent system was abandoned
and the Treasury sold all lottery tickets to contractors or stockbrokers (Woodhall 1964).
The Bank of England acted as receiver of monies raised. Lotteries authorized by annual
statute with preannounced quanta of tickets and prizes were put out to tender by the
Commissioners of the Lottery. After 1804 even the amount to be raised was subject to
the annual tender by contractors (Ewen [1932] 1972, 234). These contractors began the
practice of selling smaller and smaller shares in the tickets for which they had tendered.
This practice continued every year until 1826 with the exceptions of 1814 and 1819. It
also seems that the contractors formed a cartel to bid for lottery business because the
return to the government fell dramatically after the tender system was introduced in
1785 (Raven 1991, 372).
The cost of an individual subscription remained high throughout the eighteenth and
early nineteenth centuries (Reith 1999). In 1710, for example, subscriptions to a loan
of £1,500,000 were £10 each (the equivalent of £16,600 in 2009 terms) (Ofﬁcer and
Williamson n.d.). There were two consequences of such a high price. First, low-stake
private lotteries (colloquially called Little Goes) proliferated despite their illegality and
dubious honesty (Reith 1999). Second, subscriptions to the State Lottery were broken
into many shares and those shares into further shares5 by agents and subagents among
the poor. Often these agents failed to distribute small prizes among small sharehold-
ers. In addition, a ﬂourishing market in betting (or insuring) on the drawing of a
particular lottery number either on a certain date or within a speciﬁed period became
established.6
A bet is a contract between two parties wagering on the uncertain outcome of an
event performance which can generally be monitored and enforced by backers and
layers alike. Greater competition in betting markets can be expected to lead to higher
standards of fairness. By contrast, a lottery is a pari-mutuel form of betting that cannot
be monitored and enforced individually by bettors. Competition among a number of
lottery operators is likely to lead to increasing market uncertainty and more widespread
abuse of market power. The above arrangements for the State Lottery contain a number
of perverse incentives which the Commissioners of the Lottery were apparently unable
to eliminate. As a result, the State Lottery became increasingly notorious. Among these
perversities were
• Lottery rules were complex and not understood.
• Prizes could be changed without notice.
• The State Lottery did not offer random chances, and people who bought more
tickets had a greater chance of winning a prize.
• Subscriptionticketscouldbestolenorborrowed,insuredagainst,andsubsequently
selected.
• Agents who sold shares in successful subscriptions might abscond or not pay out
minor prizes.
• Subscriptions might be received by agents but not paid over to the Commissioners.
• Subscription receipts might be forged so that prizes could be claimed.

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lotteries and gambling machines
The extent or frequency of these possible sources of unfairness or defalcation are not
known with accuracy. Moreover, it is not clear whether they resulted from the nature
of the State Lottery itself or the system of tendering introduced in 1785 by Pitt the
Younger. Whatever the facts of the matter, by the early nineteenth century the State
Lottery had become so notorious that it was ﬁnally stopped in 1826.7
The 1993 Act
.............................................................................................................................................................................
By the time of the debate over the reintroduction of the State Lottery it was com-
monly held that the history of the State Lottery demonstrated the necessity of its strict
regulation in order to ensure that it was fair to bettors. Furthermore, it was believed
that abandonment of regulation in 1826 was a direct result of the neglect by successive
administrations to provide that essential service. It is remarkable that when the National
Lottery was re-commenced under the National Lottery etc. Act 1993 that many of the
above perverse incentives were explicitly addressed.
The National Lottery etc. Act 1993 established three discrete and separable
government interests covering the United Kingdom and the Isle of Man:
• Regulation: The National Lottery is to be run with all due propriety and players are
to be protected.
• Ownership: Once the regulatory duties are satisﬁed, maximum net proceeds are to
be obtained.
• Compliance: The disposal of monies raised and the transfer to distributing bodies
is set out in the act.
The 1993 act, as amended, provides for an arm’s-length body (ALB) called the National
Lottery Commission (NLC) to be custodian of these interests on behalf of the govern-
ment. The National Lottery is exempt from most provisions of the Gambling Act 2005,
which applies only to Great Britain.
The ownership interest lies in the government’s desire to ﬁnance good causes, in
addition to grants from the Exchequer. This additionality requirement sets the National
Lottery apart from many overseas lotteries, the proceeds of which either pass directly to
government revenue or are used for the provision of state-provided education or health
services. It is exercised by appointing an operator of the National Lottery. This appoint-
ment takes place after a competition for the right to hold the license to operate the
National Lottery. As part of that competition bidders set out their plans for future sales
and propose a payments structure by which returns going respectively to good causes
and the operator are calculated. The NLC assesses the relative worth of bids, chooses
the preferred bidder, and negotiates the detailed license to operate. By law, the NLC may
issue a general license to operate to one operator or a speciﬁc license for a particular
product or region to a number of operators. Only the ﬁrst type has ever been issued.

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615
Camelot Group is the only successful bidder for any license. The Third such license was
commenced in February 2009 initially for 10 years since extended until January 2023.
Regulation of the National Lottery consists of ensuring that the various games are fair
and safe. This is done by enforcing or manipulating the terms of the license to operate.
Fairness involves ensuring that the outcomes of the games cannot be inﬂuenced by the
operator or by forces other than chance. Checks ensure that they are random or pseudo-
random and that prizes are appropriately distributed. Safety is ensured by making it
difﬁcult to play excessively (through low ticket prices, time and wallet load limits on
interactive games and by not allowing risky games to be sold) or for children to play.8
Much effort is expended in ensuring that it is impossible to acquire inside knowledge
about the likely outcome of games. This might happen, for example, in the case of a
shopkeeper who has activated a pack of scratchcards and, having sold most of the pack
without a prize being claimed, reasons that a prize must lie among the remaining cards.
As a consequence, where the National Lottery and betting companies compete for the
supply of interactive games the gross gaming yield per National Lottery customer is
approximately one-quarter of those visiting betting websites. Finally, it is illegal to offer
bets on the outcome of the National Lottery in the United Kingdom.9
The compliance interest extends to ensuring that all operations are conducted in
accordance with license conditions and that all monies are allocated appropriately
between taxation, prizes, the operator, the National Lottery Distribution Fund (NLDF),
and the Olympics Lottery Distribution Fund (OLDF). This involves undertaking checks
on underage sales, randomness of games outcomes, and game security.
Nature of the National Lottery
.............................................................................................................................................................................
Worldwide lotteries betray their past. Some, like the New York lottery, began as draw-
based numbers games, such as those operated by organized crime. This same model
continues to predominate, in the form of lotto. Other U.S. state lotteries have always
been based around the sale of scratchcards. Still others, such as the New Zealand lottery,
began selling scratchcards but are becoming more reliant on sales of draw-based games.
The U.K. National Lottery currently consists of draw-based (pari-mutuel) games,
rafﬂes, scratchcards, and interactive games played online. These products are described
in table 31.1.
Only the draw-based games and rafﬂes bear any relation to earlier state lotteries.
However, even here there are important differences. First, there is no limitation on the
number of tickets that can be sold. Second, the ticket price is in absolute (let alone
real) terms much lower than state lotteries in the eighteenth and nineteenth centuries.
Third, customers deal directly with the lottery operator via a national computer system
and not with agents. Fourth, the government does not operate the National Lottery
and cannot inﬂuence the outcomes. Fifth, side betting on the outcome of the National
Lottery is illegal and of relatively minor proportions.

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lotteries and gambling machines
Table 31.1 National Lottery Products (Year ended March 2011)
£ Million
Percentage of Total Sales1
Draw-Based Games
Lotto
2,667
45.8
Lotto plus 52
20
0.3
Thunderball
366
6.3
Hotpicks
206
3.5
Daily play3
46
0.7
Euromillions
1,056
18.1
Dream number3
39
0.7
Total draw games
4,400
75.5
Scratchcards4
1,260
21.5
IIWGs4
165
2.8
1 Percentages may not sum to 100 due to rounding.
2 Game introduced in year ended March 2011.
3 Games no longer on offer at time of this writing.
4 Data on sales of scratch cards are not published separately from IIWG sales.
Estimated.
Source: National Lottery Commission (2011), appendix A, p 17.
All National Lottery products compete directly with products supplied by organiza-
tions regulated under the Gambling Act 2005 and, in the case of lotteries, are subject
to regulations on maximum prizes. Draw-based games compete with society and local
authority lotteries. National Lottery scratchcards compete with scratchcards sold by
private companies. Interactive games compete with identical products available on bet-
ting websites. However, only National Lottery games attract lottery duty at 12 percent
of the ticket price. Competing products are either not taxed or are charged general
betting duty of 15 percent of gross gaming yield.
After the ﬁrst draw on November 19, 1994, total sales rose to a peak in 1997–1998.
This was predominantly due to a signiﬁcant rise in lotto sales. After that, total sales
fell steadily for the next ﬁve years. However, since 2002–2003 the total sales have risen
despite relatively stagnant sales of draw games largely as a result of a resurgence of
scratchcard sales, the success of EuroMillions, and the emergence of the interactive
channel. The highest total sales in nominal terms in the history of the National Lottery
were reached in 2010–2011 (see table 31.2 and ﬁgure 31.1).
Unlike many overseas lotteries, scratchcards have never represented more than
30 percent of total National Lottery sales. Hence the economics of the National Lot-
tery is dominated by the economics of draw-based games in which the main prizes
are determined in a pari-mutuel fashion and the main prize jackpot rolls over if
not won.10

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Table 31.2 National Lottery Sales,
1995–2011 (Years
ended March)
Years
Draw Games
Scratchcards (1)
IIWGs (1)
1995
1,191
1996
3,695
1,522
1997
3,846
877
1998
4,713
801
1999
4,559
669
2000
4,533
561
2001
4,437
546
2002
4,256
578
2003
3,997
577
1
2004
3,974
635
6
2005
4,028
717
21
2006
4,148
802
63
2007
3,983
849
79
2008
3,857
1,001
108
2009
3,928
1,082
139
2010
4,138
1,184
155
2011
4,400
1,260
165
Source: National Lottery Commission.
Note: 1. From2003onwardsscratchcardsandIIWGsarenotdifferentiated
in the NLC’s Annual Report. The scratchcard and IIWG data for 2003–2011
are estimated.
0
20
40
60
80
100
1995
1998
2001
2004
2007
2010
Draws
S/cards
IIWGs
figure 31.1 Pattern of National Lottery sales, 1995–2011 (years ended March; as percentage of
total sales)
Source: National Lottery Commission.

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lotteries and gambling machines
Different games sold in different ways yield different levels of net proceeds for each
unit of expenditure. There are two main reasons for this. First, typically scratchcards
and IIWGs (interactive instant win games) offer higher (sometimes 25% higher)
prize percentage payouts (PPP) than draw-based games. Second, retailers are paid a
commission of 5 percent of face value for draw tickets and 6 percent for scratchcards,
but no commission is payable for draw games sold online or for IIWGs. Hence as the
National Lottery product structure and marketing strategies change the average PPP of
the National Lottery also may change.
The general pattern of the ﬂows of funds associated with the National Lottery is
illustratedinﬁgure31.2. Thisﬁguredoesnotaimtobecomplete. Itexcludesmanyof the
transactions between a variety of trust and government accounts by which this general
patternisachieved. Italsoignoresthedisposalof fundsbylotterydistributorsontheone
hand and the operator and its suppliers on the other. There are two lottery distribution
funds. The National Lottery Distribution Fund (NLDF) provides a source of income for
lottery distributors that operate independently of the government to distribute monies
to arts, sports, heritage, and charitable causes. The Olympic Lottery Distribution Fund
(OLDF) was founded in 2005 to help fund the London 2012 Olympic and Paralympic
Games. In outline, revenue from ticket sales net of lottery duty is split according to
the terms of the license to operate between retailers, prizes, the OLDF, the NLDF, and
overheads disbursed by the operator. Overheads cover the costs of sales, including
capital investment, operating costs, payments to suppliers, advertising and marketing,
license fees, company tax, interest, amortization, and operator proﬁt. The proceeds
accruing to the NLDF and OLDF are supplemented by unclaimed prizes and investment
income earned on accumulated balances. The gross income is available for paying
government operating costs, for distribution, and for investment by the Commissioners
for the Reduction of the National Debt (CRND) acting under instructions from the
Department for Culture, Media and Sport (DCMS). In addition, since 2007 the NLDF
has made a series of transfers to the OLDF.11 For much of the past decade drawdown by
distributors has been larger than gross income so the NLDF balance has generally fallen
from year to year. In the year ended March 2011, the cost of raising funds amounted to
24 percent of NLDF and OLDF gross income and 6.9 percent of total ticket sales. Prizes
paid out and NLDF and OLDF gross income, respectively, represented 49.6 percent and
28.8 percent of ticket sales.
The economics of the National Lottery is best considered under three headings,
• the economics of all National Lottery games,
• the economics of pari-mutuel games, and
• the economics of scratchcards and interactive games.
The economics of the National Lottery has largely been conﬁned to the analysis of
demand factors that explain the sales of draw games. So far as is known there has
been no attempt to analyze the demand for scratchcards or the inﬂuence of supply-side
factors, such as the behavior of the operator or the government.

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## Page 640

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619
NATIONAL LOTTERY FLOWS OF FUNDS (Year ended March 2011)
LOTTERY DUTY
£699.3mill
TICKET SALES
£5,824.7mill
OVER HEADS
£398.6mill
RETAILERS 
£270.0 mill
PRIZES 
£2,891.7 mill
OLDF 
£103.2mill
NLDF 
£1,461.9mill
UNCLAIMED
PRIZES
£3.6 mill
UNCLAIMED
PRIZES
£89.1mill
OLDF LOTTERY
INCOME
£106.8mill
NLDF LOTTERY 
INCOME
£1,551.0mill
INVESTMENT
INCOME
£0.9 mill
INVESTMENT 
INCOME
£18.0 mill
OLDF GROSS 
INCOME
£107.7mill
NLDF GROSS
INCOME
£1,569.0
DMO/NLC/
DCMS
EXPENSES
£0.3 mill
DMO / NLC / DCMS
EXPENSES
£4.6 mill
TRANSFER TO
OLDF £292.0
OLDF DRAWDOWN
PAYMENTS
£357.1mill
NLDF DRAWDOWN 
PAYMENTS
£1,194.3mill
figure 31.2 National Lottery ﬂows of funds (year ended March 2011)
Sources: National Lottery Commission (2011); DCMS 2011.
U.S. Experience
There have been several attempts to explain variations in total lottery sales as a result of
ﬂuctuations in economic activity. For example, John Mikesell (1994) argued that total
sales of U.S. state lotteries were part of household consumption and, hence, related

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lotteries and gambling machines
to state personal income. He argued that changes in state personal income may be
masked during recessions by transfer payments. Consequently, an indicator of short-
term cyclical downturns like the unemployment rate was also part of the explanation.
This was reinforced by the likelihood that the unemployment rate reﬂects the changed
perception of the attractiveness of the lottery gamble which increases at times of high
unemployment. Mikesell also conjectured that lottery sales had a natural tendency to
reach a maximum and to decline thereafter and to be higher if the pari-mutuel game
lotto was part of the game portfolio.
Mikesell estimated the following model:
L = f (Y ,A,U,S),
where L is state lottery sales, Y is state lottery personal income, A is the age of the
state lottery in quarters, U is the state unemployment rate, and S is the non-Lotto
share of state lottery sales. The model was estimated using quarterly data for all U.S.
states offering lotteries in 1991 with the exceptions of Rhode Island, for which quarterly
data were not available, and Texas because of its newness. Lottery sales and personal
income were expressed in per capita terms, all data were in logarithmic transformation,
and income and sales data were adjusted to 1987 price levels. Dummies were included
for each state except West Virginia to take account of state-by-state social, cultural,
demographic, and economic differences beyond those speciﬁed in the model.
S is the outcome of purchase decisions by lottery customers, which is correlated
with the error term of an OLS regression model. As a consequence the estimates of the
inﬂuence of state economic activity on lottery sales were found to be unreliable. This
effect was removed by regressing S on other independent variables together with state
population and whether the state in question has a neighbor with no lottery. The new
predicted value of S was then used to reestimate the lottery sales equation. The result
of this TSLS estimation was as follows (see table 31.3):
Table 31.3 Log Per Capita Lottery Sales,
Q4 1983 to Q4 1991
N = 820
Coefﬁcient
Standard Error
Constant
−33.846
2.104
Logy
3.899
0.224
LogU
0.171
0.057
LogA
−0.561
0.078
Logs
−1.573
0.231
R2
0.840
AdjR2
0.833
F -statistic
114.240
Source: Mikesell (1994), table 1, p. 168.

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## Page 642

the national lottery
621
This shows that the income elasticity of lottery sales is 3.9. It also shows that for
each 1 percent rise in unemployment there is a 0.171 percent rise in lottery sales. Thus
as a recession begins lottery sales rise ceteris paribus, which partly offsets the fall in
per capita income. Lottery sales decline in real terms with the age of the lottery and
with a rise in the proportion of non-lotto sales.
U.K. Explorations
So far as is known, unlike in the United States, no study has been published on the social
and economic factors underlying overall sales of the National Lottery (see ﬁgure 31.3).
It is not, therefore, possible to determine whether or not the Mikesell approach could be
employed in the United Kingdom. However, it is possible to remark that sales generally
declined during much of the unprecedented economic boom of the 1990s and early
2000s (Creigh-Tyte and Farrell 2003). Moreover, the growth of National Lottery sales
has continued unabated during the economic instability of the past three years. On the
face of it, therefore, it appears that a search for robust relationships between sales and
macroeconomic variables will prove fruitless.
The experience of the National Lottery appears to contradict the earlier ﬁndings
from the United States. In part, the absence of a readily apparent relationship between
National Lottery sales and socioeconomic variables may be the consequence of the
peculiar features of the development since 1994 of lottery sales on the one hand and
the economy on the other. It also may be because more subtle relationships lie hidden
from immediate view yet to be uncovered by sophisticated analysis. It is possible,
0
1000
2000
3000
4000
5000
6000
1995
1998
2001
2004
2007
2010
Draws
S/cards
IIWGs
Total
figure 31.3 National Lottery sales, 1995–2011 (years ended March; £millions)
Source: Table 31.2.

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## Page 643

622
lotteries and gambling machines
therefore, that the Mikesellian relationship will emerge as the U.K. economic perfor-
mance becomes less stable. Alternatively it may mean that robust causal explanations
of National Lottery sales are more likely to be found among models of retail behavior
than among those based on macroeconomic relationships.
Draw-Based Games
.............................................................................................................................................................................
Theory of Draw Games
Philip Cook and Charles Clotfelter (1993) described the main draw game, lotto, as
pari-mutuel gambling with long odds and large jackpots. They proposed that such
games display a scale effect because bettors in lotteries serving large populations only
take account of the size of the jackpot and do not consider that a larger population
means a smaller chance of winning. Lotto has the feature that each bet increases the
size of jackpot available to all players while simultaneously increasing the chance that
the jackpot will have to be split with someone else. Normally the impact on the expected
value of the jackpot is positive because the positive impact on jackpot size outweighs
the negative impact of the increased chance of splitting.
In general, then, the expected value of a lottery bet is the probability of a chosen
combination of winning the jackpot multiplied by the chance of the jackpot being won
multiplied by the risk of having to split the jackpot. So the expression of expected value
(EV ) is
EV = PROB(WIN) × PROB(JACKPOT) × EXPECTEDSHARE.
The probability of winning the jackpot with a particular bet is the probability of any bet
winning the jackpot (p) multiplied by the number of combinations (boards) purchased
(W ). Let the total number of combinations purchased by others be denoted as N.
The size of the jackpot is the price of one combination (c) multiplied by the fraction
of the board price devoted to the jackpot fund (k) multiplied by the total number of
combinations purchased (Q = W + N) all added to the size of any rollover (R). The
expected share of any jackpot won is more complex. If all combinations are chosen
randomly the probability of a jackpot being won is very small, and a large number of
independent trials indicate that the probability of a shared jackpot can be represented
by a Poisson series. Hence there are Q combinations among which sharing might
occur with probability p. The proportion of those not involving sharing is e−pQ, so the
expected proportion involving sharing is (1−e−pQ). The resulting expression for EV is
EV = pW × (R + kc(Q)) × (1 −e−pQ).
If W = 1 and R = 0 EV is a monotonically increasing function of Q.

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## Page 644

the national lottery
623
Cook and Clotfelter argued that this expression displays two features. First, if qQ is
approximately 1 when there is no rollover, the EV of a single play (W = 1) is less than
the jackpot payout rate (k). Why, then, should any rational individual buy a lottery
ticket? Second, the probability distribution of the number of winners depends only
on pQ, so larger games have the same distribution of winners as small ones but offer
larger jackpots. To the bettor, larger games offer larger jackpots at reduced probability
of winning with all other features unchanged. Because a bettor’s evaluation of lotto is
more sensitive to the size of the jackpot than the chance of winning, larger jackpots
generate larger sales than smaller ones.
Lisa Farrell and Ian Walker (1999) and Farrell et al. (2000) questioned this analysis.
They argued that the Cook and Clotfelter calculations did not apply to the situation
when there was a rollover (R > 0). In the presence of rollovers, increased sales dilute
the value of the jackpot rolled over from previous draws. Farrell and her colleagues
postulated that the relationship between EV and sales for some ﬁnite Q and for sufﬁ-
ciently large R became monotonically decreasing as the dilution effect dominated the
scale effect. For given sales the EV of rollover draws is always higher than for non-
rollover draws, implying a random variation in EV due to rollovers. This provided an
explanation for why a rational individual would participate in a draw when there are
rollovers (see ﬁgure 31.4).
Nevertheless, for many draws EV is less than the price of the ticket or board, which
is contrary to the tenets of demand theory. Farrell and Walker (1999) followed John
Conlisk (1993), who suggested that that participation in the lottery yielded positive
but unspeciﬁed non-pecuniary beneﬁts in addition to the EV of the ticket. Farrell and
Walker envisaged play as being determined by a reservation expected value (REV ).
EV
SALES
With
Rollover
No
Rollover
figure 31.4 Expected value and sales

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## Page 645

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lotteries and gambling machines
The REV of the ith individual depends on the number of combinations purchased
(W ) and a vector of characteristics of the ith individual and the W combinations.
Non-pecuniary return is assumed to be a normal good so that the marginal beneﬁt it
yields falls as W rises. Hence the REV schedule shifts upward as income rises and if
risk aversion declines. Farrell and Walker hypothesized that an individual will purchase
lottery tickets to the point at which EV falls to the level of REV. However, this equality
is randomly disturbed by increases to EV resulting from the occurrence of rollovers
and by the increases in sales that result.
The variation in EV resulting from rollovers also allowed the elasticity of demand
to be inferred. The variation in the difference between EV and the board price can be
interpreted as the cost to the bettor of the lottery bet (P). When the price of a board is
unity,
P = 1 −EV .
This relationship can be used to estimate price elasticity of demand when the board
price does not change. Over the period November 1994 to February 1997 purchases
when EV = 0.45 in non-rollover draws were compared with those when EV = 0.63 in
rollover draws. Farrell and Walker calculated that the price elasticity varied between
−1.785 and −1.456 and income elasticity between 0.449 and 0.132 depending on the
estimation method. These estimates were then used to compute the consumer surplus
of lotto (roughly £1 billion p.a.) and the annual deadweight loss (between £0.48 and
£0.51 billion). By contrast, Farrell et al. (2000), using data from the period November
1994 to February 1996, found that the implicit price elasticity of lotto ranged between
−0.80 and −1.06.
Farrell,EdgarMorgonroth,andWalker(1999)hypothesizedthatplayingthelotteryis
addictive and adapted the Becker and Murphy (1988) model of rational addiction to the
explanation of lotto sales. They reasoned that current consumption was determined,
in part, by an individual’s level of addiction generated by past consumption. Hence
the regression models of the type reported above were augmented by a measure of
the inﬂuence of past consumption on present purchases. This inﬂuence was assumed
to vary according to size and presence of rollovers. Farrell, Morgonroth, and Walker
(1999) compared the traditional speciﬁcation of lottery demand with that including
addiction using sales data for the period November 1994 to February 1997. They found
that addiction was a signiﬁcant explanatory variable in the lottery sales equation and
that long-run price elasticity of lottery demand was −1.55.
This result was questioned by David Forrest, Robert Simmons, and Neil Chesters
(2002), who argued that it should be treated with caution for three reasons. First,
it was based on the ﬁrst 116 weekly observations and so was heavily inﬂuenced by
announcement effects. Second, the National Lottery was becoming embedded into
the behavior of consumers with all the volatility and uncertainty that transition might
imply. Third, the introduction was associated with large prizes associated with rollovers,
which might shifted demand outward.

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Forrest, O. David Gulley, and Simmons (2000) estimated the elasticity of demand
for lottery tickets by computing the effective ticket price P = 1 −EV, where
EV = 1 −((I/Q)(R + kcQ)(1 −e−pQ) + EVs)
such that EVs is the expected value of the non-jackpot prizes. There is a general sim-
ilarity with the formulation of Cook and Clotfelter. Forrest and his colleagues argued
that only if the price elasticity of lotto demand was close to minus unity would the aim
of sales maximization be achieved.
However, the effective price P is only calculable ex post and so cannot be used in the
estimation of the lotto demand curve. Instead, a two-stage approach was adopted. First,
the expected effective price was estimated from variables derived from information
widely available to the public before the draws took place. This included the size of any
rollover or superdraw and the average sizes of Wednesday and Saturday jackpots in non-
rollover weeks. Forrest, Gulley, and Simmons found that estimated bettors’expectations
were not signiﬁcantly different from actual effective price calculated ex post. Second,
actual sales were regressed against the effective price estimated in stage 1, together with
other variables likely to affect lottery demand. It was found that the long-run price
elasticity of demand was −1.03. This result was conﬁrmed by Forrest, Gulley, and
Simmons (2004) when demand functions for Wednesday lotto and Saturday lotto were
separately estimated. The respective price elasticities were −0.709 and −1.074.
Nevertheless, this analysis does not consider the problem of why a rational bettor
would willingly purchase a lottery ticket, the expected value of which is usually less than
its money price. We have already reviewed Farrell and colleagues’ proposed solution to
this problem. Forrest, Simmons, and Chesters (2002) suggested, with Conlisk (1993),
that the activity of engaging in the National Lottery itself yields positive consumption
beneﬁts (see also Hartley and Farrell 2002 and Hartley and Lanot 2003). According
to Forrest and colleagues, these consumption beneﬁts are derived from the prospect
of buying the dream of winning the jackpot. This includes imagining how a jackpot
might be spent or enjoying the prospect of quitting one’s job. This view is supported
by Don Slater and Eva Neitzert (2007), who reported that purchase of lottery tickets
is associated with the formation of dreams by bettors. Moreover, they argued that the
greater the jackpot the better the dream. (In fact, Emma Casey 2007 found that the
relationship is probably not linear because most people appear to be afraid of winning
too large a jackpot lest it lead to too great a disturbance in their relationships and their
lives.) As a result, lottery sales are more closely related to jackpot size than effective
price.
The hypothesis was tested by estimating two regression models. In the ﬁrst, effective
price appeared as an independent variable but not the size of jackpots and vice versa
in the second. The results of Cox tests showed that each model was rejected against
the other. Forrest, Simmons, and Chesters (2002) interpreted this result as suggesting
that both effective price and jackpot size are important in explaining lottery sales. It is
unlikely that any regulator or operator of lotteries would disagree with this conclusion.

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lotteries and gambling machines
Nevertheless, it has yet to be explored whether jackpot size is an accurate representation
of the hypothesized consumer beneﬁt of lottery participation or is a catchall for other
factors yet to be individually identiﬁed. It is even perhaps conceivable that the demand
for lottery tickets is consistently at least myopic, infested with money illusion and risk,
and even possibly irrational.
Patrick Roger (2009) investigated the demand for EuroMillions lottery tickets across
all European markets in which it was sold. He estimated a demand equation of the type
proposed by Forrest, Simmons, and Chesters (2002). First, Roger estimated the antici-
pated value of a draw or effective ex ante price and then used the resulting price series
as an independent variable in the estimated demand equation. He found considerable
variation in the long-run price elasticity of demand between different jurisdictions.
Most price elasticities ranged between −0.82 and −0.91. However, in Spain the long-
run elasticity was −0.49, in Ireland it was −1.44, and in the United Kingdom it was
−1.76. Roger suggested that the Ireland and U.K. elasticity is the result of competition
with other forms of betting.
Lottery Design
TheNationalLotteryhasalsobeenexploredfromthepointof viewof arationaldesigner
seeking to maximize revenue. In 2001 Walker and Juliet Young argued that sales depend
on the size of the set of number that bettors choose (n) and the total numbers available
(NUM). For U.K. lotto n = 6 and NUM = 49, and it is termed 6/49 game. On the
one hand, if the game is easy to win, rollovers are infrequent and there is a danger that
the game will lose its attraction and sales will decline. On the other hand, if the game
is so hard to win that long rollovers are very frequent, ultimately people will cease to
buy tickets because they will believe they have little chance of winning. Game designers
adjust the n/NUM ratio to match the conditions of the lottery market.
In addition, they must decide the proportion of the ticket price devoted to all prize
pools, how skewed toward the jackpot prizes are, and how much weight should be given
to middle-rank prizes compared to those on the extreme. Walker andYoung called these,
respectively, the mean, skewedness, and variance properties of the prize distribution.
As rollovers occur all three properties increase in size for given sales. They found, using
OLS regression, that sales are an increasing function of the mean and of skewedness of
prize distribution. However, sales decrease with an increase in its variance.
Walker and Young attempted to model the effects of a change in the lotto format
from 6/49 to 6/53. Unfortunately, the computational model used was very complex and
did not always converge to a unique solution. Nevertheless, they felt able to tentatively
conclude that a change to 6/53 would mean lower mean return and raised variance,
both of which are likely to lower sales, and increased skewedness, which is expected to
raise them. As a result, ceteris paribus sales would be lower with 6/53 than with 6/49.
An alternative approach to the problem was taken by Roger Hartley and Gauthier
Lanot (2003), who, unlike Walker and Young, did not attempt to estimate bettor

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627
behavior. Instead, they built a theoretical dynamic model of consumption under
uncertainty, which they then parametized using the facts of the National Lottery. Each
individual is assumed to decide the optimal number of lottery tickets he or she will buy
so as to maximize the expected value of lifetime utility within a binding lifetime budget
constraint. Lifetime utility depends on the rate of discount, the time between draws,
purchases of lottery tickets, and purchases of other goods. Following Forrest et al.
(2002) and Hartley and Farrell (2003), the utility function has a “fun” term dependent
on ticket purchases, external factors, and history. Rollovers are regarded as exogenous
by consumers but are, in truth, the result of aggregate participation in the lottery.
Hence the rollover process affects participation which, in turn, affects the rollover pro-
cess. Expenditure decisions are assumed to be contingent on the number of weeks the
lottery has rolled over, which is determined by a random number (RAND). Fun is
assumed to be derived from winning a large jackpot and so is determined by RAND.
If an individual wins a jackpot he or she is assumed to quit participation because all
possible fun in contemplating the future has been extracted. This last aspect of lottery
demand is contradicted by the existence of multiple jackpot winners, which suggests
that winning a jackpot does not remove the fun of participating in the National Lottery.
Hartley and Lanot (2003) presented a series of simulations which show a variety
of trade-offs between the probability of jackpot wins and tax receipts resulting from
different model parameter settings. They found that increasing the probability of a
jackpot win and decreasing the tax rate led to a rise in tax revenue. This occurs because,
although the additional revenue associated with more rollovers falls, this effect is more
than compensated by a rise in participation due to the greater probability of jackpot
win. The greater the number of participants means more frequent sharing of jackpots.
Reducing the tax rate also increased participation sufﬁcient to offset the reduced tax
per ticket sold. As a result, Hartley and Lanot suggested that whether the tax rate on
the National Lottery is too high and the probability of winning the jackpot is too low
are questions to be investigated further. So far as is known, neither the government nor
the operator has seriously considered this suggestion.
David Paton, Donald Siegel, and LeightonVaughan Williams (2003) found that price
changes in the National Lottery had signiﬁcant effects on the demand for other gam-
bling, most notably betting. When the effective price of the National Lottery dropped
the demand for gambling in general also dropped.
Lottery Addiction
We have already noted that Farrell, Morgonroth, and Walker (1999) found signiﬁcant
evidence of lottery“addiction.”By contrast, Paton, Siegel, andVaughan Williams (2004:
857) found no evidence that the price elasticity of lottery demand was higher in the
long run than in the short run and so could be seen as addictive.12 In reality, addiction,
deﬁned as the dependency of future sales on past consumption, is likely to reﬂect a range
of explanatory factors and therefore be difﬁcult to detect using econometric methods.

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lotteries and gambling machines
Supply of Lottery Products
.............................................................................................................................................................................
The economics of the supply of National Lottery products has barely been subjected
to economic analysis. Most economists take the nominal price (c) of a lottery board as
given and usually assume that c = 1. Presumably, this assumption would be justiﬁed
by assuming that the National Lottery acts as a pure monopolist that chooses to set the
nominal board price at unity so that sales are determined solely by demand factors.
While this may be valid for lotto in the United Kingdom since 1994, it is not true of
all other draw games and has never been true of all types of scratchcards or IIWGs.
The history of the National Lottery is replete with minor product changes involving
different levels of c,13 different k, and different EV s. On closer examination, therefore, a
series of nuanced processes lead to the changing nature of the National Lottery product
offer.
In this respect the National Lottery is no different from any other supplier of low
value, mass-consumption products. However, the National Lottery is different from the
likes of Coca-Cola in that these dynamic supply-side processes intimately involve the
U.K. government in the form of the National Lottery Commission (NLC). The NLC is
custodian of a set of policy outcomes which are couched in terms of its three statutory
duties. Its mission is to appoint and supervise the lottery operator so that the outputs
that are supplied lead to these outcomes. Thus specifying the National Lottery in terms
of a sales-maximizing monopoly may not be an accurate model of reality. A simpliﬁed
idea of the dynamic relationships that exist between the NLC and the lottery operator
is given in ﬁgure 31.5.
Several features of this dynamic system should be remarked on. First, the powers of
both parties are highly constrained. On the one hand, the NLC must ensure that the
operator remains commercially viable in competition with other gambling companies.
On the other hand, the operator cannot expect to pursue sales at the expense of its
social responsibilities to prevent excessive gambling or to prevent sales to children.
Second, the government has sought to partition the gambling market so that there
is “clear, blue water” between the National Lottery and other gambling products.14
Nevertheless, the reality of these dynamic relationships reﬂects, albeit imperfectly, the
state of the U.K. gambling market. Third, the instruments each can call upon to achieve
policy outcomes or business strategies are respectively limited by the damage that the
unconstrained pursuit of one might do to the other. For example, the NLC does not
instruct the operator to market certain products, though it does exercise its right to
refuse to allow some products to be sold.15 At the same time,the operator has not sought
to actively undermine its special semimonopoly status in the gambling market. Fourth,
the relative strengths of these various dynamic relationships vary over time. When sales
are growing and the marketing strategies of the operator appear to be working well
the government is likely to express less concern about net proceeds and the operator
is likely to seek and obtain more commercial autonomy than if the opposite were the

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## Page 650

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629
STATUTORY
OUTCOMES
PERFORMANCE
MONITORING and
EVALUATION 
NLC
REGULATORY
ACTIONS 
INFORMATION
SHARING
NATIONAL
LOTTERY
OUTPUTS
MANAGEMENT
INFORMATION
OPERATOR
LICENCE
ENFORCEMENT and
NEGOTIATION 
INPUTS
INCENTIVES
and REWARDS 
figure 31.5 National Lottery supply
Adapted from Hancock (2011), ﬁgure 3.1, p. 30.
case. Nevertheless, if it were found that rapidly increasing sales were occurring at the
expense of its primary policy outcomes it is likely that the NLC would seek to instill
greater social responsibility in the operator.
The supply side of the National Lottery, therefore, takes on many of the features of
a dynamic duopolistic system formed between the operator and the owner/regulator
of the National Lottery. The regulator seeks to ensure that the outputs of the National
Lottery are consistent with policy outcomes. However, in practice it cannot directly
commandthenatureof thoseoutputs,thoughithasrefusedtoallowsometobesupplied
and has placed conditions on how others are to be sold. It neither has the ability to
directly affect the mobilization and disposition of inputs commanded by the operator
nor does it choose to dictate marketing strategies. Hence any consistency that exists
between output and outcomes results largely from the way the incentives incorporated
in the license to operate inﬂuence the day-to-day operations of the operator. These
incentives are designed to ensure that, within the limits placed on its operations by the
NLC, the operator seeks to sell as many National Lottery products as it can. In pursuing
this aim, the operator is assured of, under the terms of the license, a guaranteed share
of the after-tax, after-prize total revenue.

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lotteries and gambling machines
c = Price
Points 
Q = Number
of Boards 
DND
c1
c2
c3
Q1
Q2
Q3
figure 31.6 Demand and supply of scratchcards and instant win games
These revenue shares vary according to the type of product sold and the way in which
they are distributed. This suggests that there are a number of supply curves for the
various products sold by the National Lottery, each of which has different implications
for the total revenue of the operator. In this respect the economics of scratchcards
and IIWGs is no different from that of any other small outlay, frequently purchased
object, such as a serving of Coca-Cola or a bar of chocolate. This is illustrated in
ﬁgure 31.6.
If we consider a world in which scratchcards and IIWGs16 are supplied at three
separate price points, c1, c2, and c3, then total sales of non-draw games, SND, are the
multiple of c and Q. So
SND = c1.Q1 + c2.Q2 + c3.Q3.
However, with draw-based games there is a different relationship. If we limit consider-
ation to two price points and one rollover at each we obtain the situation illustrated in
ﬁgure 31.7.
There are four possible outcomes, A, B, C, and D. However, whether or not there is
a rollover at a particular price point is literally a matter of chance. Let us assume that
it has a probability P over a large number of trials. In that case, S bears a probabilistic
relationship with c and Q.
SD = c4(P(Q6) + (1 −P)(Q4)) + c5(P(Q7) + (1 −P)(Q5)).

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## Page 652

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631
Q = Number
of Boards 
c = Price
Points 
c4
c5
DDNR
DDR
A
B
D
C
Q4
Q5
Q6
Q7
figure 31.7 Demand and supply of lottery draws
In general terms, since
S = SND + SD,
total sales at time t are calculated as
St = f (DND; DD; P)t.
It follows that attempts to model National Lottery sales must be based on the normal
demand function for draw games augmented by the following:
• the effect of the probability of the occurrence of a jackpot on demand for non-draw
games,
• the effects of the demand for non-draw games on the demand for draw games and
vice versa,
• the effects of any variation in the costs of supply, including changes to regulatory
regime, and
• the effects of any variation in the price points at which supply takes place.

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lotteries and gambling machines
Summary and Conclusions
.............................................................................................................................................................................
Since its modern inception in 1994, the National Lottery has become deeply embedded
in the culture of the United Kingdom. It enjoys the largest turnover of any single brand
of consumer goods and is, by far, the most available form of gambling. It is played at
some time or another by nearly 70 percent of the adult population (Wardle et al. 2011)
and, illegally, by perhaps 10 percent of British children (Ipsos MORI 2011).
Unlike most forms of gambling, women and men participate in the National Lottery
with more or less equal enthusiasm. Like the BBC, It has earned high levels of public
trust (Creigh-Tyte and Lepper 2004a,2004b). Many who buy National Lottery tickets do
not regard their actions as gambling, and some even believe it to be a means of investing
for retirement. Most, whether they play or not, regard National Lottery proceeds with
a proprietary interest and strongly disapprove of the government’s use of them as an
alternative source of revenue (Lepper and Hawkes 2007).
Nevertheless, despite their ubiquity, only two National Lottery products (Lotto and
EuroMillions) have been subjected to rigorous economic analysis. In large part this
is due to the lack of publicly available comprehensive time-series data which would
make such an analysis possible (Creigh-Tyte and Farrell 2003; Forrest 2003). Despite
the fact that the National Lottery yielded in excess of £2.2 billion to the Exchequer or to
communal causes in 2010–2011, most of its activities are closed to public scrutiny. This
arises because the National Lottery is run on behalf of the government by a privately
owned company with its own commercial sensitivities unrelated to the government
business it undertakes. No data are now published on the social or geographical location
of sales,soitisnotpossibletodeterminethesocioeconomiccircumstancesfromwhence
they arose. No reliable data on participation, frequency of purchase, or purchase size
are published, which means it is not possible to seriously analyze the various markets
served by the National Lottery. No data on coverage are made available, thereby making
it difﬁcult to build models on the occurrence of jackpots. No data on boards sold in
different games are published, which means that the quantity of National Lottery
products is not precisely known and there is an imprecise reconciliation between sales
data and the variables employed in economic theory.
Two general approaches could conceivably be adapted to the study of the economics
of the National Lottery. Each complements the other, but neither can claim to present
a full picture of all the economic inﬂuences that bear on it.
First, the National Lottery could be explored from the point of view of sources and
uses of resources. We have attempted to outline a small part of the National Lottery
ﬂows of funds which could be expected to form a small element of such an analysis.
However, much remains to be done. Currently there has been no systematic analysis
of sources of National Lottery revenues or how they are distributed. There are few
publicly available data on who buys lottery tickets and none on where those purchases
take place. Hence the age-old question of whether or not the National Lottery is a
tax on the poor cannot yet be systematically approached, let alone answered, with

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## Page 654

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633
any accuracy. Moreover, economists have not attempted to assess whether or not the
National Lottery is a relatively effective, efﬁcacious, and efﬁcient method of providing
for society’s merit goods. Finally, there have been few attempts to analyze the National
Lottery in the context of the U.K. gambling industry (cf. Forrest et al. 2004, 2010). No
doubt this is due to the general paucity of accurate, complete, consistent and timely
publicly available time-series data on gambling in the United Kingdom.
Second, it is also possible to explore the demand for, and supply of, National Lottery
products. We have seen that this is the approach taken by most economists when
analyzing the National Lottery. It has led to deep and subtle analysis of the expected
value, and robust estimates of short-term and long-term price elasticities, of draw
tickets. This work has been employed to inform the design of draw-based games.
However, lacunae remain. On the one hand, the demand for scratchcards and IIWGs
has not been subjected to the same rigorous examination as Lotto and EuroMillions.
As a consequence, the economics of the demand for National Lottery products remains
substantially incomplete. Access to comprehensive information about the sales and
PPPs of different lottery games and who buys lottery tickets and where would greatly
aid investigation of the micro-economics of the National Lottery. On the other hand,
there has been no attempt to explore the economics of supply of the National Lottery.
No doubt this failure is the result of poor or nonexistent publicly available databases
on cost conditions and the fact that the nominal ticket price of Lotto has remained at
£1 since 1994, thus making simple the translation from sales to boards. Nevertheless,
as new products are introduced with different operating costs, and at different price
points, from Lotto, this lack of analysis of supply conditions represents a potential
source of systematic error. This is particularly so as the importance of Lotto in total
sales continues to weaken.
National Lottery proceeds are unusual among revenues of the general government
sector because there is no reliable method of forecasting them. This is a direct result of
the weaknesses we have noted in the economic analysis of the National Lottery. Robust
dynamic models are not available, and it is not possible to rely on such shortcuts as
correlations between National Lottery sales and on such macroeconomic variables as
household consumption. No knowable degree of accuracy can be ascribed to the future
course of National Lottery proceeds. As a consequence, the management by the general
government sector of the uncertainty which variations in those proceeds engender is
likely to be characterized by excessive risk adversity, imprecision, and high cost in terms
of resources employed and revenues forgone.
Notes
The authors are grateful to Ben Haden for helpful and perceptive comments which have
eliminated many errors from an earlier draft. The views expressed herein are those of the
authors and are neither representative of the views of nor endorsed by the Department for
Culture, Media and Sport or the U.K. Government and cannot be construed as if they are.
Any errors of fact, logic, or judgment that remain are the sole responsibility of the authors.

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## Page 655

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lotteries and gambling machines
1. All such conversions are based on average earnings.
2. By reducing the number and the value of the prizes the authorities imposed a double
reduction in the expected value of the tickets in the Lotterie Generall.
3. This did not deter many private lotteries being launched over the subsequent two and half
centuries (for a list see Ewen [1932] 1972). Notable examples included lotteries to pay
for the settlement of Virginia in 1612, 1614, 1615, and 1618–1621, the London Aqueduct
lotteries in 1635 and 1639, and the Royal Jewel Lottery 1685.
4. These boxes were six feet in diameter and wheel-shaped. They became know as wheels.
5. The Joint Stock Act permitting the issue of limited liability equity by joint stock companies
was not passed until 1823. Before that companies were forced to operate under royal
charter.
6. Roger Munting (1998, 629) reported that there were 200 insurance houses in London in
the late eighteenth century which operated like betting shops. They were made illegal in
1802 but apparently continued until the State Lottery ended in 1826.
7. Echoes of the notoriety of the state lotteries of this period can be heard to this day. For
example, the 1993 act setting up the modern National Lottery required that it be run and
promoted with all due propriety.
8. Children are deﬁned in the Gambling Act 2005 as those under 16 years of age.
9. Note that this does not prevent bookmakers from offering to lay bets on the outcomes of
lotteries in other jurisdictions.
10. There are absolute limits to the number of successive rollovers that are allowed. With lotto
it is four; in the case of EuroMillions, 12. If the jackpot is still not won once the rollover
limit is reached, the jackpot pool that has accumulated rolls down and is shared among
winners of the next highest prize tier.
11. Beginning on February 1, 2009, and for a further 12 quarters these transfers were at the
rate of £73 million per quarter. In addition, on May 1 and August 1, 2012, two further
transfers of £68 million were made. The London Olympics and Paralympics were held
during August-September 2012.
12. One of the authors was once assured by a very senior psychiatric consultant that in more
than 35 years she had yet to come across anyone who was addicted to lotteries. This view is
conﬁrmed by a succession of prevalence surveys which have shown that playing National
Lottery games is associated with relatively low prevalence rates of problem gambling (War-
dle et al 2011). Nevertheless, it should be remembered that the meaning of addiction in
economic theory may bear only an indirect relationship with that employed in the study
of problem gambling.
13. In the lottery trade a particular c is termed a price point. In the United States, large increases
in sales of lotteries heavily dependent on scratchcards have been attained by inducing a rise
through the price points over time. This has often been accompanied by a rise in k (or the
prize percentage payout).
14. One example of this is the fact that the National Lottery operates largely outside the
Gambling Act 2005 under which most of the rest of the British gambling industry is
regulated.
15. In 2010, for example, the NLC refused Camelot Group permission to use National Lottery
terminals to supply payment services.
16. In practice it is likely that the demand curve for scratchcards is different from that for
IIWGs. Given the direct competition faced by National Lottery IIWGs from other gaming
websites, the demand for IIWGs is likely to be more price-elastic than that for scratchcards.

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For simplicity’s sake, and because sales of IIWGs are small relative those of scratchcards,
they are aggregated for the purpose of this argument.
References
Ashton, John. [1893] 2011. A history of English lotteries: Now for the ﬁrst time written. Reprint,
London: General Books.
——. [1898] 2011. The history of gambling in England. Reprint, Milton Keynes, U.K.: Lightning
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Becker, Gary S., and Kevin M. Murphy. 1988. A theory of rational addiction. Journal of Political
Economy 96(4):675–700.
Casey, Emma. 2007. Women and UK National Lottery play. Birmingham, U.K.: National
Lottery Commission.
Cohen, Jacob. 1953. The element of lottery in British government bonds, 1694–1919.
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Conlisk, John. 1993. The utility of gambling. Journal of Risk and Uncertainty 6(3):255–275.
Cook, Philip J., and Charles T. Clotfelter. 1993. “The peculiar scale economies of lotto.
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chapter 32
........................................................................................................
THE BENEFITS AND COSTS OF
SLOT MACHINE GAMBLING
........................................................................................................
scott farrow and chava carter
1 Introduction
.............................................................................................................................................................................
Consider designing a meta-analysis to determine the net economic beneﬁts and costs
of slot machine gambling in a speciﬁc jurisdiction. The major steps would likely be
(1) identifying studies that have internal and external validity, (2) collecting outcome
data from these studies, (3) gathering the key characteristics of the studies, and (4)
running a regression to identify the statistically signiﬁcant determinants of the net
beneﬁts. Attempting such an analysis quickly founders on the paucity of studies that
would pass step 1, in large part due to ongoing disputes among economists as well as
other parties on the elements of an internally valid study.
Consequently, this chapter begins by introducing major issues and deﬁning the slot
machine segment of the gambling industry. Section 2 reviews basic economic welfare
criteria as implemented via beneﬁt-cost analysis, sections 3 through 9 summarize issues
in the conceptualization of beneﬁts and costs as well as framing issues, section 10
introduces a scorecard for key elements of a beneﬁt-cost analysis,section 11 summarizes
illustrative empirical studies, and section 12 concludes with areas for further research.
1.1 Who Deﬁnes Beneﬁt-Cost Analysis?
Within economics and applied policy analysis there is a large body of literature on
theoretical welfare economics and its implementation through beneﬁt-cost analysis,
including such texts and collections as Baumol and Wilson (2001), Boardman et al.
(2011), Just, Hueth, and Schmitz (2004), Zerbe and Bellas (2006), Schmitz and Zerbe
(2009), Brent (2006), and Jones (2005), among others. The core of the theory is static,

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lotteries and gambling machines
partial equilibrium analysis with certainty, but the literature has expanded to include
ever more complex analyses involving general equilibrium, dynamics, and uncertainty
(e.g., Baumol andWilson 2001; Arrow and Lind 1970; Goulder andWilliams 2003; Gra-
ham 1981; Freeman 2003). Economists understand that the result of an applied welfare
or beneﬁt-cost analysis, while built from potentially positive or objective analyses of
many components, ultimately contains a normative element when individual values are
aggregated to form “bottom line” measures, such as the aggregated net present social
value (e.g., Baumol and Wilson 2001; Foster and Sen 1997; Adler and Posner 2006;
Lave 1996). Nonetheless, many economists and policy analysts, us included, advocate
the use of beneﬁt-cost analysis as providing an accounting structure for the integration
of positive and negative impacts into monetary terms. Further, a demand exists for
beneﬁt-cost information as demonstrated when many governments and organizations
require beneﬁt-cost analysis as part of regulatory or investment processes (e.g., U.S.
OMB 1992, 2003; EU–Regional Policy 2008; HM Treasury 2013; Treasury Board of
Canada 2007).
Although general elements of theory exist, and even though textbooks outline many
simpliﬁed applications, such as taxes, pollution regulations affecting health, changes
in market structure, and so on, any particular application typically involves theoretical
and empirical customizations to the problem context. For gambling, and slot machine
gambling in particular, that customization has not yet solidiﬁed into a canonical form of
analysis. Key elements without consensus remain the deﬁnition of price and its relation
to consumer surplus measures, the integration of uncertainty, the classiﬁcation of var-
ious impacts among transfers and externalities, and partial versus general equilibrium.
This lack of consensus among economists, who often depend on multiple disciplines to
identify and quantify the impacts of an action, has been further obscured by the interest
and participation of noneconomists into the deceptively clear debate about beneﬁts and
costs. Alternative forms of integrative analysis, such as socioeconomic impact analysis
or multi-attribute utility, have been used and suggested outside of the formal context
of beneﬁt-cost analysis but may at times use similar terminology. This chapter focuses
on the welfare and beneﬁt-cost issues deﬁned by the economics literature in the hopes
of improving clarity in that one domain without asserting that beneﬁt-cost analysis is
the only information that can or should be used in the analysis of decisions related
to slots.
1.2 Slot Machines: Industry Deﬁnition and Relevance
The gambling industry around the world contains a huge variety of ways, legal and
illegal, for people to place wagers on outcomes, including human sports, animal con-
tests, card games, dice games, and other methods to generate random or nonrandom
outcomes. Slot machines are one approach to generating a random outcome, if there
is no tampering, which dates back over one hundred years (Fey 2006). The Ameri-
can Gaming Association (AGA 2010) deﬁnes a slot machine as “Any mechanical or

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639
electrical device in which outcomes are determined by a random number generator
located inside the terminal” while deﬁning the closely related video lottery terminal
(VLT) as “an electronic game of chance played on a video terminal that is networked
and can be monitored, controlled and audited by a central computer system. These
games are authorized through the state lottery and considered by law to be lotteries,
not commercial gaming.”The designation electronic gaming device (EGD) covers both
categories and represents “Any mechanical or electrical game of chance, including slot
machines, video lottery terminals (VLTs), video bingo, video pull-tabs and video poker
machines”(AGA 2010). For the purposes of this chapter, slots is the popular shorthand
that will include both these deﬁnitions as well as the more generic EGD. Within the
deﬁnition of slots there are many variations around the world which go by other names,
including pokies, video poker games, fruits, and so on. Getting their name from the
historical manner in which money was fed into a machine with mechanically spinning
wheels (Fey 2006), modern slot machines typically accept wagers or bets as small as
one cent ($.01) or as high as one hundred dollars. Current machines allow payoffs
on one or more “lines” or combinations of symbols with a frequency of appearance
controlled by a computerized random number generator (Turner and Horbay 2004;
AGA 2010). Ultimately playing slots requires no special skills or prior knowledge of
the game; neither does it require such of other players (Stewart 2010). The games have
low stakes and a relatively high reward rate, and the machines themselves use sight and
sound effects to encourage betting (Fisher and Grifﬁths 1995; Breen 2004).
While dependent on the legal regime of a given jurisdiction, slot machines can
become dominant in a casino-like setting yet can also operate well in small, disbursed
locations. Although this chapter focuses on physical slot machine gaming, the Internet
provides new venues for slot machine gambling that have been little studied (National
Gambling Impact Study Commission 1999; Australian Productivity Commission 2010;
European Commission 2006). Evidence prepared for the American Gaming Associa-
tion indicates that in a mature casino environment in the United States, such as Atlantic
City, the share of revenue generated by slot machines has increased from 40 percent
of revenue in 1978 to about 70 percent by 2010. Similarly, William Eadington (1999)
reviewed data demonstrating that slots are the dominant revenue source in U.S. casinos
while Richard Thalheimer and Mukhtar Ali (2003) reported that slots accounted for
about 80 percent of riverboat revenues in 1998. Statistics Canada reported that about
40 percent of net revenue is earned by slot and VLT machines outside Canadian casinos
and that slots dominate inside casinos, which, from slots and other games, generated
34 percent of net revenue in 2010 (Statistics Canada 2010). Thalheimer (2008) reported
that after legalization of VLTs in the racetrack setting in West Virginia total wagering
increased while pari-mutuel betting decreased. However, different casino and legal
structures inﬂuence this balance, with historically lower levels of slots in the United
Kingdom and in various locations within Europe (Eadington 2008). At the same time,
a broader survey of gambling in the United States by John Welte et al. (2002) updat-
ing several earlier national surveys reported that 17 percent of respondents indicated
that they had used gambling machines as compared to the two most popular forms of

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lotteries and gambling machines
gambling, “Lottery,” with 66 percent, and “Ofﬁce Pools, Rafﬂes, Charity,” with 48 per-
cent; 27 percent reported participating in casino gambling (generally including a large
but undeﬁned component for slots) as an independent category.
Although growth in a regulated market such as gambling need not follow the dictates
of supply and demand, it is clear that slots are an important technology in the gam-
bling industry. As such, it is likely to embody many of the issues that are barriers to a
consensus in determining net beneﬁts of gambling. For example, research is investigat-
ing hypotheses that slot machines may be disproportionately associated with problem
gamblers as a result of the very rapid feedback from slot machines to the gambler and
other elements of environmental control (Chóliz 2010; Harrington and Dixon, 2009;
Williams and Wood 2004; Volberg 2001; Smith, Hodgins, and Williams 2007). Empir-
ical results do reﬂect a high degree of correlation between slot machines and problem
gambling. Katherine Marshall and Harold Wynne (2003) cited Canadian Community
Health Survey data showing that approximately 25 percent of VLT players are at-risk
or problem gamblers. Based on a prospective diary study, Robert Williams and Robert
Wood (2004) attributed almost 60 percent of slots revenue in Ontario to moderate or
severeproblemgamblers. RachelVolberg(2003)reportedthatintheUnitedStatesprob-
lem gamblers are more likely to identify slot machines as their favorite type of gambling,
whereas Elisardo Becoña et al. (1995) reported a disproportionately high incidence of
pathological gamblers among slot machine players in Spain; notably, neither of these
results appears inconsistent with the volume of gambling represented by slots. A recent
review by Nicki Dowling, David Smith, and Trang Thomas (2005) concluded, however,
that the existing evidence was insufﬁcient to conclude that slots are relatively more
addictive than other forms of gambling but that further research on addiction and on
the characteristics of the machines and games themselves is warranted.
In a study of VLT players in Alberta, Garry Smith and Wynne (2004) found 61.1 per-
cent to be either moderate-risk or problem gamblers (39.3% and 21.8%, respectively).
About 79 percent of these problem gamblers reported spending over $300 per month
(not including winnings) on gambling; in comparison, only 6.4 percent of the non-
problem gamblers spent over $100 per month on gambling, and none spent over $300.
While the majority of all VLT players gave “winning” as their primary attraction to
VLTs, 17.8 percent of the problem gamblers chose“excitement/thrill/rush”as compared
to 5.1 percent of the nonproblem gamblers. Moderate-risk and problem gamblers most
often played VLTs alone, while low-risk and nonproblem gamblers did not. Of problem
gamblers 34 percent reported that VLT playing had created problems in their lives as
compared to 2.4 percent of nonproblem gamblers and 0 percent of low-risk gamblers.
About 58 percent of problem gamblers expressed a desire for VLTs to be removed from
their communities.
Somewhat more broadly, research by Brad Humphreys et al. (2011) found substan-
tial differences in the impacts of speciﬁc forms of gambling. The study differentiated
between electronic gaming machines (EGMs) located at racetracks or casinos and
those located in bars. The study, the results of which were generally consistent with
those reported by Smith and Wynne (2004), also found that slot machine gambling is

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the benefits and costs of slot machine gambling
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linked to reductions in self-reported stress levels but an increased probability of self-
reported health problems. Another stream of economic research links “addiction” to a
time dependence of purchases with increasing purchases over time (Becker and Murphy
1988; Guryan and Kearney 2010). With speciﬁc regard to slot machine gambling, newly
detailed evidence from loyalty cards at a U.S. casino where 90 percent of the revenues
accrued from slot machines indicates that about 8 percent of the gamblers could be
classiﬁed as “economically addicted” (Narayanan and Manchanda 2011).
Consequently, slot machines appear to be a worthy subset of gambling for economic
investigation.
2 Benefit-Cost Theory and Slots
.............................................................................................................................................................................
A strength of beneﬁt-cost analysis and its welfare foundation is that similar theoretical
concepts are used across application areas. Textbooks in beneﬁt-cost analysis typi-
cally place all beneﬁt and cost impacts into the four categories of consumer surplus
(CS), producer surplus (PS), government revenue (GR), and external effects (ES) (e.g.,
Boardman et al. 2011; Zerbe and Dively 1994; Bellinger 2007). Note is often made that
the change in government revenue comes from the other categories, but interest in the
distributional effect on government is sufﬁciently broad that government is standardly
broken out in the above manner. Changes in these categories deﬁne the change in social
welfare or social surplus (SS) from an action compared to a baseline, so that
	SS = 	CS + 	PS + 	GR + 	ES = Total Beneﬁt −Total Cost.
The same textbooks show that total beneﬁt less total cost is equivalent to the surplus
factors outlined above when beneﬁts and costs are appropriately deﬁned. Nonetheless,
the broader use of beneﬁts and costs is so intuitive that users may not realize the
framework provided by the more jargon-based use of “surplus” measures from which
the theory is developed. In general, “surplus” refers to the gain or loss to participants
on the early or intra-marginal units obtained, even if they only break even on the
ﬁnal unit (Boardman et al, 2011; Australian Productivity Commission 1999; Walker
2007a; Grinols 2004). For producers, the surplus measure is akin to operating proﬁt;
for consumers, it is a monetary measure of getting a good deal as you would have been
willing to pay more for it.
Thiscoretheoryhowever,ignoresriskof varyingoutcomes,whichdependsonproba-
bility, clearly a central element of slot machine gambling as well as many other activities.
However, it is the excitement and the bane of the current era that understanding and
modeling decisions with risk (or uncertainty) remain unsettled. The theoretical frame-
work is that of expected utility (Baumol and Wilson 2001; Friedman and Savage 1948;
Markowitz 1952), which provides the well-known models of risk aversion, risk loving,

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lotteries and gambling machines
and risk-neutral preferences, but sufﬁcient observation of behavior counter to the the-
ory has prompted proponents of the behavioral economics school to seek to develop
alternative risk-based theories (Thaler 1992; Machina 1987; Camerer, Loewenstein, and
Rabin 2004; Starmer 2000). As a consequence, measures that integrate risk have been
proposed to replace some measures, especially consumer surplus, in equation 1. Each
of the following sections takes one of the four components of equation 1 and identiﬁes
key theoretical issues in their application to slot machine gambling.
3 Consumer Surplus for Slots
.............................................................................................................................................................................
This core theoretical element beneﬁt-cost analysis has been much discussed in regard to
gambling but is often omitted in practice (Australian Productivity Commission 1999;
Walker 2007a; Grinols 2004; Crane 2008). To focus on consumer surplus the analyst
assumes that gambling is like other products in which probability does not play an
explicit role. In particular, the consumer is expected to gain satisfaction (utility) from
the act of gambling regardless of winning or losing. This is gambling as entertainment.
Further, the consumer must be responsive to the price of the activity as consumer
surplus only exists with a downward sloping demand curve such that more is con-
sumed if the price is decreased. The Australian Productivity Commission (APC) (1999,
appendix C) used surplus as an element in its analysis of beneﬁts while Yuliya Crane
(2008) extended the consumer surplus analysis and applied it to the United Kingdom.
It is important to note that these analyses were driven by information about the price
elasticity of demand and the functional form of demand for gambling, about which
relatively little is known. Yet the consumer surplus beneﬁt with a linear demand curve
can be estimated as gross gaming revenue divided by twice the absolute value of the
elasticity (APC 1999, appendix D; Crane 2008, 161). Thus consideration of this factor
can be a major component, in the neighborhood of the gross gaming revenue, if this
framing of consumer beneﬁts is utilized.
3.1 Non-normal Gambling and Consumer Surplus
Substantial interest exists across health care professions, policy analysts, economists,
and the gambling industry regarding individuals who score high on diagnostic tests
identifying behavior that deﬁnes a mental disorder focused on gambling or, in a pos-
sible revision of American psychiatric terminology, to addiction and other disorders
(American Psychiatric Association 2010). A large literature exists on problem and
pathological gamblers, those who have various personal and interpersonal difﬁculties
associatedwithgamblingandwhoaredisproportionatelythesourceof gamblingexpen-
ditures and hence revenues (National Research Council 1999; Smith et al, Hodgins, and

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the benefits and costs of slot machine gambling
643
Williams 2007). Economics deals somewhat differently with addiction, including its
various forms, such as drug, alcohol, and tobacco use and, more recently, gambling. In
the economic models of time-consistent and rational consumers there is the possibility
of “rational addiction” where such behavior represents an individual’s unique prefer-
ences (Becker and Murphy 1988; Gruber and Köszegi 2001). Related to the emerging
behavioral economics literature are counterarguments as well as evidence that some
“addicts” would prefer to exist in an unaltered state and are willing to pay to change
their behavioral accordingly but are unable to do so (Vining and Weimer 2010). While
the issue is still seeking resolution, an alternative consumer surplus model for some
gamblers has been presented by the Australian Productivity Commission (1999), David
Weimer, Aidan Vining, and Randall Thomas (2009), and Vining and Weimer (2010) in
whichanadjustmentissuggestedforthoseaddictedwhosedemanddoesnotreﬂecttheir
“true” preferences. In such cases the addicted person, perhaps a gambler, is modeled as
receiving the beneﬁts that a “normal” gambler would receive should a normal gambler
engage in a large quantity of gambling, but the addicted gambler is not accorded the full
surplus that that gambler’s “addicted” demand curve appears to imply. Consequently
there is a downward adjustment in the surplus apparently accorded to addicted gam-
blers based on their observed behavior. This is illustrated in ﬁgure 32.1, where the blue
area is the consumer surplus for a normal gambler, determined in the standard way as
the area beneath the “normal” demand curve and above the price line. The “addicted”
gambler has the larger demand curve, DA, and consumes a larger quantity of gambling,
QA, than does a normal gambler. The adjustment suggested, for which Weimer,Vining,
and Thomas (2009) as well as the APC (1999) developed formulas for speciﬁc func-
tional forms, is to use the normal demand as the reference point so that an addicted
gambler still receives the blue-shaded consumer surplus accorded a normal gambler
Price
P
QN
QA
DA
Quantity
DN
figure 32.1 Surplus for a normal and addicted gambler

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lotteries and gambling machines
while the addicted gambler loses the value colored orange given the speciﬁc illustration
in the ﬁgure.
This innovation in consumer surplus for non-normal gamblers usefully breaks up
the monolithic composite consumer of gambling into two types while clearly paving
the way for greater heterogeneity of gambling consumers.
The distinction between normal and addicted gamblers may be especially important
for slot machines in ways that are not yet fully understood. First, if all types of gam-
bling are equally “addictive,” then the large proportion of slot machine revenues to the
gambling industry would indicate an expected association with slot machines and the
observed number of non-normal gamblers. However, work such as that by Mariano
Chöliz (2010) and Harrington and Dixon (2009) suggest that slot machines may be
more than averagely addictive. If so, any associated consumer surplus adjustments,
and impacts discussed as externalities below, may be increased when analyzing slot
machines if further research justiﬁes such an empirical adjustment.
3.2 Location and Distance Consumer Surplus
Distance to a venue is an important determinant of consumer gambling behavior
(e.g., Thompson, Gazel and Rickman 1995; Grinols 2004; Baker and Marshall 2005).
An additional component of consumer surplus links consumer value to the distance
to their gambling locations as introduced by Earl Grinols (1999, 2004) and used by
PolicyAnalytics (2006) and Scott Farrow and Judith Shinogle (2010). Grinols developed
a model where the usual consumer surplus based on the direct gambling price does
not change, but instead policies that expand gambling locations appear to increase
frequency and change the expenditures of existing gamblers and expand the set of
those who gamble. Grinols modeled distance as entering directly into a utility function
and used industry data to infer modest beneﬁts for an average resident who may or may
not gamble. He modeled a representative consumer as deriving utility from gambling,
v, a composite of other goods,x, and enjoyment, E(g,m), that is a function of the
amount gambled per visit, g(also said to be price or cost), and distance, m, to deﬁne a
utility function of the general form U(x,v, E(g,m)). Grinols (1999, 2004) continued
by deriving an optimal expenditure function and specifying two constant elasticity
forms for the utility function. The speciﬁc function was calibrated based on data such
as income, the average amount gambled per visit, and the number of visits to derive
monetary values for increased value, which are conveniently presented in tabular form.
As this was derived for a representative consumer, it appears to apply to all citizens,
though some number of people chose not to gamble.
While integrating site accessibility into value appears useful and insightful, Grinols’s
approach is unusual as utility is modeled as a function of enjoyment and prices are com-
bined with quantities in the utility function. In contrast, there is an important history
of using travel cost models to infer beneﬁts for recreational consumers as surveyed in
Freeman (2003). A direct travel cost approach, noted by Grinols, builds quality of a site

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645
into utility while random utility models build discrete choice for a consumer among
qualitatively different sites. These models are not without problems, but Grinols’s
approach appears to be a different and relatively unexplored approach.
The role of distance and its link to consumer value appears to be a useful direction
for further research designed to integrate the distance estimation into more widely
accepted procedures. Internet slots or other online gambling also may open up new
ways of assessing distance beneﬁts, as there is effectively no distance between computer
access and a gambling site, though the quality of site may differ from a traditional site.
Speculatively, such an analysis will bring to the fore the previously ignored value of
individual time as part of the price of gambling and highlight the question“What is the
price people pay to gamble?” This question will be brieﬂy investigated in section 4.
3.3 Risk-loving Preferences, Integrated Models,
and Option Price
Modeling slot machine gambling as one of many sources of entertainment seems to
capture some element of the activity, but would people gamble as much if there were
zero probability of winning more than the amount wagered? Many survey respondents
reply that they gamble in the hopes of winning, as discussed above. If so, the con-
sumer surplus model of the gambler as only seeking entertainment omits an important
component of gambling.
The willingness to give up money in order to accept a gamble, that is, risk-loving
behavior, is a core part of basic expected utility theory (Eeckhoudt, Gollier, and
Schlesinger, 2005). The amount a risk-loving person would give up in order to take
an unfair bet, one whose statistical expected value is less than the wager, will vary by
individual preferences and the probabilities and payoffs. A person with those pref-
erences will rationally accept an unfair bet. Famous economists tried to resolve the
paradox that many people both gamble and buy insurance (Friedman and Savage 1948;
Markowitz 1952). That paradox has not been fully resolved, though there are many
theoretical contenders (Starmer 2000).
Risk-loving preferences suggest an alternative measure to consumer surplus for the
maximum willingness to pay in order to maintain the same level of utility. The ex-ante
amount a person is willing to pay to accept a gamble has been called an option price.
While usually framed as the amount a risk-averse person would give up to avoid vari-
ability in income, for risk-loving persons it is the amount they are willing to pay to
have access to the gamble. This ex-ante option price has not to the author’s knowledge
been used to value the beneﬁts of slots to consumers although it directly models the
consumer’s intent to gamble. Such an approach is implicit, however, in the market
equilibrium of gamblers investigated as part of the longshot bias literature (Gandhi
2008; Humphreys and Weinbach 2010).
It is not surprising that models have been developed that allow gambling to generate
both pleasure and variability in income (Conlisk 1993; Sauer, 1998). These models,

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lotteries and gambling machines
however, have retained the risk-averse assumption for consumers such that gambling
occurs because the pleasure of entertainment dominates the risk aversion. While this
may be appropriate for some gamblers, it may also suggest that for some people, those
who may be risk loving and gamble at least in part to improve their wealth, risk
preferences and entertainment purposes mutually create demand for gambling instead
of partially offsetting each other.
Further, behavioral economics identiﬁes several ways that people have difﬁculty
assessing probabilities in a purely rational way and may instead apply various heuristics
to situations (Thaler 1992; Camerer, Loewenstein, and Rabin 2004; Starmer 2000).
With respect to gambling, particular attention has been paid to implications of the
behavioral “Law of Small Numbers” (Tversky and Kahneman 1971; Narayanan and
Manchanda 2011). Generally, consumers may have difﬁculty with small samples and
independent probabilities, mistakenly assuming either a negative correlation between
outcomes (Gambler’s Fallacy) or a positive correlation (“hot hand”) in the context
of what are actually random draws. A behavioral approach, and less than perfectly
informed consumers,may well lead individuals to believe probabilistic properties of slot
machines that are at odds with their actual design. For instance, following a mistaken
“hot hand” belief, consumers may misinterpret such signals as “near misses” on a slot
machine line as indicating that one is closer to winning on the next trial than is justiﬁed
by a random draw.
Taken together, the theory of beneﬁts to consumers indicates that consumers are
heterogeneous, that multiple motivations may exist, and that consumer surplus or
risk-based measures are the appropriate constructs to evolve into positive models of
the gambling consumer, though no single widely accepted approach is agreed upon in
the literature.
4 Framing Issues
.............................................................................................................................................................................
The analysis of the consumer led directly into controversial issues in conceptual mea-
surement and illustrates the usefulness of framing the background conditions for the
analysis. Motivated by behavior of the consumer but also relevant to business (pro-
ducer’s surplus), government, and external factors, the issues of marginal effects, price,
standing, partial and general equilibrium, and employment beneﬁts are described here.
4.1 Marginal Effects
The incremental costs and beneﬁts compared to a well-deﬁned baseline are the desired
measures for a beneﬁt-cost analysis. The baseline of what would exist in the absence
of a policy can be difﬁcult to determine. The standard baseline is the status quo of
what exists, for instance, what gambling may be permitted in and around a jurisdiction

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the benefits and costs of slot machine gambling
647
being analyzed. However, there may be some dynamic aspect to the baseline as well, for
instance, if a neighboring jurisdiction might be expected to retaliate by altering their
conditions for gambling if a new jurisdiction changed their position (Walker 2007a).
Similarly, for an individual, the beneﬁts and costs should be determined incrementally.
The analyst may observe that a person becoming a problem gambler increases social
costs by a particular magnitude, but what is the baseline? Problem gambling can often
coexist with depression, drug and alcohol abuse, and higher levels of stress (Walker and
Barnett 1999; Walker 2007b; Eadington 2003). Empirical difﬁculties arise in attempting
to determine whether problem gambling acts as a catalyst for these conditions or
vice versa, particularly if the direction of the effect varies by individual. Comorbidity
likewise raises questions as to the degree to which problem gambling inﬂuences negative
outcomes. The U.S. National Opinion Research Center (NORC) compares expected
rates of negative outcomes for nonproblem gamblers with rates for problem gamblers,
attributing the difference (after controlling for chance and for confounding factors) to
gambling. The Australian Productivity Commission (1999, 7.11 and 9.9) employed a
“causality adjustment” based on the premise that approximately 20 percent of problem
gamblers would have experienced a given negative outcome even in the absence of their
gambling problem.
4.2 Price
Price is fundamental to the analysis of both consumers and producers, but it is a slippery
concept when one is buying a service that may have multiple outcomes, such as a payoff
or no payoff. The Oxford Dictionary of Economics (2009) deﬁnes price as the “amount
of money paid per unit for a good or service” while noting that deﬁning price can be
more complex for some goods. In the case of gambling, what appears to be the direct
price for access to the gamble (the good or service) may in fact return money to the
purchaser after the outcome is determined. The gross price initially bet is generally
called the wager (American Gaming Association 2010), but most economic analysis
(e.g., Eadington 1999; Paton, Siegel, and Vaughan Williams 2004; Thalheimer 2008)
deﬁnes price as the long-run cost from repeated play expressed as a percentage of the
amount wagered, though the price for any particular run of bets may vary substantially
and, with some probability, be positive. Thus if a slot machine is designed to pay back on
average 95 percent of the amount wagered,the price is said to be 5 percent of the amount
wagered. The deﬁnition of price is important in the estimation of consumer surplus,
which depends on consumer responsiveness to price; in the deﬁnition of effective tax
rates; and in deﬁning the seller’s revenue and tax obligation (Clotfelter and Cook 1990;
Paton, Siegel, and Williams 2004).
Travel costs add an additional complication to the price of gambling. The full cost
of the gambling experience can involve some, perhaps large, travel costs though other
co-activities also may also, such as dining, entertainment, and so on. The beneﬁt-cost
literature has made heavy use of the hedonic travel cost model whereby surplus is

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lotteries and gambling machines
inferred from the costs incurred when people choose different destinations based on
the characteristics of the destination (Freeman 2003). Such an approach seems not to
have been used in the gambling literature, but Grinols’s (1999, 2004) accounting for
distance consumer surplus is a similar concept.
4.3 Standing
The issue of standing in beneﬁt-cost analysis usually applies to a geographic area or to a
characteristic of the consumer (Boardman et al. 2011; Zerbe and Bellas 2006). Deﬁning
whose beneﬁts and costs are to be included through a determination of standing is
particularly important to slot machine studies, which are often focused on a region or
smaller political jurisdiction. In addition, the determination of standing can affect how
transfers among parties are deﬁned.
Regional analysis creates several problems in the deﬁnition of standing. If standing
is deﬁned as the citizens of a state, then only costs and beneﬁts to those individuals
count. This deﬁnition plays a central role in many gambling studies, as what is gained
as a beneﬁt by one jurisdiction, such as governmental revenues and producer surplus
from locally owned businesses, may be lost as a cost to another jurisdiction. A regional
analysis will only show the limited beneﬁts or costs to its own citizens. The choice
of standing may make it difﬁcult to determine the “ownership” of some impacts. A
problem gambler may be from another jurisdiction, or business owners may not in fact
reside in the state. This issue can also be a policy motivation to legalize gambling when
it appears that some beneﬁts of gambling, such as government revenue, are “lost” to
another jurisdiction, a framing that implies some limitation on standing.
One characteristic affecting the standing of a consumer that has generated debate is
that of thievery. As some believe that gambling increases crime, the issue is whether the
thief has standing in a beneﬁt-cost analysis (Grinols 2007; Walker 2007b). If standing is
granted, then crime is partially a transfer as the thief gets a beneﬁt from what is stolen
and the victim both loses what is stolen and may well suffer nonmonetary damages.
The more common approach is to use the law as declaring a social value that declines
standing for the thief and hence to not count the beneﬁt, unless the law itself is being
analyzed (Boardman et al. 2011, 39).
4.4 Partial and General Equilibrium, and Employment
The majority of beneﬁt-cost analyses are partial equilibrium that includes impacts in
one or a few markets, in contrast with general equilibrium, which seeks to take into
account a larger number of interrelated markets. A partial equilibrium analysis is most
easily justiﬁed when markets are believed to be reasonably competitive and without
major distortions, including tax distortions (Goulder and Williams 2003; Boardman
et al. 2011; Baumol and Wilson 2001; Chetty 2009). Time and resources may also limit

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the benefits and costs of slot machine gambling
649
analyses to the direct impacts modeled in a partial equilibrium analysis, and analytical
methods in practice may include a behavioral response reﬂecting feedbacks from other
markets into the main markets of concern (Boardman et al. 2011; Chetty 2009). How-
ever,theconceptualbasisforgeneralequilibriumanalysisiswellestablished,andincases
with large tax distortions, signiﬁcant unemployment, or many and large substitutes or
complements the general equilibrium analysis becomes more important (Hazilla and
Kopp 1990; Goulder and Williams 2003). However, the information required to imple-
ment a general equilibrium analysis typically involves cross-market impacts which may
not be available, such as cross-price elasticities. Econometric models are available for
some markets but may lack the detail necessary for a relatively minor market such
as gambling (e.g., Nevada Commission on Economic Development 1999; Treyz and
Treyz 2002). Alternatively, analysts often resort to the assumption of ﬁxed-proportion
production relations as modeled in input-output analysis (e.g., Miller and Blair 2009;
Regional Economic Applications Laboratory 2003). The work of Grinols (2004) builds
on a macroeconomic trade approach that is more analogous to a general equilibrium
approach, though the framework is relatively less common in beneﬁt-cost analysis.
Consequently, many applied general equilibrium analyses are substituting another set
of assumptions for those used in partial equilibrium analysis. Ideally, the analyst may
investigate the impact of alternative framing assumptions, but this is seldom done.
Whether or not employment beneﬁts exist is a high-proﬁle implication of the choice
of partial or general equilibrium analysis and of the determination of standing. The
costs of employment are almost universally included in costs of operation, part of
the determination of producer surplus. However, advocates of gambling (as well as
many other regional development projects) tend to list employment as an important
beneﬁt of the gambling industry. Standard guidance indicates that such beneﬁts are
to be included only in well-deﬁned and limited circumstances. For instance, guidance
from the U.S. government (U.S. OMB 1992, 6) states that generally “analyses should
treat resources as if they were likely to be fully employed. Employment or output
multipliers that purport to measure the secondary effects of government expenditures
on employment and output should not be included in measured social beneﬁts or
costs.” The default presumption in beneﬁt-cost is that of well-functioning markets
in which unemployment is at its natural rate due to turnover and transitional issues.
Similar default guidance appears in textbooks, such as Boardman et al. (2011), with
caveats as discussed below. In the natural rate of unemployment (full-employment)
case, labor is paid its opportunity cost at the margin, the payment just compensates
the employee for giving up his or her time, and no incremental employment beneﬁts
accrue in the labor market.
However, two important cases may justify an employment beneﬁt that is a portion of
labor expenditures. The core exception is a signiﬁcantly higher rate of unemployment
than the natural rate, with signiﬁcant typically a matter of judgment. Such a higher rate
of unemployment indicates disequilibrium in the labor market and the potential for
labor expenditures to exceed the opportunity cost of labor, creating a partial, additional
beneﬁt to the worker in excess of the cost to induce the labor supply. Recent discussions

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lotteries and gambling machines
of accounting for labor in times of high unemployment include Boardman et al. (2011)
and Haveman and Farrow (2011), which contain guidance on assumptions for the
amount of labor expenditures that might be considered as an additional beneﬁt. The
second case is a subset of the ﬁrst when a regional analysis, as for a city or state, deﬁnes
whose costs and beneﬁts have standing in the analysis. While it would still be necessary
for high unemployment to exist in the receiving jurisdiction to provide the potential
for additional labor beneﬁts, a regionally focused analysis may exclude lost jobs in other
jurisdictions and thus overstate beneﬁts from a broader perspective.
5 Producer Surplus
.............................................................................................................................................................................
Conceptually similar to consumer surplus, producer surplus is typically measured as
the excess of price over marginal cost for the appropriate market duration of short or
long run. As the marginal cost is driven by technological and regulatory considerations
in the industry, the result is case dependent. In a constant-cost, perfectly competitive
industry, in the long run there would be zero producer surplus while in a market with
regulatory protection against entry there may be signiﬁcant producer surplus, though
the potential exists that competition for economic rent may dissipate a potential surplus
(Walker 2007a).
Regional gambling impact studies may include changes in local proﬁts (Anielski and
Braaten 2008), although some beneﬁt-cost analysts assume with little justiﬁcation that
there is no producer surplus in the gambling industry while others apply an average
rate of proﬁt pending better information.
Two important modeling issues arise in estimating producer surplus beyond the
issue of marginal cost. The ﬁrst is whether to include taxes (gross surplus) or to exclude
them (net surplus). As there is typically substantial interest in government revenues
in the analysis of gambling, most producer surplus measures would be net of taxes,
although at times it is useful to be clear that the tax revenues can also be accounted for
as reductions in consumer and producer surplus (Boardman et al., 2011; Krutilla 2005).
The second issue is the selection of partial or general equilibrium analysis and the role of
substitution and complements to gambling. If a jurisdiction is considering gambling,
other industries may be affected, such as substitute entertainment opportunities or
other purchases (Grinols 2004, 2007; Walker, 2007a). If in moving toward a general
equilibrium analysis one includes additional markets, then producer (and consumer)
surplus may be lost or gained in other markets as well.
6 Net Government Revenue
.............................................................................................................................................................................
The change in government revenues was identiﬁed as a core element of net beneﬁts in
equation 1. It is common in some analyses to read the statement that taxes are transfers

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651
from consumers and producers to the government and so cancel out as a negative
item to one party and a positive item to another (U.S. OMB 1992, 2003; Boardman
et al. 2011, 85–96). This “exact” netting out is only true if such transfers are costless
to implement and have zero efﬁciency cost in contrast to an approach that explicitly
recognizes such costs or the efﬁciency cost of taxation, termed the marginal excess
burden (Boardman et al. 2011). For some applications, such as gambling, the impact
on government revenue is a central issue of concern, and it is useful to reduce consumer
or producer surplus and track the changes in government revenue. Also, in a regional
analysis when those outside the jurisdiction are taxed, the “zeroing out” of transfers
neednotapply. Consequently,mostgamblingstudiestrackthechangesingovernmental
revenue.
Changes in net revenue may result both from added expenditures and added rev-
enues. If gambling or its removal is being considered in a jurisdiction, then there are
likely impacts on monitoring and enforcement costs incurred by the government. In
some cases this may be transparent as new agencies are established by the government
to oversee gambling activities; in other cases there may be a diversion of funds used for
other purposes to cover new oversight. Increasing revenue is often an explicit purpose
of the change. In such circumstances the tax or other named revenue from gambling
is an important beneﬁt so long as it is not double counted as part of consumer or
producer surplus.
Several interpretative issues exist related to price, effects on competing goods and
services, and the earmarking of funds. With regard to price, the effective tax rate is
importantly determined by the speciﬁc regulation and the calculation of price. For
instance, assume a tax regulation requires 25 percent of the casino slot machine “win”
(wagers minus payout) to be paid to the government. Assume the win is 5 percent of
the amount wagered; for a $1 bet the“tax”collection is 1.25 cents, a small percentage of
the amount wagered (1.25%) but 25 percent of the price based on the payout rate. With
regard to competing goods, the government may be competing with itself and observe a
decline in some already legal types of gambling if new types of gambling are introduced
(Walker 2007a). This is a speciﬁc illustration of general equilibrium concerns where the
analyst may wish to include other signiﬁcantly affected markets. Finally, changes to the
legal status of gambling are sometimes justiﬁed by earmarking changes in government
revenue to particular purposes, such as for the elderly or education. This political
linking of source of funds and use of funds is counter to standard beneﬁt-cost practice,
which assesses the opportunity cost of funds based on a discount rate. Alternatively, the
use to which the funds are to be put could be analyzed through a beneﬁt-cost analysis
by deﬁning several different alternatives, such as, (1) raise funds via gambling (which
can have a marginal burden of taxation), (2) raise funds directly via taxes, which is
likely to include a marginal excess burden of taxation, and (3) combine a speciﬁc use
of funds with both fund-raising methods and include doing nothing as an alternative.
Such an analysis would at least indicate whether a potential efﬁciency improvement
exists; it would not, however, indicate whether the largest potential improvement is
being chosen, as the uses of the funds are restricted to a small set.

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lotteries and gambling machines
7 External Effects and Shadow Prices
.............................................................................................................................................................................
Market imperfections have a long history in economics, and various cases are well
worked out demonstrating changes in economic efﬁciency and transfers from one party
to another. Monopoly market power is one early example; the rise of environment and
health issues brought externalities, public goods, and information asymmetries to the
fore. A concern about gambling is that there may be effects, often detrimental, on other
parties who are not part of the direct purchase of gambling services. Examples include
concern about additional criminal activity, including white collar fraud or burglary;
community well-being” or negative effects on household and friends often involving
money or behavior linked to problem gamblers; and so on. Numerous papers, especially
impact analyses identify various candidate effects (Anielski and Braaten 2008; Grinols
2004; Volberg 2003; Thompson, Gazel and Rickman 1997). In contrast to impact
approaches, economic welfare approaches (Walker 2007b; Collins and Lapsley 2003;
Eadington 2003) are likely to place impacts on those actually gambling primarily in the
consumer or producer categories while putting into the external category those affected
but who were not a part of the original gambling transaction between buyer and seller.
The default economic position is that voluntary exchanges must beneﬁt both parties
in some way, not necessarily ﬁnancial, while involuntary transactions may not be fully
considered in prices and result in an externality. Douglas Walker and A. H. Barnett
(1999), Walker (2007a), Grinols (2007), and Eadington (2003) worked to apply various
deﬁnitions of social costs that are related to but somewhat distinct from those in broader
use in beneﬁt-cost analysis. For instance, Boardman et al. (2011, 91) used a typical
deﬁnition of externalities from the environmental literature, stating that an externality
is “an effect that production or consumption has on third parties-people not involved
in the consumption or production of the good.” John Roman and Graham Farrell
(2002) linked this approach to the crime literature where businesses, government,
or other actors may alter incentives for criminal activity and so externalize some of
the actions of an industry. The potential for increased burglary or other criminal
activitytosupportcompulsivegamblingisanexample. Orconsiderfraudulentbehavior
to obtain money, illustrated in the nonﬁction book and movie Owning Mahowny,
which are about a compulsive gambler who creates fraudulent loans at his bank job in
order to support his gambling (Ross 1987). Increased criminal activity, whether white
collar or street level, would generally be considered to create involuntary harm to third
parties and constitute an externality (whether a thief has standing was discussed in
section 4.2).
Information asymmetries are also considered a market imperfection when there
is unequal information on one side of the market, for instance on the probability
of default. Consider, for instance, a gambler who borrows funds from a ﬁnan-
cial institution or informally from family or friends. The ﬁnancial institution will
gather what information it may and charge interest on the exchange that adjusts

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653
for risk. If there is asymmetric information, such as risky unobserved characteris-
tics of the borrower, that market will work imperfectly in the sense that the price
may be too low leading to inefﬁciency but also result in a transfer, if legal, to the
buyer in this case or conversely if the seller has the imperfect information (Boardman
et al. 2011, 89). Some of the gambling literature (APC 1999; PolicyAnalytics 2006;
Crane 2008) has moved toward an empirical identiﬁcation of the amount transferred
between creditor and debtor in the case of default but not including that amount as
a social cost, instead using the resource opportunity costs involved in a bankruptcy
ﬁling.
In the face of externalities and other market imperfections, individuals, or the gov-
ernment on their behalf, may take defensive action to reduce the frequency or severity
of an impact. Individuals may invest in better locks or avoid some areas. The gov-
ernment may invest in social policies to reduce social costs or its own budgetary
costs (which are separate objectives), such as providing therapy or increased polic-
ing. Such defensive expenditures are frequently considered a lower bound on the social
cost of the causing activity. Particularly in the case of government one may ques-
tion whether the defensive expenditures are economically optimal but do represent
an existing expenditure of resources to reduce a problem (Walker 2007b). While such
expenditures may be relatively easy to observe empirically, they are presumably reduc-
ing the costs relative to a no-policy equilibrium. Hence a government that spends
nothing on treatment may have a different proﬁle of social costs than one which does
expend funds.
Finally, some authors include elements of personal or community morality as an
external cost of legalized gambling. Two aspects of beneﬁt-cost analysis appear relevant,
though neither is common in the existing literature. The ﬁrst is analysis related to
the provision of public goods suggesting that different jurisdictions will specialize in
certain characteristics and that people will sort themselves into those jurisdictions. At
times the legalization of gambling is subjected to direct vote and so reﬂects a political-
economic representation of community values. The second approach is the inclusion
of “moral values” in beneﬁt-cost analysis (Zerbe 2002; McConnell 1997; Flores 2002).
Richard Zerbe has suggested that as long as people are willing to pay for certain states
of the economy, say willing to pay based on their own preferences for others not to
have gambling (a paternalistic cost), then those preferences should be represented
in the analysis. The analysis becomes more complex when models of nonpaternalistic
altruism are included but there are some conditions where nonpaternalistic preferences
are appropriate to include (Flores 2002).
While conceptual issues can continue to be clariﬁed, there remains the search for
a consensus on shadow prices (Boardman et al. 2011, chap. 16) relevant to gambling
where shadow prices are the marginal efﬁciency cost of an impact. This author’s reading
is that while there is some evolution of thought toward omitting the transfer compo-
nent of some elements, more work remains to be done in the conceptualization and
estimation of the shadow price of numerous impacts relevant to gambling.

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lotteries and gambling machines
8 Framing Issues between Impact Studies
and Benefit-Cost Analysis
.............................................................................................................................................................................
In contrast to the standard economic categories and questions, impact analyses appear
to gather a number of potentially positive and negative impacts together with less
conceptual structure to the organization, of which the Socio-Economic ImpactAnalysis
of Gambling framework (SEIG) (Anielski and Bratten 2008) is a leading example.
From an economist’s perspective, impact studies often contain double counting of
some impacts, as with gambling revenues and regional income; or include partial
accounting, as with including gross labor expenditures as a beneﬁt. For instance,Wynne
and Howard Shaffer (2003) listed the following items as the most frequently cited
impacts of gambling in the literature. To illustrate this tension, a welfare economic
perspective is provided following each point on their list, and though stated below in
an assertive way, many of the complexities of estimation justify further research.
Positive impacts (bullets identify impacts as presented in Wynne and Shaffer (2003):
• revenues for the public good, including health care, education, social services, and
community infrastructure:
• Welfare approach: change in government revenues (as appropriately netted from
consumer and producer surplus), regardless of the use of the funds but net of
governmental costs (Boardman et al. 2011).
• capital projects including parks, recreation facilities, museums, and cultural arts
centers:
• Welfare approach: Either omit the use of funds or deﬁne the alternatives of
the project more carefully. The gambling policy presumably raises funds. A
government decision to provide capital projects can be funded in several ways,
including raising taxes. An alternative could be deﬁned that allows gambling
with no capital projects, that allows gambling with capital projects and that
allows gambling, tax increases, and capital projects. In general, the use of funds
is generally analyzed separately from the source of funds.
• job creation:
• Welfare approach: The default in times of full employment is that there is zero
beneﬁt from employment. In times of high unemployment or when a regional
analysis denies standing to those employed in another jurisdiction, there may
be beneﬁts from employment that should be estimated as net of the reservation
price of labor (Boardman et al. 2011; Haveman and Farrow 2011).
• economic development:
• Welfare approach: Changes in producer and consumer surplus appropriately dis-
counted for impacts over time, though see “capital projects” or “employment”
above.
• opportunities for indigenous peoples:
• Welfare approach: Use distributional weighting on net beneﬁts accruing to
different groups (Boardman et al. 2011; Farrow 2011).

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the benefits and costs of slot machine gambling
655
• the entertainment value that gambling affords to the many players:
• Welfare approach: Analyze consumer surplus as a core concept but also likely
including some element of risk preferences.
• “legal” gambling formats that keep “illegal” gambling in abeyance,
thus
reducing crime that can be associated with unsanctioned, illegal gambling
alternatives:
• Welfare approach: legalizing gambling in this context would be a defensive
expenditure which should explicitly be compared to an alternative where gam-
bling is illegal. As the alternatives in this case investigate the law itself, the
alternatives would likely add insight if analyzed with standing both granted
and not granted to the person doing illegal activity. When gambling is legal,
there is a consumer surplus; when it is illegal the same surplus may be denied
standing.
Negative Impacts:
• rise in the number of people with severe gambling problems:
• Welfare approach: An increase in the number of people causing social costs
increases the ﬁnal outcome, social costs; the number of people is a cause and not
an effect.
• the havoc that problem gamblers wreak on themselves, their families, and the
community at large:
• Welfare approach: The impact on gamblers themselves is either excluded in a
standard analysis or compared to a“normal”gambler, as in the discussion of con-
sumer surplus. Speciﬁcity is needed on “havoc” to identify the external impacts
on others and their willingness to avoid the damage caused by the problem gam-
blers. Care should be taken with issues involving transfers, as there may be no
net effect on the economy.
• lost productivity at work:
• Welfare approach: The labor market is relatively highly developed and is expected
to adjust to observed productivity. To the extent there is asymmetric informa-
tion or illegality, analyses of asymmetric information or crime would apply or,
possibly, any real additional costs, such as training or search costs, that are
incrementally increased in timing.
• increased crime, notably fraud, theft, domestic violence, suicide, counterfeiting,
and money laundering:
• Welfare approach: Criminal activity is viewed as an externality for which there is
a beneﬁt-cost literature. Suicide has components of both externalities and costs
internalized by the individual.
• the possible cannibalistic effects that large casinos, bingo halls, and electronic
gambling in bars and lounges have on local small business revenues and employees:
• Welfare approach: General equilibrium effects are well understood in concept but
difﬁcult to measure in practice. The term cannibalistic is generally not applied
to business with positive and negative cross-price elasticities.

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lotteries and gambling machines
• increased need for health care, social service, policing, and other public service
costs that governments must bear to deal with the negative fallout from legalized
gambling:
• Welfare approach: In general, changes in cost should be considered as part of
the evaluation of net changes in government revenue. However, care should be
taken in deﬁning the baseline. A positive impact item listed above by Wynne and
Shaffer includes reductions in illegal activity; the governmental costs should be
assessed in comparison to the stated alternative.
An even broader set of impacts is contained in the SEIG framework (Anielski and
Braaten 2008), which is based around six “impact themes.” A total of 60 impacts are
grouped into the themes of health and well-being, economic and ﬁnancial, employment
and education, recreation and tourism, and legal and justice.
To illustrate the contrast in framing, the major categories in the SEIG for a regional
analysis are included in ﬁgure 32.2 while a possible structure for economic analysis that
focuses on markets is included as ﬁgure 32.3.
Region/Province
Employment
& education
Legal
Recreation
& tourism
Culture
Health &
well-being
X*
X* - each impact has an associated attribution
fraction; an attribution fraction in the degree
to which the gambling activity in a 
contributing factor to the impact
Financial &
Economic
Increased
government
tax revenues
More $ for
health services
& com. dev.
Problem
gambling
support services
Opportunity costs
to other government
programs
Perceived harm
resulting from
gambling
activities
Perceived harm to
social and community
programs reliant on
gambling revenues
Increased
tourism
Spill-over
impacts on other
businesses
Increased
employment in
rec and tourism
industries
Losses to other
local recreation
businesses
Net
employment
increases
Reduced
unemployment
Perceived
increase in
crime levels
Decreased
illegal
gambling
Increased
economic
activity
Adverse
impacts on other
local businesses
figure 32.2 SEIG framing
Source: Anielski and Braaten (2008, 53)

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657
Input Markets
Labor Market
Gambler's income 
Regional employment
Financial Markets
Borrowing/lending
External Effects
Household
Crime
Community
Government
Revenues and
expenditures
Legal conditions, standing, and
multiple market interactions 
Gambling market
Consumers: CS
Producers: PS
figure 32.3 Economic framing
9 Distributional Effects
.............................................................................................................................................................................
The default in beneﬁt-cost analysis in the United States is that monetary valuations are
added up equally across individuals with no adjustments for income status or other
status aspects of individuals. Such an assumption implies an equal individual and social
marginal utility of income, an assumption whose impact can be investigated through
distributional analysis. In many international applications the default more frequently
involves some kind of distributional weighting (Boardman et al. 2011; Farrow 2011;
Brent 2006).
Governmental guidance varies signiﬁcantly for the incorporation of distributional
effects in a beneﬁt-cost analysis. The U.K. government (HM Treasury 2013) speciﬁes
a particular function for weights on costs and beneﬁts accruing to different income
classes. The United States is more ambivalent, suggesting a supplemental analysis to
the default of no distributional impact (U.S. OMB 2003). The people who play slot
machines often span a wide range of the population, but there is evidence that gambling
participation in the United States has trended such that those with lower socioeconomic
status are participating more with higher ﬁnancial involvement and are disproportion-
ately affected (Welte et al. 2002). Consequently, there may be some usefulness in
investigating distributional weighting of beneﬁts and costs if the evidence suggests that
beneﬁts or costs accrue to others than the average of the population (Boardman et al
2011). As many gambling legalization issues have involved indigenous peoples, a sepa-
rate weighting or net beneﬁts analysis can be carried out for that population of concern.
In an analysis of the beneﬁts and costs of slot machine gambling in the U.S. state of
Maryland, Farrow and Shinogle (2010) found that an initial determination of positive

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lotteries and gambling machines
net beneﬁts to Maryland could be reversed depending on the degree of distribution
weighting, though there was signiﬁcant uncertainty surrounding the estimate.
10 An Analytical Scorecard
.............................................................................................................................................................................
Data collection instruments in the form of scorecards have been found useful to sum-
marize the results of regulatory beneﬁt-cost analyses (Hahn and Dudley 2007; Belzer
1999; U.S. OMB, 2010). Such an approach has not yet been applied to gambling studies,
though there are bibliographic categorizations of gambling studies (Shaffer, Stanton,
and Nelson 2006). Below is an adaptation of such scorecards to include issues relevant
to gambling; in the interest of brevity, the line items are terse reminders of issues and
are not repeated for what may be multiple beneﬁt and cost categories. Such a scorecard
may assist in distinguishing some impact approaches and in clarifying the nature of
debates as for variations in surplus measures that have been considered (see table 32.1).
11 Illustrative Empirical Analyses of the
Benefits and Costs of Slot Machine
Gambling
.............................................................................................................................................................................
Gambling has generated a large empirical literature on numerous subjects, including
early work by Martin Weitzman (1965), which helped begin but not resolve empirical
modeling debates that continue to this day. Adam Rose (1998), for a background paper
for the National Gambling Impact Study Commission (1999), focused on regional
impact studies as of that date and found 36 suitable for a meta-analysis, some of which
incorporate slot machine use. Tom Coryn (2008) surveyed more recent analyses of
various kinds but found few applications in Europe. There are relatively few complete
beneﬁt-cost analyses done speciﬁcally on slots. A computerized search for empirical
studies was done using the databases Google Scholar and Econlit and search combina-
tions including one term from each of the following two groups: Group I: economic
analysis, economics, beneﬁt cost, social costs, consumer surplus; and Group II: slot
machine(s), fruit machine(s), VLTs, video lottery, EGMs, and gambling. The result
yielded numerous studies but few speciﬁcally on slots. Many studies are done by con-
sulting ﬁrms, advocates (for or against), and by state government and often reﬂect
various problems associated with advocacy and time sensitivity. Consequently, only a
few empirical cases are summarized below to illustrate the issues and results.
The illustrative beneﬁt-cost analyses summarized in table 32.2 demonstrate the
methodological variability that exists in the beneﬁt-cost analysis of slots. The highest

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Table 32.1 A Proposed Scorecard for Beneﬁt-Cost Studies of Gambling
Item Number
Variables
Evaluation
1.
Is the economic issue identiﬁed, including whether there
are market failures?
2.
Is standing clear?... Whose beneﬁts and costs count?
3.
How is time incorporated? If a discount rate; source,
nominal, real?
4.
How are transfers to be accounted for, by including both
sides, netted to zero or?
5.
Is uncertainty in conditioning variables or parameters
considered?
6.
Does uncertainty alter the behavior of individuals and, if so,
how is it included (e.g., risk loving)?
7.
Is the choice of partial or general equilibrium explained?
8.
Are distributional impacts considered?
Estimation of Beneﬁts
9.
Is each beneﬁt economically, conceptually justiﬁed?
10.
Is each beneﬁt quantiﬁed where possible using appropriate
methods?
11.
Is each beneﬁt monetized where possible using appropriate
methods?
12.
If employment beneﬁts are included, are they justiﬁed by
the deﬁnition of standing or high levels of unemployment?
Estimation of Costs
13.
Is each cost economically, conceptually justiﬁed?
14.
Is each cost quantiﬁed where possible using appropriate
methods?
15.
Is each cost monetized where possible using appropriate
methods?
Comparison of Costs and Beneﬁts
16.
Are net beneﬁts calculated or is there a cost-effectiveness
measure?
Evaluation of Alternatives
17.
Is at least one variation of the policy deﬁned and analyzed?
Clarity of Presentation
18.
Contains executive summary or abstract
19.
Reports impacts in natural units
20.
Reports monetized impacts by category
21.
Text contains summary net beneﬁt table
22.
Does the report appear credible and unbiased, including any
appropriate consideration of source of funding?
23.
Is the conclusion clear, as well as caveats?
Other Comments

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lotteries and gambling machines
Table 32.2 Illustrative Empirical Studies of Slot Machine Beneﬁts and Costs
Application and Source
Standing
Beneﬁt Factors
Key Cost Factors
Australian Gambling
(APC 1999; Crane 2008)
Nationwide
Consumer surplus,
government and
community revenue
Bankruptcy, crime,
emotional distress items,
job-related costs,
treatment costs
Indiana Riverboat
Gambling
(PolicyAnalytics 2006;
Walker 2006)
State
(subnational)
Distance CS, tax
beneﬁts, net change in
proﬁts, change in
transactional
constraints
Bankruptcy, crime, loss of
productivity, health
problems, divorce,
regulatory costs net of
transfers
Wisconsin Native
American casinos
(Thompson, Gazel, and
Rickman 1995; NRC 1999)
State
(subnational)
Casino spending in
state and local
economy
Forgone local business
expenditures, social costs
(crime and problem
gambling)
Electronic gaming
machines in Bendigo,
Australia
(Pinge 2008)
City
Expenditures in the
local economy
Productivity loss, health
costs, crime, gambling
losses
Slots in Maryland
(Farrow and Shinogle
2010)
State
(subnational)
Consumer, producer
surplus, government
revenue, external costs
Numerous items
associated with problem
and pathological
gamblers; secondary
market impacts;
uncertainty, distributional
effects
geographic level of analysis observed is for a country, including Australia (APC 1999;
2010), the United Kingdom (Crane 2008), and the United States (Grinols 2004). The
APC report is a touchstone report on many issues, and because it has an allocation of
net beneﬁts by mode of gambling, including slots, will be brieﬂy summarized here with
a more detailed critique embedded in Crane (2008). The APC report used a beneﬁt-
cost framework that included consumer surplus and change in government revenues
(including community contributions that may be seen as coming from producer sur-
plus) and considered but did not include general equilibrium effects. Producer surplus
appeared to be assumed to be competed to zero, as only one mention, related to taxes,
was found by an electronic search. The APC investigated social costs in great detail
and formalized the adjustments for problem gamblers discussed above. Further, they
considered the incremental effect of gambling and its frequent comorbidity with other
socially costly outcomes and so applied a “causality adjustment” to many social costs
on their reading that about 80 percent of the social costs of problem gamblers was due
to gambling (APC 1999, 7.11; 9.9).

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the benefits and costs of slot machine gambling
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Numerous components were included in social costs driven by non-normal gam-
bling while some debt transfers were excluded from social costs. Depending on one’s
framing regarding the rationality of problem gamblers, a portion of these costs may
be excluded. Crane (2008) was able to analyze several different framings of these social
costs. Ultimately, the APC concluded that its estimates of the net beneﬁts of total
gambling in Australia, nicely caveated, may be either negative or positive primarily
depending on the elasticity of demand used in the calculation of consumer surplus.
Beneﬁts and costs were further allocated to gambling modes, with costs allocated on
the basis of gambler’s expenditures. Slots (gaming machines) had the largest potential
to generate negative net beneﬁts among the modes, though a range of positive net
outcomes also was possible, including the second largest potential positive net beneﬁt
among the modes (APC 1999, 11.7)
The next two studies looked at the state-level impact of casino gambling while the
latter two focused more speciﬁcally on slot machine gambling. The analysis of the
state of Indiana’s riverboat casinos, including but not limited to slots, developed a
beneﬁt-cost analysis in which only Indiana residents have standing (PolicyAnalytics
2006). Cost factors in this study included bankruptcy, crime, unemployment and loss
of productivity, poor health and mental health problems, divorce, and regulatory costs
with relatively careful attention paid to the role of transfers. In particular, estimates
related to bad debts netted out in the estimates due to equivalent gains and losses from
creditor to debtor, though resource costs related to bankruptcy were included. The
report used a sensitivity analysis for social costs using two cost valuations, one based on
the work of Grinols (2004) and the other based on research by the National Opinion
Research Center. Beneﬁt factors include distance consumer surplus, tax beneﬁts (net
changeinstatetaxrevenue),andthenetincreaseinproﬁtsaccruingtoIndianaresidents.
In large part due to the importance of non-Indiana gamblers at the riverboat casinos,
the net beneﬁts to the state of Indiana are estimated at about $700 million (in 2005
dollars) with a beneﬁt-cost ratio greater than 8. This report was reviewed by Walker
(2006). While generally supportive of the analysis, including its analysis of transfers,
Walker identiﬁed issues that he believed understated consumer surplus and overstated
the social costs of crime due to gambling.
An earlier analysis of Native American casino gaming of all types, including slots,
in Wisconsin is illustrative of hybrid impact studies (Thompson, Gazel, and Rickman
1995)and was also included in a review by the National Research Council (1999). This
study is more consistent with an impact study framework than beneﬁt-cost analysis in
its deﬁnition of beneﬁts; direct beneﬁts were calculated as the summation of local casino
expenditures, including wages, supplies, maintenance and new construction, and visi-
tors’ non-casino expenditures, such as lodging, dining, shopping, and transportation.
Direct costs were calculated as the summation of forgone local business expenditures
that result from residents’casino spending and expenditures by non-casino tourists who
would have visited the area even in the absence of the casino and thus did not represent a
new source of income. The report gives three levels of cost estimates (low, medium, and
high) for comparative purposes. Indirect beneﬁts and costs were calculated via the use

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lotteries and gambling machines
of industry-based multipliers provided by the U.S. Department of Commerce’s Bureau
of Economic Analysis (BEA) and indicate a regional general equilibrium approach. The
analysis is particularly notable for its survey of gamblers onsite to obtain information
about travel, socioeconomic information, and gambling and non-gambling patterns.
For the state of Wisconsin, the net effect could be either positive or negative, depending
on uncertainty in the values of social cost that were used (estimates were also presented
for more local economies). The National Research Council (1999) noted that this report
was an advance on earlier efforts but still contained methodological weaknesses, such
as in the deﬁnition of several major social cost items that likely overstated social costs.
The next two studies focused on slot machines and like the total gaming studies
illustrated above, have promising aspects but also contain weakness. The beneﬁt-cost
analysis of EGM gambling in the city of Bendigo, Australia, employed an input-output
methodology that hypothetically redistributed expenditures from the machine gaming
industry to other industries. The goal of this impact study was to evaluate the effect of
shutting down the gambling sector and redistributing expenditures to alternate sectors
(retail trade and lodging and dining) within the city. While machine gambling did
confer positive net beneﬁts compared to a complete loss of gaming activity, the study
showed that the gains were substantially lower than the net beneﬁts that would be
incurred by shutting down the EGMs and redistributing spending and savings to other
sectors based on the amount of productivity and interregional leakage of the estimated
gaming sector compared with other sectors. This is an example of consideration of
an alternative which may or may not be feasible in the local context. While an advo-
cacy document, the study illustrates the challenges in adapting available input-output
models, leakages, and social costs to a smaller geographic area. In general, the beneﬁts
of those gambling were not considered and gambling losses by non-normal gamblers
were counted as social costs in their entirety in an added section which, in terms of
ﬁgure 32.1, would be equivalent to modeling social costs as the rectangle P∗QA of the
difference between the orange and blue areas in ﬁgure 32.1.
Research by Farrow and Shinogle (2010) continued to illustrate the problems in
moving from an impact analysis to a beneﬁt-cost analysis. Based on an impact analysis
to inform a statewide vote on whether to allow slot machine gambling in the state
(Shinogle et al. 2008), the beneﬁt-cost structure was imposed while attempting to
use estimates from the impact study. Heavily using results summarized in Grinols
(2004) as adapted to Maryland, there was use of distance consumer surplus but not
of standard surplus, of producer surplus, government net revenues, and external costs
that included components of transfers in its measures of social costs. Extensions in
the work included the use of Monte Carlo simulation to model uncertainty in many
of the individual elements, of probabilistic beneﬁts from employment in periods of
high unemployment, and of distributional weighting based on lottery behavior in
Maryland. While crudely indicating that a point estimate of the annual net beneﬁt was
likely positive, the simulation analysis indicated the wide range of possible outcomes
while the distributional analysis indicated that the net beneﬁts could become negative
with distributional weighting.

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12 Gaps and Directions for Research
.............................................................................................................................................................................
This chapter articulated an economic approach to cost-beneﬁt analysis of slot machines,
though it should be clear that there is not an off-the-shelf template of conceptual and
empirical guidance for the beneﬁt-cost analysis of slots. Some views stated here may
subsequently evolve with new research, and it is toward that end that several areas
needing analytical improvement are brieﬂy summarized as follows:
1. Integrating conceptual consumer surplus models: There are currently several surplus
and risk-based consumer models, most obviously, “standard” surplus, addicted
gambler’s surplus, and distance surplus; and substitute ex-ante measures based on
risk-loving behavior or a combination of risk aversion and entertainment. Each
provides some insight, but none appears to fully capture the heterogeneity and
motivation of observed gamblers or to clearly link the various observable concepts
of price to the analysis.
2. Empirical estimation of surplus concepts, including the role of distance and its implicit
price as one element: It may be possible in locations with state-run casinos and
frequent player cards or with cooperating casino owners to develop travel cost
models of surplus that are more common in other areas of recreational demand
research.
3. Are slot machines more or less addicting than other forms of gambling? An important
driver of external effects appears to be the number of“abnormal”gamblers. Deter-
mining whether and how much a differential impact exists by type of gambling is
an important question. For instance, to obtain the partial derivative of the num-
ber of non-normal gamblers per change in amount wagered on different games
could be informative or, more complexly, the total derivative of the number of
non-normal gamblers in which game type is one factor. Newly available datasets,
such as those for loyalty cards, may allow such analyses.
4. Canonical accounting reporting formats: Much discussion occurs in the literature
about transfers as distinct from losses in economic efﬁciency. As noted in the
discussion of market imperfections, some market failures have aspects of both.
Developing the alternative accounting templates, one showing transfers and the
other omitting them, could be a useful way of illustrating the importance of
different impacts. In many cases the magnitude of transfers may exceed economic
welfare losses and so has little effect on economic efﬁciency but possibly a large
effect on the political economy of gambling debates.
5. Shadow prices and transfers. The empirical challenge in almost all application
areas is to estimate credible shadow prices for the efﬁciency cost or bene-
ﬁt of what are typically nonmarket actions. Deﬁning efﬁciency-based shadow
prices generally implies a corollary deﬁnition of what transfers are. None of the
impacts directly central to gambling are listed in a standard text as shadow prices,
which tend to focus on injuries, recreation, and the environment. The gambling

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lotteries and gambling machines
literature appears to be reducing its variability of approach in some areas, such as
bankruptcy, but disparate framings and estimates continue to exist on numerous
topics. This likely indicates both a lack of consensus and perhaps coverage in the
economics literature. Improvement is likely to depend on the usual slow accretion
of science and review, but much appears to be at stake.
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chapter 33
........................................................................................................
THE ECONOMICS OF LOTTERIES:
A SURVEY OF THE LITERATURE
........................................................................................................
kent grote and victor a. matheson
Introduction
.............................................................................................................................................................................
Lotteries represent one of the oldest and most common forms of gambling around
the world, with origins dating back at least to ancient Rome and possibly even earlier,
to the Han Dynasty of China in the second century b.c. A lottery involves the sale by an
organizing body, typically the government but also occasionally private businesses or
charities, of a ticket giving the possessor a potential monetary reward. Lotteries differ
from casinos in that lottery ticket sales generally do not take place at a location speciﬁ-
cally set aside for gambling, and modern lotteries are usually operated by governments
instead of by private ﬁrms.
Lotteries are of particular interest to scholars for a variety of reasons. First, they rep-
resent an important source of government revenues in many states and countries. Thus,
they are of interest to public ﬁnance economists. Second, lotteries provide researchers
interestedinmicroeconomictheoryandconsumerbehaviorwithatypeof experimental
lab that allows economists to explore these topics.
This chapter surveys the existing literature on lotteries organized around these two
central themes. The ﬁrst section examines the microeconomic aspects of lotteries,
including consumer decision-making under uncertainty, price and income elasticities
of demand for lottery tickets, cross-price elasticities of lottery tickets to each other and
to other gambling products, consumer rationality and gambling, and the efﬁciency
of lottery markets. The second section covers topics related to public ﬁnance and
public choice, including the revenue potential of lotteries; the tax efﬁciency and dead-
weight loss of lottery games; the horizontal and vertical equity of lotteries, including
potential externalities associated with gambling; earmarking and the fungibility of
lottery revenues; and individual state decisions to participate in public lotteries.

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the economics of lotteries: a survey of the literature
671
Thecurrentliteratureontheeconomicsof lotteriesissoextensivethatitisimpractical
to cover every paper on the topic. Thus, this chapter focuses on the most inﬂuential
papers in the ﬁeld. A more extensive bibliography of lottery related papers is available
from the authors upon request or through Research Papers in Economics (RePEc at
www.repec.org).
Microeconomics: Demand for Lottery
Much of the literature on lottery markets focuses on the demand for lottery products,
be they in the form of estimating demand equations, determining the regressive nature
of ticket purchases, or discussing the concepts of consumer rationality and market
efﬁciency. Indeed, why people demand lottery tickets in the ﬁrst place is a real ques-
tion. Milton Friedman and Leonard Savage (1948) (and subsequently Harry Markowitz
1952) suggested that the curvature of individuals’ utility functions changes as they get
richer (or move away from their “normal” income), thereby providing a theory for
why individuals exhibit risky behavior through their participation in lottery markets at
the same time that they exhibit risk-averse behavior elsewhere. These theories provide
motivation for the idea that lottery purchases can be considered rational behavior; if so,
consumers of lottery products should have typical demand functions that include some
familiar microeconomic variables, including price, income, consumer preferences,
number of consumers, price of related products, and product characteristics.
Effective Price
The price of lottery tickets has received much attention in the literature, which may
at ﬁrst seem surprising since the actual price paid for tickets tends to remain constant
unless the lottery authority decides to change it. The “effective price” of a lottery ticket,
which considers the price as well as the return, however, may change over time and
across lottery jurisdictions. Evidence on the effect of the effective price on ticket sales is
mixed, with early studies (Vrooman 1976; Vasche 1985; Mikesell 1987) concluding that
the effective price of tickets does not have a signiﬁcant impact on the sales of tickets and
later studies (DeBoer 1986; Clotfelter and Cook 1989; Miller and Morey 2003) ﬁnding
a signiﬁcant and negative relationship between the takeout rate and lottery sales.
While earlier studies used the takeout rate (or “vigorish”) to calculate the effective
price, subsequent studies have tended to use the difference between the nominal ticket
price and the expected return as the measure of effective price. For many lottery games
there is no difference between the expected return and the net difference between
the ticket price and the takeout; however, lotto is a common lottery game that is
distinguished by the characteristic that if there is no jackpot winner in a given drawing
period, the prize pool rolls over into the next drawing, increasing the potential jackpot
in the next period. Higher jackpots typically lead to higher expected values for ticket
purchases, which in turn lead to lower effective prices even if the actual dollar price

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lotteries and gambling machines
of a ticket remains constant. Because changes in game structures, ticket prices, and
takeout rates are rare, many of the studies of lottery demand examine lotto games,
taking advantage of the constant changes in effective price by including either jackpot
or expected return as an explanatory variable.
Many studies of demand also estimate price elasticities in order to determine whether
the existing lottery structures maximize the potential gaming revenues. Both IanWalker
(1998) and David Forrest, O. David Gulley, and Robert Simmons (2000a) concluded
that the U.K. National Lottery has an optimal takeout rate of 50 percent based on an
estimated price elasticity of demand that is close to −1. Many other empirical studies
also estimated that price elasticities are approximately equal to −1; however, there
are studies that found relatively more elastic demand (Farrel and Walker 1999 and
Farrell, Morgenroth, and Walker 1999 for the U.K. lottery, particularly in the long run;
Papachristou and Karamais 1998 for the Greek Lotto; and Gulley and Scott 1993 for
the Mass Millions game), implying that a lower takeout rate would increase revenues.
Other studies have suggested relatively less elastic demand, as low as −0.66 short-run
price elasticity for the U.K. National Lottery as found by Forrest, Gulley, and Simmons
(2000a),−0.382 in the Taiwan lotto game as measured by Chuan Lee,Chin-Tsai Lin,and
Chien-Hua Lai (2010), and −0.19 for the Mass Millions game as measured by Gulley
and Frank Scott (1993), implying higher takeout rates would increase government
revenues.
Forrest, Simmons, and Neil Chesters (2002) argued that lottery demand depends
more on jackpot size than expected value because players tend to participate in games
with very low odds of winning in order to “dream big” about substantial winnings.
Thus such studies as Larry DeBoer (1990) and Philip Cook and Charles Clotfelter
(1993) included jackpot size and jackpot size squared to test for a nonlinear and positive
relationship between jackpot size and ticket sales. Jackpot rollovers are such a distinctive
part of the literature in terms of measuring the effect of “price changes” that Forrest,
Simmons, and Chesters (2002), George Papachristou (2006), and George Geronikolaou
and Papachristou (2007) calculated a “jackpot elasticity of sales (demand)” that has a
similar interpretation as price elasticity of demand, except with a positive expected
relationship with ticket sales.
Income Elasticity
Like the price of a product, income is another signiﬁcant factor in the demand for
any good and is particularly important for empirical studies on lotteries in order to
determine whether the “lottery tax” in a particular jurisdiction is regressive. Studies
typically use income level, per capita income, disposable income, or real income in
order to estimate this effect, though some studies also use variables like the poverty
rate in order to capture the regressive nature of lottery spending (Blalock, Just, and
Simon, 2007). While the measurements of income elasticity vary from study to study,
empirical research uniformly ﬁnds income elasticities less than one, indicating that a
relatively greater percentage of income is spent on lottery products at lower income

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the economics of lotteries: a survey of the literature
673
levels (Suits 1977; Clotfelter 1979; Clotfelter and Cook 1987, 1989). Instant games
tend to have lower income elasticities than other games (Mikesell 1989; Jackson 1994;
Garrett and Coughlin 2009) while lotto games with large jackpots tend to appeal to
more afﬂuent customers. Indeed, Emily Oster’s (2004) study of Powerball sales in
Connecticut predicted that at exceedingly high jackpot levels the Powerball game could
actually become progressive, the only such ﬁnding in the literature.
Other indirect measures of income also tend to suggest that lotteries are a regressive
form of taxation. Studies by John Laitner (1999), Allan Layton and Andrew Worthing-
ton (1999), and Cletus Coughlin and Thomas Garrett (2009) all found that individuals
in government income assistance programs are more likely to participate in lottery
markets. The observed effect of unemployment on ticket sales is mixed, with John
Mikesell (1994) and Frank Scott and John Garen (1994) ﬁnding that unemployment
rates tend to have a positive impact on lottery ticket sales, while Garrick Blalock, David
Just, and Daniel Simon (2007) found a negative relationship and DeBoer (1990) found
no correlation.
Demographics
Demographics also inﬂuence ticket sales, and empirical studies are in wide agreement
as to their signiﬁcant inﬂuences on ticket sales. The old adage that the lottery is a “tax
on people who are bad at math”is borne out in the data. Level of education typically has
a negative relationship with ticket sales (Clotfelter and Cook 1987, 1989; Kitchen and
Powells 1991; Farrell and Walker 1999). With respect to race and gender, studies tend
to ﬁnd that black and Hispanic individuals are more likely than whites to buy lottery
tickets (Jackson 1994; Scott and Garen 1994), and men are more likely to play than
women are (Clotfelter and Cook 1987, 1990; Kitchen and Powells 1991; Farrell and
Walker 1999), though the effect can vary by location, time period, and type of game.
Studies also have found that people who live in urban areas and, therefore, are closer
to more lottery vendors tend to buy more lottery tickets than do people in rural areas
(Hersch and McDougall 1989; Clotfelter and Cook 1989, 1993; Kitchen and Powells
1991). Studies of other demographic variables, such as age and marital status, do not
exhibit consistent effects on lottery ticket sales (Clotfelter and Cook 1989, 1990; Kitchen
and Powells 1991; Jackson 1994; Farrell and Walker 1999).
Other Products: Substitutes and Complements
Lottery authorities typically offer multiple games, and lotteries may coexist with other
types of gambling, so a ﬁnal issue relating to the demand for lottery tickets is the
extent to which other products are complements or substitutes for lotteries. The lit-
erature provides mixed empirical results on this issue. Cook and Clotfelter (1993),
Gulley and Scott (1993), and Forrest, Gulley and, Simmons (2004) concluded that
lotto rollovers do not impact sales of other lottery products in the lotteries they
studied. Paul Mason, Jeffrey Steagall and Michael Fabritius (1997) found that the
two Florida lotto games are substitutes for one another, while Forrest, Gulley, and

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674
lotteries and gambling machines
Simmons (2004) found some substitution effects between scratchcard purchases and
the U.K. lotto. Conversely, in Ireland, Catriona Purﬁeld and Patrick Waldron (1999)
and, across the United States, Kent Grote and Victor Matheson (2006a) found that
different lottery games serve as complements to one another. While it is more natural
to suppose that lottery products are substitutes for one another, Grote and Matheson
concluded that transactions costs and the ability to buy multiple types of game tickets
at the same time are responsible for the complementarities exhibited by lottery ticket
buyers.
A topic related to the concept of substitution is what happens to overall spending
on lottery games in a lottery jurisdiction when new games are introduced. Presumably
the purpose of introducing new lottery games should be to increase overall lottery
spending, but if new lottery games merely attract ticket sales from already existing
games, an effect often referred to as cannibalization, then the lottery authority has not
beneﬁted from introducing a new game to the lottery mix. Mikesell and C. Kurt Zorn
(1987), Grote and Matheson (2006a), and Matheson and Grote (2007) all found that the
introduction of new lotto games does have a negative impact on sales for existing lottery
products, but the addition of new games increases overall lottery ticket sales. Matheson
and Grote (2007) go on to note that the overall increase in ticket sales is larger if the
new game is sufﬁciently different in odds or prize structure from the existing games.
Finally, it is well documented that the introduction of lotteries in neighboring states
serves to reduce lottery spending within a state, as people will cross state boundaries
to buy lottery tickets (Suits 1979; Mikesell and Zorn 1987; Walker and Jackson 1999;
Garrett and Marsh 2002).
Lottery ticket sales can also affect or be affected by the availability of other gambling
activities in a jurisdiction. Some studies (Scott and Garen 1994; Calcagno, Walker,
and Jackson 2010) have found that the presence of a lottery increases participation in
other gambling activities, such as casino gaming and dog and horse racing, presumably
reﬂecting a general attitude or preference toward gambling in a society. Most of the
literature on gambling activities and their relationship to lotteries, however, ﬁnd that
either they are unrelated to each other or that they are substitutes for one another. Dou-
glas Walker and John Jackson (2008) and Forrest, Gulley, and Simmons (2010) found
that sales revenues in racing and lotteries are not strongly related. Donald Steinnes
(1998) found that casino gambling does not have a signiﬁcant impact on lottery sales,
whereas Melissa Kearney (2005b) found that lottery spending does not signiﬁcantly
reduce spending on other forms of gambling. The remaining studies tended to ﬁnd
that lotteries and other forms of gambling are substitutes for one another (Gulley and
Scott 1989; Siegel and Anders 2001; Elliott and Navin 2002).
Microeconomics: Lottery Structure and Demand
In addition to the other factors affecting demand for lottery tickets described in the
previous section, other characteristics of lottery games, including the odds of winning,

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the economics of lotteries: a survey of the literature
675
the prize structure, and the payout rate of the game, affect the demand for tickets as
well. If consumers have preferences for certain lottery game characteristics, then it is
logical to assume that states can and should structure their lottery games to attract the
most consumers in order to maximize lottery revenues. This is often referred to in the
literature as achieving an “optimal structure” for a lottery. A lottery association must
determine a payout rate, the odds of winning, and the distribution of payouts among
different size prizes for each game it offers.
While lotto games also offer smaller consolation prizes to ticket buyers who fail to
win the largest prize, the jackpot prize is arguably the primary attraction of the game
(Forrest, Simmons, and Chesters 2002), so it seems logical that states should structure
the odds of winning the jackpot in order to attract the most consumers within a lottery
district. Both DeBoer (1990) and Stuart Thiel (1991) concluded that the New York
state lottery and Washington state lotteries, respectively, should provide worse odds of
winning in order to attract more players to their lotto games. Longer odds would result
in more rollovers leading to higher jackpots, and if consumers care more about the size
of the lottery prize than about the odds of winning, such a strategy will result in higher
sales.
The ability of lottery associations to generate additional demand by lengthening the
oddsof winningthejackpotisnotunlimited,however,aseventuallytheoddsof winning
the grand prize become so low that the jackpot is won too rarely, causing players to
lose interest (Forrest and Alagic 2007). Thus the optimal jackpot odds depend on how
many potential consumers there are in the jurisdiction offering the tickets. Cook and
Clotfelter (1993) referred to this as the “scale economies of lotto” and found that states
often select their game formats so that the probability of winning the jackpot multiplied
times the population within the state is approximately equal to one. Lottery associations
have taken this ﬁnding to heart, and the past 20 years have witnessed a rise in multi-state
or multi-country lotto games offering huge jackpots at increasingly long odds.
Cook and Clotfelter’s ﬁndings are dependent on the particular risk preference of
lottery consumers in the United States. The question of the optimal odds of winning has
also been studied in the United Kingdom, Greece, and Spain. Walker and Judith Young
(2001) used simulations of sales for the U.K. lotto to demonstrate that reducing the
odds of winning may, in fact, reduce sales because reducing the odds of winning reduces
the expected return on a lottery ticket while increasing the variance and skewness of
expected return, which may not be favorable to the risk preferences of consumers
in the United Kingdom. Papachristou (2009) demonstrated mathematically that scale
economies likewise affect the mean, variance, and skewness of expected returns. Forrest,
Levi Pérez, and Rose Baker (2010) found that sales for the Spanish National Lotto game
increase when the odds of winning decline and additional lower tier prizes are added
to the game structure.
Aside from the odds of winning the jackpot, a second important characteristic of
lottery games is the prize structure offered. While the jackpot prize may be of primary
interest to purchasers of lottery tickets, it is not the only characteristic, and the prizes
offered as well as the percentage of sales used to fund the prizes offered (the payout rate)

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676
lotteries and gambling machines
may have an impact on consumer preferences and consumer demand. John Quiggin
(1991) has provided a mathematical model of lottery demand which shows that, though
smaller prizes do not have much impact on the overall expected value of a ticket, they
do reduce the expected losses so that consumers may prefer lottery games with multiple
prizes and prize levels. The model also suggests that product differentiation of lottery
tickets is particularly important when consumers of lottery products have very different
risk preferences.
A number of empirical studies have been offered in the literature to test Quiggin’s
propositions. John Scoggins (1995) found that Florida lottery ofﬁcials should increase
the percentage of sales allocated to the jackpot prize from 25 to 30 percent in order to
increase sales. Garrett and Russell Sobel (1999) found that lottery players in 216 U.S.
games in 1995 appeared to be risk averse and to favor skewness of returns, recommend-
ing that lottery providers can achieve more skewness by offering smaller consolation
prizes along with larger jackpots. Conversely, Walker and Young (2001) recommended
that the U.K. lotto game reallocate the funding of prize money from the jackpot to
smaller prizes in order to stimulate demand. Demand for tickets should increase due
to higher overall expected return and lower variance, which should offset the reduced
skewness of returns. Garrett and Sobel (2004) performed a statistical study on 135 U.S.
lottery games and concluded that ticket sales for these games depend only on the size
and odds of winning the jackpot prize, not the expected value of lower tier prizes.
A ﬁnal characteristic that receives substantial attention in the lottery literature is the
optimal takeout rate of lottery games. A higher takeout rate means a larger percentage
of the ticket price is kept as revenue but also means lower ticket sales if consumers
are responsive to effective price. A lottery association will maximize revenues when
the effective price elasticity of demand nears a value of −1. Empirical tests of takeout
rates have concluded that many lottery games approximate an optimal takeout rate,
and researchers have been quick to recommend changes to takeout rates when effective
price elasticities of demand deviate from the revenue-maximizing ﬁgure. (Refer to the
previous section on effective price for more details.)
In one ﬁnal contribution of note on this topic, Shu-Heng Chen and Bin-Tzong Chie
(2008) demonstrated that there is an associated Laffer curve based on the takeout rate
(or lottery tax rate) that is ﬂat at the top, concluding that this provides a rationale for
the varying takeout rates offered by different lottery games, since there is no single
“optimal takeout rate” for all games.
Behavioral Economics: Rationality and Market
Efﬁciency in Lottery Markets
While it is reasonable to question whether gambling by otherwise risk averse individu-
als can ever be considered rational, both Friedman and Savage (1948) and Markowitz
(1952) offered theories about the shape of utility functions that establish a rational
demand for lottery products across all income levels. Others have justiﬁed gambling as

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the economics of lotteries: a survey of the literature
677
rational by assuming that gambling entails consumption beneﬁts as well as expected
winnings or losses (Conlisk 1993). From these bases rational participation in lot-
tery markets can be tested empirically along with tests of efﬁciency in those markets.
There are several different methods of testing for rationality in lottery markets that are
related to the numbers that individuals choose to play, the consumer response to lottery
rollovers and changes to the form of jackpot payouts, and where ticket buyers purchase
their tickets, among others.
Related to the numbers selected, two particular types of irrational behavior are tested
in lottery markets: the presence of the gambler’s fallacy and the conscious selection of
numbers. The gambler’s fallacy occurs when players change their beliefs about the prob-
ability of a particular combination of numbers being drawn again after those numbers
come up as the winning combination even though each drawing in the lottery is an
independent random event (Vaughan Williams 2005b). Clotfelter and Cook (1993),
Dek Terrell (1994), and Papachristou (2004) all found evidence of the gambler’s fal-
lacy in various games, that is, that players tend to not play numbers that have recently
won. Jonathan Simon (1999), on the other hand, found evidence of an overselection of
recent winning numbers in the U.K. lottery. On a similar note, Jonathan Guryan and
Kearney (2005, 2008) found evidence of a“lucky store”effect in Texas. After a store sells
a winning ticket, consumers increase their purchases of lottery tickets anywhere from
12 to 38 percent at that store relative to other stores in the community, an effect that
cannot be explained with rational behavior.
Theconsciousselectionof numbersinlotterygameshasreceivedevenmoreattention
in the literature. If people have preferences for certain combinations of numbers based
on such “lucky numbers” as birthdays, multiples of seven, or patterns on a play slip,
then certain combinations of numbers will be selected more frequently while other
combinations will be relatively ignored. If prizes are pari-mutuel in nature, however,
“lucky numbers”will actually result in lower payouts, since consumers playing common
numbers will have to share their winnings among more people, violating rationality.
Conscious number selection has been widely identiﬁed in lottery games. Clotfelter
and Cook (1989) noted that lottery associations even encourage conscious selection in
marketing related to their products perhaps to increase demand by players who wish
to “control their destiny.” Conscious selection also reduces the coverage of number
combinations in any given draw, increasing the probability that a jackpot prize will roll
over and potentially attract additional sales in future draws in response to the higher
advertised jackpots. Walker (1998), Simon (1999), Farrell et al. (2000), and Ursula
Hauser-Rethaller and Ulrich Konig (2002) all found that conscious selection results in
more rollovers in lotto games but that the impact on ticket sales tends to be minor.
Other studies concentrate not on whether conscious selection occurs but whether
its effect on expected returns is strong enough to allow individuals an opportunity to
make money by betting on the unpopular numbers. While Papachristou and Dimitri
Karamanis (1998) did not ﬁnd that conscious number selection in the Greek lotto is
large enough so that unpopular numbers ever become a fair bet (i.e., a bet with a
positive expected return), other studies of the Canadian Lotto (Ziemba et al. 1986), the

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lotteries and gambling machines
Massachusetts numbers game (Chernoff 1981), 6/49 lotto games in the United States
(Thaler and Ziemba 1988), and the U.K. lotto (Baker and McHale 2009) have all found
potentially proﬁtable bets among unpopular number combinations. All of the studies
caution, however, that it is difﬁcult to make proﬁts over a reasonable timeline by playing
these numbers because of the low odds of winning.
Other tests of consumer behavior relate to whether the bettors’ responses to lottery
rollovers are irrationally high (referred to as“lotto fever”or“lottomania”) or irrationally
low (referred to as“lotto apathy”or“jackpot fatigue”) and how lottery players’behavior
changes immediately subsequent to the jackpot prize being won, a phenomenon known
asthe“haloeffect.”Lottofeveroccurswhenajackpotrolloverattractsenoughadditional
purchases of tickets to actually reduce the expected return on a ticket in spite of the
higher jackpot being offered due to the increased probability of having to share a
jackpot prize should it be won. Michael Beenstock and Yoel Haitovsky (2001) found
statistical evidence of lotto fever consistently occurring after the third rollover in the
Israel lotto game. Matheson and Grote (2004, 2005), in a cross-sectional study across
U.S. lotto games, found that lotto fever is very rare, occurring in less than 0.1 percent
of the drawings in their analyses of the phenomenon in more than 17,000 and 23,000
drawings, respectively.
Lotto apathy occurs when tickets sales do not increase despite an increase in jack-
pot and the expected return. Matheson and Grote (2005) found lotto apathy to be a
much more common experience in U.S. lotto games, though it still occurs in less than
2 percent of the more than 10,000 drawings examined and is concentrated in states that
simultaneously offer both a high-jackpot, multi-state lotto game and a smaller in-state
game with a jackpot that can be easily overshadowed by the larger game. Similar to
lotto apathy is the concept of jackpot fatigue, the concept that even with high jackpots
lottery participants lose interest in the lottery after the lottery has been around awhile.
Most models of lottery demand include a time trend as an independent variable in
order to explain lottery ticket sales (Vasche 1985; Mikesell 1987; Mikesell and Zorn
1987; DeBoer 1990). Beenstock and Haitovsky (2001) commented particularly on the
fact that the lotto in Israel does not have a positive time trend in spite of that country’s
growing economy. Stephen Creigh-Tyte and Farrell (2003) also proffered that it is the
declining trend in sales for the U.K. lottery which has encouraged the Camelot Group
to offer new lottery games and innovations to current games in order to keep the public
interested in purchasing lottery tickets.
Several papers have examined the halo effect, the tendency for ticket purchases
immediately following the award of a large jackpot to be unexpectedly high despite the
jackpot resetting to a lower level. The ﬁnding of a halo effect demonstrates a degree
of irrationality among lotto players and can be seen as a type of gambling addiction.
Farrell,EdgarMorgenroth,andWalker(1999),GroteandMatheson(2007),andGuryan
and Kearney (2010) all found degrees of addiction among various lotto games in the
United States and the United Kingdom.
A ﬁnal topic relating to bettor rationality is consumer understanding of lottery
payouts. Allen Atkins and Edward Dyl (1995) demonstrated that individuals who win

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the economics of lotteries: a survey of the literature
679
the lottery should choose the annuity, or the prize paid out over many years, rather than
a lump sum paid out immediately because of the tax implications of the two payouts.
However, they also concluded that most people will choose the lump sum (a conclusion
that is validated by the empirical evidence), arguably because a lump sum can make
them feel much wealthier, an argument consistent with Friedman and Savage’s (1948)
rationale for participating in lotteries in the ﬁrst place. Irrespective of the wisdom of
the lump sum versus the annuity, Matheson and Grote (2003) have shown that ticket
buyers tend to be rational with respect to changes in the annuity lengths of jackpot prize
payouts. They demonstrated that consumers are not fooled into buying more tickets
when state lottery associations artiﬁcially increase advertised jackpots by increasing the
annuity length of the prize payout.
Market Efﬁciency
If consumers, as a whole, display rationality in lottery markets, then lottery markets
should also tend to be efﬁcient. Leighton Vaughan Williams (2005a, 2005b) has dis-
cussed the concepts of weak form, semi-strong form, and strong form efﬁciency in
gambling markets in general as well as the empirical literature related to efﬁciency.
Weak form efﬁciency is stated to exist when there are no betting opportunities in lot-
tery markets that offer positive expected returns (which means that, on net, there are
no fair bets), and strong form efﬁciency exists when wagers have expected values of
(1 minus the takeout rate) times the amount of the wager (Thaler and Ziemba 1988).
If players are rational there should be few if any opportunities for lotteries to violate
weak form efﬁciency, as the presence of a fair bet should attract more ticket purchases,
reducing the expected value of a ticket back down to the ticket price (or lower). Aside
from opportunities provided by purchasing rare number combinations discussed pre-
viously, studies covering a number of lotteries typically have found that opportunities
for fair bets when purchasing a single randomly selected ticket are rare or nonexistent
(Thaler and Ziemba 1988; Krautmann and Ciecka 1993; Papachristou and Karamanis
1998; Scott and Gulley 1995; Ciecka, Epstein, and Krautmann 1996; Grote and Math-
eson 2006b). In the most expansive study, Matheson and Grote (2005) found fair bets
in roughly 1 percent of the more than 23,000 drawings in the U.S. state and multi-
state lotteries they examined, with positive expected values occurring most frequently
in minor games in smaller states where relatively high jackpots attract little consumer
attention.
Numerous authors also have examined the possibility of purchasing every number
combination, a strategy dubbed the “trump ticket.” In all cases these studies found
that the purchase of the trump ticket is far more likely to provide a fair bet than is the
purchase of a single ticket (Thaler and Ziemba 1988; Ciecka, Epstein, and Krautmann
1996; and Grote and Matheson 2006b), a result mathematically proven by Matheson
(2001). Matheson and Grote (2005) found that 11 percent of all lottery drawings they
examined would represent a fair bet with the purchase of the trump ticket; this is an
astonishingly high number. They, like Thaler and Ziemba (1988), concluded, however,

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lotteries and gambling machines
that this ﬁnding does not necessarily indicate a violation of weak form efﬁciency, as
the transaction costs involved in purchasing all possible combinations are too high
to make this strategy feasible, creating an effective barrier to purchasing the trump
ticket. Anthony Krautmann and Ciecka (1993) noted that a consortium attempting to
purchase every combination of a 1992 drawing in the Virginia lotto was unsuccessful
in covering every combination despite enlisting help from numerous lottery retailers.
Tests for strong form efﬁciency in lottery markets are provided by Scott and Gulley
(1995) and Forrest, Gulley, and Simmons (2000b). Both papers report evidence in favor
of strong form efﬁciency and conclude that bettors are able to accurately forecast sales
for a lotto drawing. In addition, the ability to forecast improves with the number of
draws that have taken place, reaching a reasonable level of accuracy within the ﬁrst 30
drawings of the game.
Public Finance: Revenues and Efﬁciency of Lotteries
As a signiﬁcant contributor to government ﬁnances in the United States and the rest of
the world, lotteries have been widely examined by public ﬁnance economists focusing
primarily on their revenue potential and desirability as a method of taxation. Scholars
generally acknowledge that even under the most optimistic assumptions, lotteries are
unlikely to provide more than a few percentage points of the revenue needed for a
modern state or national government (Humphreys and Matheson 2013; Mikesell and
Zorn 1986, 1988) . However, it is important to note that they frequently approach
or exceed in magnitude tax collections on goods such as alcohol or tobacco. Unique
among tax collection agencies, revenue maximization is an explicitly stated goal of
lottery organizations, and numerous papers have explored ways in which variations
in product variety, lottery structure, and payout rates could be adjusted to increase
revenues. All of these topics have been discussed previously in the sections on demand
for lottery and lottery structure and will not be repeated here.
The efﬁciency with which lotteries generate revenues is a topic of some debate. As ﬁrst
noted by Roger Brinner and Clotfelter (1975), lotteries are an unusual form of taxation
in that participation is voluntary and the government actually creates the consumption
good that is then taxed. The creation of a new consumption good should raise welfare
even if dead-weight loss is created when the good is taxed (Rodgers and Stuart 1995; Far-
rell andWalker 1997). John Livernois (1986) disputed the notion that lotteries should be
considered voluntary, since spending on lotteries simply substitutes for spending else-
where in the economy, and William Rodgers and Charles Stuart (1995) noted that while
the creation of an untaxed lottery would raise welfare, the tax levels typically associated
with state lotteries reduce welfare in comparison to other methods of taxation.
Aside from the high takeout rates of government lotteries, the large dead-weight loss
of lottery taxation is also a result of high administrative costs, especially when payments
to vendors (Mikesell and Zorn 1988) and advertising expenses (Heberling 2002) are
considered. DeBoer (1985) and Stephen Caudill, Sandra Johnson, and Franklin Mixon

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681
(1995), however, stressed that while administrative costs of lotteries are indeed relatively
high, lottery associations generally experience economies of scale in lottery provision,
and average administrative costs per ticket can be reduced by pooling resources with
other agencies and by expanding sales.
Both Mikesell and Zorn (1988) and Szakmary and Szakmary (1995) have empha-
sized that an additional problem with lottery revenues is their volatility. Humphreys and
Matheson (2013) countered that while lottery and gaming revenues may be subject to
signiﬁcant change from year to year, the variation in gaming revenues is negatively cor-
related with changes to other common revenue sources so that lottery revenues as part
of the system of taxation serve to reduce the overall volatility of government revenues.
Public Finance: Incidence, Equity, and
Externalities of Lotteries
One of the strongest criticisms of lotteries as a means of revenue collection is that
they constitute a regressive tax. Indeed, on this point there is universal agreement
among economists. Much of the literature on the correlation between income and
lottery purchases has been reviewed in the previous section on income elasticity, and
it is not necessary to revisit it here. Many lottery studies have focused speciﬁcally on
the distributional incidence of lottery revenues instead of the general factors affecting
lottery demand, including Wisman (2006), Kearney (2005a, 2005b), Campbell and
Finney(2005),andCombs,Kim,andSpry(2008). Likethoseongenerallotterydemand,
these studies have uniformly found that lotteries represent a highly regressive form of
taxation, though individual products offered by lottery association may vary widely
in their regressivity, with instant games generally faring the worst in terms of vertical
equity. Elizabeth Freund and Irwin Morris (2005, 2006) found the presence of lotteries
associated with higher levels of income inequality economywide.
Others have noted that when lottery proﬁts are earmarked, a proper accounting of
where the spending goes is as important as who buys the tickets when assessing the
income equity of the lottery system as a whole. Patrick Feehan and Forrest (2007) and
Harriet Stranahan and Mary Borg (2004) found that wealthy individuals and regions
tend to beneﬁt disproportionally from money earmarked toward cultural programs and
education, potentially exacerbating the regressivity of the revenue side of lotteries. Peter
Gripaios, Paul Bishop, and Steven Brand (2010) and Noel Campbell and R. Zachary
Finney (2005) noted that inequalities in the distribution of lottery proceeds are not
limited to income levels but apply also to geography and race, though both studies
suggest that inequalities in lotteries on the expenditure side are either nonexistent or at
least less severe than inequalities on the revenue side.
The presence of lotteries may also affect other measures of well-being. On the down-
side, Kearney (2005b) found that the presence of a state lottery reduces expenditures
on other consumption goods by up to 2.4 percent, echoing a general concern of Borg,

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lotteries and gambling machines
Mason, and Stephen Shapiro (1991). As is often found in studies of casino gam-
ing, Mikesell and Maureen Pirog-Good (1990) found a signiﬁcant positive correlation
between crime rates and the adoption of a lottery. Moreover, Robert Williams and
Robert Wood (2007) noted that over one-third of gaming revenues in Ontario are
generated by a small number of problem gamblers but that lottery sales are less prone
to abuse than are casino gaming or horse racing. On the upside, Mark Skidmore and
Mehmet Tosun (2008) found that the introduction of video lottery spurred general
retail sales in West Virginia. Eric Lin and Shih-Ying Wu (2010) found that lottery sales
are positively correlated with charitable giving, thus allaying fears that the establishment
of a “good works” lottery would reduce other types of donations.
Public Finance: Earmarking and Fungibility
In order to encourage consumers to play (Landry and Price 2007) and to overcome
opposition to state-sponsored gambling (Erekson et al. 1999; Pierce and Miller 1999;
and Ghent and Grant 2007), governments frequently designate proﬁts from lotteries
toward speciﬁc agencies. Well over half of state lotteries in the United States, and some
foreign lotteries, including the U.K. lottery, earmark all or part of the revenues gener-
ated for speciﬁc government programs, with education being the primary beneﬁciary
(Matheson and Grote 2008).
An important empirical question is whether these earmarked funds actually enhance
spending dollar-for-dollar for the designated programs or if governments simply sub-
stitute earmarked dollars for dollars that would have come from the state’s general
funds had earmarking not occurred. The extent to which different sources of state
funds can substitute for one another is known as“fungibility.”Studies of the fungibility
of lotteries have focused on educational spending and nearly uniformly have found
that the introduction of a state lottery increases total educational spending by less than
the amount of the new earmarked lottery revenue, suggesting at least some degree of
fungibility is present when funds are earmarked for speciﬁc state and local programs.
Mikesell and Zorn (1986), Borg and Mason (1988, 1990), and Garrett (2001a) all
found that education spending in states that adopted earmarked lotteries for edu-
cation failed to experience increases in educational spending despite the additional
lottery funds. Borg, Mason, and Shapiro (1991) found that states with lottery funding
earmarked to education have a statistically signiﬁcantly lower level of spending per
student. Taken as a whole, these works suggest that when lotteries provide a dedicated
stream of revenue to education, lawmakers are able to divert general fund resources
away from schools, leading to an indirect indication of fungibility.
Charles Spindler (1995), Steven Stark, R. Craig Wood, and David Honeyman (1993),
Susan Summers et al. (1995), and Vance Land and Majeed Alsikaﬁ(1999) all found
that government appropriations to education in a number of different states tend to
fall after the introduction of an earmarked lottery. O. Homer Ereksonet al. (2002) and
Neva Novarro (2005) conducted cross-sectional, time-series analyses of all 50 states.

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683
Erekson et al. (2002) found that the expenditure on education as a percentage of
general revenues falls as lottery revenues per capita rise, indicating that fungibility is a
real phenomenon. In addition, for every $1 per capita in lottery revenues generated as
funding for a state, there is a loss of approximately 1 to 1.5 percent of education funding
available. Novarro (2005) found that earmarked lottery proﬁts for education tend to
increase spending on education by approximately 79 cents for every $1 in lottery proﬁts,
while $1 in non-earmarked lottery proﬁts tends to increase education spending by only
43 cents, on average, ﬁndings similar to those of William Evans and Ping Zhang (2007).
Forrest and Simmons (2003) noted that earmarked funds for sport development in
the United Kingdom raised total spending on sport while slightly reducing other local
government spending on athletics but that the full degree of fungibility present in
earmarked lotteries outside the United States is a largely open question.
Public Choice: State Adoption of Lotteries
Beginning with New Hampshire in 1964, lotteries have spread across the United States
and Canada to the point where by 2011 governments offered lotteries in all Canadian
provinces and 43 of U.S. states. Numerous studies have examined the factors inﬂuenc-
ing states to adopt lotteries, though the literature on what causes countries to adopt
lotteries is lacking. Theoretical models of lottery adoption are grounded in the pub-
lic choice models of regulation, ﬁrst introduced by George Stigler (1971) and Sam
Peltzman (1976), in which legislators seek to maximize political support through their
legislative decisions. Several contributions provide differing rationales for the predic-
tion that higher incomes should lead to lottery adoption. John Filer, Donald Moak and
Barry Uze (1988) argued that concern for the regressivity of lotteries will limit their
implementation in poor jurisdictions, whereas Robert Martin and Bruce Yandle (1990)
suggested that the relative political power of the wealthy in rich areas will induce the
adoption of lotteries as a means of transferring income from the poor to the wealthy.
Erekson et al. (1999) argued that rich states will adopt lotteries simply due to the higher
potential for lottery revenues.
Empirical studies typically have found strong connections between income, poverty
levels, and income changes and the adoption of lotteries. Most papers have found a
signiﬁcant positive relationship between income and lottery adoption (Filer, Moak, and
Uze 1988; Hersch and McDougall 1989; Martin and Yandle 1990; Erekson et al. 1999).
James Alm, Michael McKee, and Mark Skidmore (1993) focused not on income levels
but instead trends in income theorizing that a decline in income adds to the ﬁscal stress
of a state, increasing the likelihood of a state to add a lottery.
Existing tax levels, debt, state government spending, and legal restrictions on the
ability of a state to collect other forms of revenue all may affect the decision to offer
a lottery, since ﬁscal stress can create a motivation for states to seek alternative forms
of revenue. Numerous papers have proffered that if tax levels are high states are more
likely to add a lottery as an additional or alternative form of funding (Filer, Moak,

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lotteries and gambling machines
and Uze 1988; Alm, McKee, and Skidmore 1993; Jackson, Saurman, and Shughart
1994; Erekson et al. 1999). One signiﬁcant deviation from the predicted relationship
of variables measuring the ﬁscal stress in a state has been provided by Martin and
Yandle (1990), who found a statistically signiﬁcant negative relationship between per
capita taxes paid and the decision to add a lottery, though they also found a positive
relationship between the per capita debt of a state and the addition of a lottery.
“Tax exporting” is another signiﬁcant factor in a state’s decision to add a lottery. Tax
exporting occurs when states earn tax revenues from constituents of other states or
conversely lose revenues to other states. If a state is losing out on tax revenues because
its residents are purchasing lottery tickets from other states that have already adopted
lotteries, this may increase the likelihood of that state adding its own lottery. Numerous
studies have considered the effect of the lottery status of neighboring states on lottery
adoption and found statistically signiﬁcant evidence of this effect (Davis, Filer, and
Moak 1992; Alm, McKee, and Skidmore 1993; Jackson, Saurman, and Shughart 1994;
Ghent and Grant 2007). Ronnie Davis, Filer, and Moak (1992) also measured tax
exporting in a slightly different manner and found a direct relationship between the
number of tourists in a state and a state’s decision to add a lottery.
Since adding a lottery is a political decision by legislators and/or voters in a state, it is
also necessary to consider organized opposition to lotteries. Many studies have found
that the percentage of a state’s population identifying themselves as a member of a con-
servative religious group (often Baptists) has a statistically signiﬁcant negative effect
on the adoption of lotteries (Hersch and McDougall 1989; Martin and Yandle 1990;
Jackson, Saurman, and Shughart 1994; Erekson et al. 1999; Pierce and Miller 1999). In
part to overcome some of the opposition to lotteries, some states have speciﬁcally ear-
marked lottery revenues to be used for speciﬁc (and relatively popular) state programs,
often education. If earmarking can ease political opposition, states that earmark their
funding for education should be more likely to adopt lotteries relative to states that do
not intend to earmark lottery revenues, an effect uncovered by Erekson et al. (1999),
Patrick Pierce and Donald Miller (1999) and Linda Ghent and Alan Grant (2007).
A ﬁnal factor that is considered in many of the empirical models is the presence of
other forms of betting in a state, though the hypothesized direction of the effect is not
certain. On the one hand, if a state already allows for other forms of gambling, it is
reasonable to assume that it may also be more willing to offer state lottery products
to its constituents. On the other hand, other organizations offering gambling products
represent an obvious interest group that would typically be opposed to the introduction
of a competitor. As a case in point, Nevada, home to the largest casino industry in the
United States, is also one of the few states that does not offer a state lottery. Empirically,
Davis, Filer, and Moak (1992), Ernest Wohlenberg (1992), and Jackson, David Saurman
and William Shughart (1994) all found that the presence of other forms of gambling
increases the likelihood of a state adopting a lottery, suggesting that outside of Nevada,
where casinos and other forms of gambling may be present on a smaller scale, there
are less organized interests against competition and the presence of gambling indicates
that there would be a demand for additional gambling products such as a state lottery.

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685
Conclusions and Suggestions for Future
Research
.............................................................................................................................................................................
This chapter has explored the existing literature regarding the economics of lotteries. A
substantial amount of research has focused on the demand for lottery products and the
lottery’s impact on public ﬁnances. More of this empirical evidence has been focused
on lotteries in the United States, Canada, and the United Kingdom. There have been few
studies of lotteries in other countries. Thus, analysis of international lotteries is a fruit-
ful area for additional scholarly work. Even more pressing, while Garrett (2001b) and
Matheson and Grote (2009) have provided cross-country studies of lotteries, very little
work has been done comparing lottery demand, structures, and adoption among dif-
ferent countries. While the existing literature is extensive, many new frontiers yet exist.
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chapter 34
........................................................................................................
THE TAXATION OF GAMBLING
MACHINES: A THEORETICAL
PERSPECTIVE
........................................................................................................
leighton vaughan williams and david paton
1 Introduction
.............................................................................................................................................................................
The U.K. gambling sector has experienced a number of regulatory shocks over the
past decade, which have led to considerable debate and controversy within the industry
and policy-making communities. Although there is a well-established literature on the
economic impact of the growth of gambling facilities on local and regional economies
in the United States (e.g., Walker and Jackson 2011; Kearney 2005; Siegel and Anders
2001; d’Hauteserre 1998) and the United Kingdom (e.g., Paton, Siegel, and Vaughan
Williams 2002, 2004; Paton and Vaughan Williams 2013; Forrest, Gulley, and Simmons
2010), there has been relatively little research on optimal taxation of gambling machines
within these facilities.
In this chapter we address this gap by examining the theoretical arguments for taxing
gambling machines by means of a levy on machine takings, rather than by means of a
license fee levied per machine. Recent tax debates in the United Kingdom provide an
ideal context for such a discussion.
A particular feature of the tax debate in the United Kingdom since 2000 has been
a stated desire by the government to use economic theory and evidence as a basis for
policy changes. As a result, several gambling sectors (in particular betting and bingo)
have moved to a system of taxation based on gross proﬁts (gross win)—see Paton,
Siegel, and Vaughan Williams (2002) for an introduction to this context. The gambling
machine sector proved more resilient, however, to taxation reform for reasons that
include successful challenges to tax policy in the courts.1
Prior to the implementation of changes announced in the 2012 budget statement
in the House of Commons, U.K. gambling machines were taxed in two ways. A value

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added tax (VAT) was levied at the standard rate on machine takings (cash-in-box) and
could be partially offset by recovery of VAT paid on inputs. The Amusement Machine
Licence Duty (AMLD) also was also levied as a ﬁxed amount paid for each machine up
front on an annual basis. The level of AMLD was linked to the type of machine (higher
for higher stakes and prizes machines). In the 2012 budget, however, the Chancellor
of the Exchequer announced the introduction of the Machine Games Duty (MGD), a
new gross proﬁts tax for machines, to replace AMLD and VAT on machines. The date
announced for the introduction of the new duty was February, 1, 2013.
In the following section we present the theoretical arguments underlying the case for
a switch from a license fee system of taxation (as with AMLD) to one based on machine
takings, that is, a gross proﬁts tax (GPT). In section 3 we consider a few other relevant
issues, including equity and externalities. The new duty was introduced on February 1,
2013.
2 Economic Basis for GPT
on Gambling Machines
.............................................................................................................................................................................
2.1 Background
Since2001theU.K.governmenthasmovedtowardtheuseof aGPTforgambling. Partly
this was in response to arguments (see Paton, Siegel, and Vaughan Williams 2000) that
a GPT would lead to a more allocatively efﬁcient outcome than would a tax on stakes.
A GPT represents a tax on margins and is likely to encourage ﬁrms to shift from a high-
price/low-quantity strategy to a low-price/high-quantity strategy. Under quite general
assumptions, David Paton, Donald Siegel, and LeightonVaughan Williams (2000, 2001,
2002) have shown that a tax revenue-neutral shift from a stakes tax to a GPT leads to
lower prices in equilibrium and a reduction in the dead-weight loss.
There is a range of published evidence suggesting that the beneﬁt from the intro-
duction of GPT on general betting has indeed been realized (e.g., Paton, Siegel, and
Vaughan Williams 2003; National Audit Ofﬁce 2005).
The question we seek to answer here is whether there is anything in the particular
institutional framework surrounding gambling machines which means that the theo-
retical arguments in favor of a shift to GPT do not apply or that they apply to a lesser
extent.
2.2 Economic Efﬁciency
When economists refer to allocative efﬁciency, they are referring to the allocation of
scarceresourcestotheirbestavailableuses. Abasicpremise(undercertainassumptions)

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lotteries and gambling machines
is that, unimpeded, the economy produces optimal outcomes as the forces of demand
and supply interact so that resources can be allocated to where they are most desired
and, therefore, yield the highest beneﬁt. Because taxes will distort this result, it is
generally optimal to keep this distortion to a minimum.
It is useful to model the decisions taken by ﬁrms in the gambling machine market in
two stages. In the ﬁrst stage ﬁrms decide how many machines to operate and where to
locate them. In the second stage ﬁrms decide on the optimal pricing strategy for each
machine, given the number of machines chosen in stage 1. We analyze the impact of a
switch from AMLD to a form of GPT on each stage separately. Note that in the analysis
below we deﬁne price in the standard way in the gambling literature as 1 minus the
expected value of a £1 bet. For example, if a machine pays out, on average, 70 pence
for each £1 wagered, then the price of a £1 bet on that machine in our model would be
30 pence.
2.2.1 Stage 1: Decision on Number of Machines
We consider the case of a switch from a system in which all tax is levied by means of
AMLD to a system in which all tax is levied by a GPT. In either case it is optimal for
ﬁrms to decide to install machines until the marginal revenue, which declines with each
additional unit, is equal to the marginal cost. For simplicity we consider the case of a
linear marginal revenue curve and constant marginal cost of installation, c.
Consider ﬁrst the case of AMLD. Denoting marginal revenue as MR, marginal cost
of production as MC, the cost of the license as L, and the number of machines as N,
we have
MR = a −bN
MC = c + L.
The equilibrium number of machines under AMLD (N AMLD) is then found, where
MR = MC.
a −bN AMLD = c + L
N AMLD = a −c −L
b
(34.1)
In the case of a GPT, levied at a rate t, we have
MR = (a −bN)(1 −t), where t = the rate of GPT.
MC = c.
The equilibrium number of machines, N GPT, is again where MR = MC.
N GPT = a −c −at
b(1 −t)
(34.2)

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In the simplest case where c equals zero, it is easy to show that any value of t less
than 1 will lead to a greater number of machines under GPT than under AMLD. Put
another way, if t is set so that N AMLD = N GPT, then tax revenue under a GPT will
always be greater than under AMLD. A consequence of this is that total surplus (tax +
producer surplus) will be greater under GPT, and a GPT is allocatively more efﬁcient
than AMLD.2
If c > 0, it will not always be the case that a shift to GPT will improve allocative
efﬁciency. To see this consider the case in which GPT is set at a rate that maintains the
same number of machines as under AMLD, that is, N AMLD = N GPT, so that
a −c −at = (1 −t)(a −c −L)
t =
L
c + L
(34.3a)
or
L =
ct
1 −t
(34.3b)
If t is levied at a lower rate than
L
c+L , then the quantity of machines will increase under
a GPT. A corollary of this is that if the revenue-neutral rate of GPT (t ∗) is such that
t ∗<
L
c+L , then the shift to GPT will lead to an increase in the total number of machines.
The example in ﬁgure 34.1 helps to illustrate the intuition behind this result. The
result holds true also for the case of variable costs, that is, that an increase in the
number of machines is more likely the larger the license fee is relative to the marginal
cost. However, in this case, the condition under which a shift to GPT will increase the
number of machines will be less easy to satisfy.
The example shows that under a GPT the ﬁrm is relatively better off (post-tax rev-
enue of £464 [= 1,200–736] instead of £305 [= 1,000–695], the government beneﬁts
from higher revenue (£736 under GPT compared to £695 under AMLD), and con-
sumers beneﬁt by being provided with a preferred activity (inferred from the fact that
consumers are willing to pay more to participate in it).3 In sum, AMLD distorts the
economy from the optimal outcome.
It can also be argued thatAMLD constitutes an entry barrier. In general entry barriers
impede the competitive process and innovation. The point is that there is a dynamic
• A ﬁrm is choosing between installing machines in its urban pubs or its rural pubs; it has £2000 capital available.
• In rural pubs, each machine costs £1000 and yields gross proﬁt of £1600.
• In urban pubs, each machine costs £2000 and yields gross proﬁt of £3000.
• Under AMLD with a licence cost per machine of £695: the ﬁrm sets up a single machine in an urban pub where
the added value to the economy is £1000. No machines are set up in the rural pubs. The total tax raised is £695.
• Under GPT with a rate of 23%: the ﬁrm sets up two machines in the rural pubs and none in the urban pubs. The
added value to the economy is 2 × £600 = £1200. Total tax collected is £736.
figure 34.1 The AMLD versus GPT comparison

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lotteries and gambling machines
loss to efﬁciency, in addition to the static loss considered here. For this reason AMLD
acts in favor of incumbents—a classic case, indeed, of regulatory capture.
In summary, a key question is whether a switch from AMLD to GPT is likely to lead
to an increase in the number of machines. If we assume that the unit of analysis is an
individual ﬁrm, the equilibrium number will increase subject to our condition, but this
may not translate to any additional machines, especially if N is small. The effect of the
switch would be that some ﬁrms will increase the number of their machines, some will
not, while some new operators will set up. Aggregating up to industry level, the net
effect is that the total number of machines increases. The second question is whether we
would expect a price reduction in those venues where the number of machines has not
increased. Unless all venues are treated as monopolies, we would expect prices overall
to decrease following the industry-wide increase in numbers. However, the size of any
price decrease will vary between venues and will be related to the nature and extent of
competition.
2.2.2 Stage 2: Pricing Decision
Once a machine is installed, variable costs associated with extra stakes are close to zero,
and hence the proﬁt-maximization problem is equivalent to revenue maximization,
noting that gambling revenue is by convention measured as “cash-in-box,” that is, total
stakes net of any payouts to punters. It is easy to show that the revenue-maximizing price
(themargin)giventhenumberof machinesisnotrelatedtothechoiceof AMLDorGPT.
In contrast, for a quantity-setting ﬁrm with some monopoly power, the equilibrium
price is affected by a stakes tax.
Where a ﬁrm has price p and sales q (where for gambling p refers to the margin and
q refers to the stakes), revenue can be given by R = q · p(q).
In the case of no taxation, a ﬁrm will maximize revenue by identifying the quantity
level, p∗and associated price (p∗), that maximizes R. Under a GPT tax is levied directly
on revenue at a rate, t. The revenue function now becomes R = (1 −t)q · p(q). As
(1−t) is a constant, the revenue-maximizing quantity and price remain unchanged at
(p∗, q∗). Under AMLD levied at a ﬁxed value of L per machine, the revenue function
becomes R = q · p(q) −L and again the equilibrium is (p∗, q∗).
The case of a stakes (or quantity) tax, like the old general betting duty, is somewhat
different. A tax levied at a rate of g per unit leads to a revenue function of R = (1−g)·
q ·p[(1−g)·q]. As long as the demand curve facing the ﬁrm is downward sloping, the
revenue-maximizing equilibrium must result in a price, p > p∗. The intuition behind
this result is that, as the tax is essentially levied on quantities, there is an incentive for
ﬁrms to prefer a high-price, low-quantity strategy.
In sum, a GPT and an AMLD are less distorting, in terms of price and quantity
decisions, than a stakes tax, which leads to a relatively higher price than either a GPT
or an AMLD. This analysis is relevant, however, only for the pricing decision given a
ﬁxed number of machines. Inasmuch as abolishing AMLD leads to an increase in the
number of machines at stage 1, it will likely lead to a reduction in price. Thus, in the

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## Page 718

the taxation of gambling machines: a theoretical perspective
697
long run, an AMLD works very much like a stakes tax—it is (indirectly at least) a tax on
quantity. In particular, if the number of machines increases, we would expect a lower
equilibrium price. If the total number of machines in a region were to increase, then
the proﬁt maximizing price will alter. This point is clearest in the context of a single
venue.4 For example, if the number of machines in a casino increases from 1 to 20, then
it is clear that the proﬁt-maximizing price for each machine will decrease.
Given this, the theoretical conclusion is similar to that used in the context of LBO’s
(licensed betting ofﬁces); if there is monopoly power, AMLD is allocatively inefﬁcient
compared to GPT.
3 Other Issues
.............................................................................................................................................................................
3.1 Tax Pass-on
We would expect that if one ﬁrm sets the “monopoly” proﬁt-maximizing price that
its neighbor ﬁrm would run its machine on a lower margin and capture most of the
market (assuming there is no product differentiation), thereby forcing the ﬁrst ﬁrm to
also lower its margin. This would continue until any further lowering of the margin
makes the machine unviable (this story ﬁts with industry suggestions that players are
sensitive to odds). In this case a tax increase would mean that the margin would have to
be increased by all to retain viability, and a tax cut would cause margins to fall. It would
also mean that machines in places with high costs, like town centers, would justify their
position with higher margins. To suggest that prices would not be altered is to assume
that players are not sensitive to odds in other venues and behave irrationally.
3.2 Equity
In terms of fairness, tax levels under a GPT would be linked to the revenue-generating
potential of machines and decisions would not be distorted as much as under the license
regime. For example, although the demand for a machine may be low, the machine
may still be viable insofar as its costs are covered, notably rent and tax. The key point,
therefore, is that while under the current system the machine may not cover the ﬁxed
cost of the license, its viability may well be maintained under an equivalent GPT.
3.3 Externalities in Gambling
High taxation on machines (relative to other gambling products) may be justiﬁed on
the basis that they pose particular risks to players, in term of the potential for problem
gambling (part of the "social cost" of gambling). This is part of the wider literature

---

## Page 719

698
lotteries and gambling machines
on problem and compulsive gambling (e.g., Ladouceur, Lachance, and Fournier 2009).
The problem may perhaps be linked also to the number of machines available, insofar
as this is linked to access. If so, this would seem to be a matter for regulatory rather
than tax policy.
3.4 VAT
Given a wish to tax gambling machines as a proportion of machine takings, a further
issue is whether this should be done on the basis of VAT,by GPT (as with other gambling
sectors), or by a mixture of both.
A consequence of removing VAT would mean that many ﬁrms that currently operate
machines would be brought into partial exemption for the ﬁrst time, as machines form
only a part of their business.
Allowing ﬁrms to recover the tax they have paid on inputs will lead to less distortion
within an industry than will a straight output tax with no recovery—a situation where
a ﬁrm has positive added value but where tax solely on output would be greater than
that added value. A lack of provision for input tax recovery will also create distortions
that encourage vertical integration—a ﬁrm that produces and operates machines will
not have to pay a VAT on machine rent while a ﬁrm that only operates machines will.
VAT recovery also provides an incentive to invest, through the capital goods scheme.
Removing this provision is likely to lead to less investment, a point that could, of course,
be made for all betting sectors.
VAT is already levied on an efﬁcient basis and makes up a signiﬁcant proportion
(over half) of tax on machines. This means that the arguments put forward for a GPT
as linking to externalities and removing distortions to decisions are slightly tempered—
the fact that VAT is already levied means that the advantages are less than for a total
move from AMLD to GPT.
The VAT treatment of gambling machines has, however, been subject to legal chal-
lenges, a factor highlighted by the Chancellor of the Exchequer in his 2012 budget
statement (HM Treasury 2012).
One area where I am today making substantial changes is gambling duties. The VAT
treatment of gambling machines is being repeatedly challenged by operators in the
courts. So I will introduce a new Machine Games Duty—with a standard rate of
20% and a lower rate for low stakes and prize machines of 5% of net takings.
4 Conclusions
.............................................................................................................................................................................
Our theoretical analysis leads us to conclude that there are strong arguments from
economic theory for the replacement of the AMLD with a system in which all taxation

---

## Page 720

the taxation of gambling machines: a theoretical perspective
699
is levied as a proportion of machine takings. In particular, it is likely that, with respect
to some ﬁrms and some machines, the AMLD constitutes an entry barrier. On its
abolition, the most plausible scenario is that the number of machines in operation
would increase. This, in itself, provides an economic argument in favor of the abolition
of the AMLD. We also argue that the change in the equilibrium number of machines is
likely to lead to a reduction in the average price (or an increase in the average payout)
and that this will lead to a net welfare gain.
A possible implication of the above analysis is that an increase in the number of
machines will be associated with a rise in negative externalities associated with machine
gambling. Although this outcome is a possibility, licensing individual machines is
unlikely to tackle the problem in an efﬁcient way. It is reasonable to suppose that this
issue may be better dealt with by “social regulation” of the location of these machines.
In terms of equity, a move toward taxation of a proportion of machine takings would
also be likely to bring this sector more in line with other gambling sectors.
The issue of a VAT is less clear-cut. There are theoretical arguments as to why a VAT
may be more efﬁcient than a GPT. However, it might be argued that all gambling sectors
should be treated on the same basis, in which case this is an argument for shifting from
a GPT to a VAT across the gambling sector.
Another option is to retain a VAT on machine takings and to replace the AMLD with
a GPT. Having two tax systems may seem overly complex and lead to dead-weight loss
in itself, but this issue is outside the immediate scope of this analysis. Given that a VAT
is already levied on cash in-box under the current system and that many operators will
be liable for a VAT anyway in other areas, it may be that the complexity of operating
two systems will be less than the practical problems of partial exemption. There is also
the legal context regarding the VAT treatment of gambling machines, highlighted by
repeated challenges by operators in the courts.
In conclusion, there is a clear and strong case for gambling machines to be taxed
in proportion to machine takings rather than with a ﬁxed tax per machine. The
appropriate balance between the use of a GPT and a VAT as the means of taxing
machines is less clear-cut, however, and should take account of legal as well as practical
considerations, most notably the ease, cost, and convenience of administration and
collection.
Notes
1. For an example of this see Paton and Vaughan Williams (forthcoming).
2. If an increase in the number of machines leads to an increase in negative externalities from
gambling, then we cannot be sure that this increase in allocative efﬁciency will be welfare
improving. The issue of problem gambling is brieﬂy considered in section 2.4.
3. An alternative setup is to remove the capital restriction and let the £1,000 and £2,000 ﬁgures
be annual running costs—in this case only the urban machine is installed under AMLD
while under GPT the rural machines are also installed, and there is beneﬁt for consumers,
producers, and government from their installation.

---

## Page 721

700
lotteries and gambling machines
4. Note, though, that we are not assuming that every venue will increase the number of
machines, only that the total number increases. In practice we might expect some venues
to increase the number, others not to change, and others still to enter the market.
References
d’Hauteserre, Anne-Marie. 1998. Foxwoods Casino Resort: An unusual experiment in
economic development. Economic Geography 74:112–121.
Forrest, David, O. David Gulley, and Robert Simmons. 2010. The relationship between betting
and lottery play. Economic Inquiry 48(1):26–38.
HM Treasury. 2012. Budget 2012 statement by the chancellor of the Exchequer, the Rt. Hon.
George Osborne MP, March 21; www.hm-treasury.gov.uk/budget2012_statement.htm.
Kearney, Melissa S. 2005. The economic winners and losers of legalized gambling. National
Tax Journal 58(2): 281–302.
Ladouceur, Robert, Stella Lachance, and Patricia-Maude Fournier. 2009. Is control a viable
goal in the treatment of pathological gambling? Behaviour Research and Therapy 47(3):
189–197.
National Audit Ofﬁce. 2005. HM Customs and Excise: Gambling duties, HC 188 session 2004–
2005, January. London: National Audit Ofﬁce.
Paton, David, and Leighton Vaughan Williams. Forthcoming. Do new gambling products
displace old? Evidence from a postcode analysis. Regional Studies, 47(6): 963–973.
Paton, David, Donald S. Siegel, and Leighton Vaughan Williams. 2000. An economic analysis
of the options for taxing betting: A report for HM Customs and Excise, September. London:
HM Customs and Excise.
——. 2001. Gambling taxation: A comment. Australian Economic Review 34(4):437–440.
——. 2002. A policy response to the e-commerce revolution: The case of betting taxation in
the UK. Economic Journal 112 (480): F296–F314.
——2003. Evaluation of the gross proﬁts tax on betting: A report for HM Customs and Excise,
January. London: HM Customs and Excise.
——. 2004. Taxation and the demand for gambling: New evidence from the United Kingdom.
National Tax Journal 57(Dec): 847–861.
Siegel, Donald S., and Gary Anders. 2001. The impact of Indian casinos on state lotteries: A
case study of Arizona. Public Finance Review 29(2):139–147.
Walker, Douglas M., and John J. Jackson. 2011. The effect of legalized gambling on state
government revenue. Contemporary Economic Policy 29(1):101–114.

---

## Page 722

Name Index
..................................
A
Adams, John Quincy, 572
Anne (queen of England), 614
B
Belmont, August, 574
Benedict XV (pope), 564
Bignell, W. A., 567
Boston, Sam, 577, 587n
Buchanan, James, 572
Buffett, Warren, 421, 422
Bush, George W., 8
C
Carpenter, Chris, 205
Carruthers, David, 139
Churchill, Winston, 586n
Clay, Henry, 572, 585n
Cohen, Jay, 141n
Cooper, William, 571
Crossley, Archibald, 577
D
Dandolo, Matteo, 564
Davydenko, Nikolay, 137
Defoe, Jermain, 368
Doyle, John, 576, 577, 587n
E
Elias, Gower W., 567
Elizabeth I (queen of England),
xviii, 613
F
Fabb, Richard C., 587
Fermat, Pierre de, 179
Fox, Charles James, 564
G
Gallup, George, 577
Gombaud, Antoine, chevalier de Méré,
179
Gould, Jay, 586n
Grant, Ulysses S., 574
Gregory XIV (pope), 564
Greinke, Zack, 205
Gural, Jeff, 270
H
Halladay, Roy, 205
Haren, Dan, 205
Hayes, Rutherford B., 574
Helmbold, H. T., 574
Hernandez, Felix, 205
Hoyt, Jesse, 572
Hughes, Charles Evans, 576
J
Jackson, Andrew, 571, 572
K
Kaplan, Stephen, 139
Keynes, John Maynard, 420, 421
Kolleher, Daniel, 138
L
LaGuardia, Fiorello, 577
Landon, Alfred, 577
Leach, John, 571
Lee, Cliff, 205
Leo XIII (pope), 564
Lidge, Brad, 205
Lincecum, Tim, 205
Lincoln, Abraham, 574
M
Mahoney, Charles, 575
Matsuzaka, Daisuke, 205
McClellan, George B., 574
McDonald, Ramsay, 567
Morrissey, John, 574
N
Nelson, Admiral Horatio, 582n
Nevitt, John, 572
O
Obama, Barack, 211
P
Pascal, Blaise, 179
Pigou, A. C., 29
Pileggi, Nicholas, 274
Pius IX (pope), 564
Polk, James K., 572, 573
Pollard, Ron, 568, 582n

---

## Page 723

702
name index
R
Ritner, Joseph, 585n, 586n
Rivera, Mariano, 205
Roca, Joseph Oller, 233
Rodriguez, Francisco, 205
Roosevelt, Franklin, 577,
587n
Roper, Elmo, 577
S
Sabathia, C. C., 205
Santana, Johan, 205
Schumm, Fred, 576
Shirreffs, Dottie, 269
Silinsky, Abraham, 587n
Silinsky, Frank, 587n
Silinsky, William, 587n
Simons, James, 422, 423
Soros, George, 421, 422
Stout, Robert, 570
T
Taylor, J. Kinsey, 574
Thorp, Edward O., 422
Tilden, Samuel J., 574, 585n
Trauman, Jeffrey, 141n
Trevelyan, George Otto, 564
V
Van Buren, John, 572
Van Buren, Martin, 572, 573
Vasquez, Javier, 205
Vassallo Argüello, Martin, 137
Verlander, Justin, 205
W
Wainwright, Adam, 205
Webb, Brandon, 205
Wilkes, John, 564
Wilson, Woodrow, 576
Wright, Silas, 573

---

## Page 724

General Index
...........................................
21. see blackjack
5Dimes.com, 194
60 Minutes (TV show), 269
6/49 lotto games, 149, 416, 417, 593, 600, 602, 628,
681
A
abnormal proﬁts, 535, 596, 599, 600, 602, 605. see
also abnormal returns
abnormal returns, 217, 447, 526, 600, 605. see also
abnormal proﬁts
absence of arbitrage, 211
accumulator bets, xvii, 341, 355, 356, 357, 358,
367, 368, 369n, 468
accumulator gambles, xvi
addiction to gambling, 4, 20, 63, 479, 601, 608n,
626, 629, 636n, 642, 643, 644, 645, 646,
665, 681
adjusted gross receipts, 18, 20, 21–23, 30, 89, 236
admissions taxes, xiv, 18, 19
adverse selection risk, 283, 284, 292, 294n
Afghanistan, 57
Africa, 56, 310n, 570
Alabama, 242, 252n
Albany Argus (newspaper), 541
alcoholism, 120
Allen v. Maur, 580n
Almack’s Club, 564
Alton, Illinois, 86, 89, 90, 91, 92, 93, 94, 96, 97, 99,
102, 103
American Institute of Public Opinion, 577
American Racing and Entertainment, 270
American Revolution, 564
American Wagering (sportsbook), 131
Ameristar, 92, 96
AmTote, Inc., 258
Amusement Machine License Duty, 296
analysis of variation (ANOVA), 205
Ancient Rome, 673
Anglo-Dutch War, 569
annuities, 598, 606, 607n, 614, 682
Anomalies Test Account, 418
anti-gambling statutes, 132, 142n
Antigua, 134, 141n
Antigua and Barbuda v. United States, 134
Aqueduct Racetrack, 271
Argentina, 146
Argosy Casino, 89, 92, 96
Arizona, 6, 26
Arkansas, 242
Arrow securities, 545
ask price, 275, 281, 283, 549–550, 596
assumption of equilibrium, 189
Aston Villa, 361, 362, 363, 364–365, 366
Atherfold v. Beard, 580n
Atlantic City, New Jersey, 3, 9, 15, 31, 49, 94, 107,
641
ATP World Tour, 138, 141n
Australia, xiii, 41
betting markets, 497
bookmakers, 175, 303, 309n, 311n, 312n, 505
casinos in, 68, 122
election betting, xviii, 569, 570
gambling in, 3, 50n
gambling machines, 662
gambling regulation in, xiii
insider trading, 297, 333, 335
lottery sales in, 24
market manipulation, 482
online gambling in, 133, 258
problem gambling in, 63
racing in, 256, 300, 301, 304, 309n, 311n, 315,
318, 331, 505, 506
social impact of gambling, 663
average return, 166, 167, 169, 209, 226, 470, 480
B
baby boomers, 14, 15
baccarat, 32, 39, 371, 372, 375, 377, 378, 379,
387
balanced book model, 205
Bank of England, 615
bankroll risk management, 341
Baptists, 687
Barcelona (football team), 158
baseball, 204, 267. see also pitchers, baseball
balanced book hypothesis, 193
betting markets, xv, 185, 192, 193, 194, 195
betting motivation, 192
betting systems, 175
betting volume, 193, 194, 196, 198, 199, 204
favorite-longshot bias, 193, 218
ﬁxed-odds betting, 193
Galileo Managed Sports Fund, 140
gambling corruption, 483
point spreads, 175

---

## Page 725

704
general index
basketball, 511, 537
betting strategies, 480, 507, 509, 510, 535, 538n
gambling corruption, 482, 483
heavy favorite, 539n
point spreads, 175, 485, 510, 529, 532, 538–539n
Battle for Britain, 567
Bayes’ theorem, 521, 523, 525, 526
Bayesian information criterion, 46
Bayesian probabilistic models, 397
BBC, 634
behavioral biases, 192, 195, 205, 317, 320, 513, 522,
523, 530, 531
behavioral economics, 456, 520, 546, 644, 645, 648,
679
behavioral ﬁnance, xvii, xviii, 219, 546, 608n
Belize, 194
Belmont Park, 271
Bendigo, Australia, 662, 664
Berkshire Hathaway, 421, 422
Bernoulli function, 523, 524
best case scenario, 235, 236
Bet Bull Holdings, 209
Bet&Win, 165
Bet365, 165, 166, 355, 368
Betbull.com, 209
Betfair, 138, 162, 170, 207, 416, 432, 433, 434, 460,
477, 562
betting volume, 287, 433
bookmakers, 286
corruption detection, 137
and favorite-longshot bias, 218, 219
ﬂat vs. national hunt racing, 286
horse race market, 434
and information efﬁciency, 219, 221, 223, 225,
226
in-play betting, 208–213
limit orders, 278, 284
odds scale, 433, 435
overrounds, xvi, 277, 280–283, 291
prices, 288, 289
returns, 227
revenue, 279, 460
starting prices, 276, 279, 280, 290, 446
trading activity, 294n
Betfair.com, 210, 227, 275, 279, 287
BetOnSports.com, 138–139
betting behavior, 292, 301, 305, 317, 453, 454, 457,
459. see also bettor behavior; investor
behavior
betting boards, 191, 192
betting exchanges, 207, 208, 210, 217, 276,
278–280, 281, 460, xv. see also Betfair
as anti-corruption tool, 137
arbitrage/hedging trades, 430
betting systems, 170, 176, 188, 454, 459, 460, 462
compared with bookmakers, 226
costs, 209
customer volume, 209, 432
efﬁciency, 176
favorite-longshot bias, 218
features, 271, 463
functions, 432
growth of, 477
information arrival, 226
regulation, 208, 446
for sports gambling, 138
success of, 209
use by bookmaker ﬁrms, 209
Betting Houses Act of 1853, 565
Betting Houses Act of 1874, 565
betting markets. see gambling markets
betting media, 453, 455, 459, 460, 473
betting options, xvi, 310n, 464
betting prices, 162, 164, 169, 216, 221, 227, 477
betting strategies, 167, 506, 535, 539n
behavioral based, 532
betting the over, 192, 194, 195, 202, 204, 205
betting the under, 192, 194, 195, 196, 202, 203,
204, 205
ﬁxed odds, xv, 162, 163, 164, 165, 214, 341, 545
hedging, 271, 443, 480, 576
home team, 225
and irrational behavior, 531
Kelly strategy, xvii, 342, 402, 403, 414
in poker, 400
portfolio, xvii, 341
proﬁtability of, 162, 166, 171, 179, 185, 193, 217,
510, 534, 535
small expected return, 168
spread, 216
strength and weight, 533
in Texas hold ’em, 398
betting venues, 254, 262, 268, 271, 272
betting volume, xv, 49
and betting behavior, 503
and betting strategies, 433
and gambler’s fallacy, 508
in horse racing, 257, 258, 259, 261, 262, 264,
266, 270, 271, 283, 294n
in Major League Baseball, 195, 196–199
betting-to-lose, 258
bettor behavior, 193, 281, 292, 459, 469, 521, 523,
531, 532, 536, 592, 628. see also betting
behavior; investor behavior
bettor bias, 193
bettor demographics
and casino gambling, 114
and casino gambling elasticity, 49
and casino legalization, 108
change in, 14, 473
and gambling legalization, 113
and gambling revenue, 112
and lottery sales, 622, 676
and problem gambling, 63
bettor risk taking
and betting motivation, 461, 479
and betting performance, 455
change over time, 466

---

## Page 726

general index
705
in election gambling, 576
gender differences in, 468
and mean staking levels, 466
measurement of, 466, 467, 492
operational measures of, 464–465
BetUS.com, 194
bid price, 275, 281, 283, 550–551
bid-ask spread, 276, 277, 280, 281, 282, 283, 291,
294n, 553, 566
bingo, 88, 608n, 641, 657n, 695
blackjack, 378
betting strategies, xvii, 368, 374, 388, 400,
412–414, 422, 423, 484
hold percentage, 371
house advantage, 38, 376, 377, 379, 387
as Internet game, 136
price of, 39, 375
at race tracks (racinos), 241, 247, 250
statistical properties of, 40
table drop, 90
Blue Square, 165, 166
Boodle’s Club, 564
bookmaker overrounds, 277, 291, 293n, 433
Bookmaker.com, 135
bookmaking, 151, 153, 176, 188, 300, 458
demand for, 22
illegal, 132, 311, 575
legal establishments, 22, 130, 133
market, 175
at race tracks (racinos), 459
regulation, 132
Brandywine Bookmaking LLC, 131
breeders
awards, 252n, 264
incentives, 264
racehorse, 246
revenue, 252n
Breeders’ Crown events, 263, 265
Breeders’ Cup races, 258, 265, 269
bridge-jumpers, 272
Brooks’ Club, 564
Buckshot War, 568n
Buddhism, 57, 60, 62
Burma, 57, 59, 66, 70
C
calibration test, 218, 219, 220, 221, 222, 223
California, 41
casino gambling, 8, 45
casinos, 378
horse racing, 257, 259
lotteries, 598
takeout rates, 257
tribal casinos in, 3
California Horse Racing Board, 257
California v. Cabazon Band of Mission Indians
1987, 107
call option framework, 315
call option markets, xvi
call options, 306, 317, 323, 324, 325, 335, 368
Cambodia, 57, 59, 65, 66, 70
Cambridge Chest, 420
camel racing, 310n
Camelot Group, 617, 636n, 681
Canada, xviii, 3, 41, 49, 63, 122, 146, 194, 242,
251n, 562, 569
6/49 lotto game, 416, 602
election betting, 570, 571, 583n
lotteries, 686, 688
Canadian Lotto, 680
Canadians (betting type), 369
Canberra, Australia, 570
cannibalization, 7, 106, 110, 146, 149, 154, 155,
156, 607n, 657, 677
Cantor Fitzgerald, 130
Cantor Gaming, 130, 138
Cantor Index Limited’s Spreadfair, 209
card counting, 375, 388, 390, 412, 413, 484
card rooms, 242, 370, 387, 388
Caribbean, 193
Caribbean stud, 371, 372, 375, 377, 398
CaribSports.com, 194
carryover wager, 260
Casino Australia, 3, 133
casino gambling, xvi, 26, 29, 36, 49, 50, 54, 56, 61,
74, 75, 76, 109, 271
cannibalization of lotteries, 27
cannibalization of other entertainment venues,
7, 106, 110
competition, 7, 39, 41, 44, 70–71, 88, 92, 239,
240, 248, 249, 250, 667, 677
competition, regional, 9, 36, 42, 50n, 68–69, 108
competition from online gambling, 15, 49
competition with economic sectors, 14
competition with other gambling venues, xiv,
14, 25, 37, 49, 54, 110
demand for, xiv, 15, 19, 20, 21, 54, 60, 61, 62–64,
65, 71, 72, 76, 78, 80, 88
economic impact of, xiv, 4, 5, 7, 14, 15, 55, 106,
107, 110, 121–122
employment effect, 4, 6, 7, 9, 15, 26, 76, 77, 93,
106
expansion of, 48, 53, 54, 55, 58, 65, 67, 69, 72,
76, 78, 79, 80
ﬁscal impact of, 14, 77, 106, 108
house advantage, 37, 38, 39, 40
income elasticities, xiv, 37, 45, 48, 49, 64
legalization of, 30, 59, 65, 69, 72, 75, 81n, 107
Macau, 31–32, 67, 68, 70, 72
organization, 53, 56–58, 69, 70, 71, 73
Pigouvian tax, 29
price elasticities, xiv, 22, 23, 24, 36, 37, 40, 42, 49
proﬁtability, 15, 15n, 31, 68
public sector, 59–60, 67, 77, 78
regulation, 20, 21, 24, 36, 46, 59, 67, 68, 73, 75,
95
regulation by state, 3, 24, 47
regulation of games, 20, 22

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## Page 727

706
general index
casino gambling (Cont.)
regulation of prices, 25
regulation on monopolies, 25
regulations on outlets, 20
regulations on zoning, 94
regulatory structure, 40, 59, 71
regulatory system, 53, 58, 76, 78, 80
revenue sharing, 8
smoking ban effects on, xiv, 44, 85, 89, 249
social impact, 59, 76–77, 77–78, 79, 106, 108,
121–122, 685
table games, 18, 22, 24, 32, 37, 38, 39, 41, 42, 44,
47, 49, 54, 58, 62, 68, 69, 87, 90
taxation, xiv, 18, 23, 29, 55, 72
Thailand, 57, 59
wages, 6, 106
casino gaming. see casino gambling
Casino Queen, 86, 89, 92, 96
casino war (poker variant), 372
casinos, commercial, 8, 9, 106, 107, 110, 112
Catholic Church, 564
Catholics, Roman, 57, 582n
cell phones, 306, 310n, 312n, 432
Centaur, 140
Central Asia, 56, 57, 64, 67, 73, 75
cesta punta, 171
change-point analysis, 87, 91–92
Charlie chasing, 285
Chelsea (football team), 210, 211, 361, 362, 363,
364–365, 366
Chicago, Illinois, 89
children, 267, 617, 630, 634, 636n
China, 31, 54, 56, 57, 58, 59, 63, 64, 67, 68, 69, 74,
76, 80n, 81n, 146, 673
Christ’s Hospital Bluecoat School, 614
Churchill Downs, 131, 260
Clark County, Nevada, 119
closing spread, 529, 532, 535, 537, 538n
Club Cal Neva Satellite Race and Sportsbook
Division, 131
Coase theorem, 129
Cochrane-Orcutt method, 10
cognitive biases, 477, 521, 522, 523, 524, 526, 532,
536
Colorado, 16n, 30, 45, 47, 48, 119
commercial casinos, 8, 9, 106, 107, 110, 112, 122n
Commissioners for the Reduction of the National
Debt, 621
Commissioners of the Lottery, 614, 615
commodity markets, 423
commonwealth countries, 299, 570
competitive environment, 36, 40, 42, 49
compound annual growth rates, 64
Computer Poker Research Group, 397
conditioned races, 260
Confucianism, 57, 60
Congress, U.S., 3, 132, 133, 134, 139, 141, 571
Connecticut, 8, 45, 47, 48, 171, 676
Consensus Point, 546
Conservative Party, 566, 567, 568, 582n
consumer decision making, xix, 673
consumer price index, 5
consumption-based gambling, 195, 204
continuous arrival of information, 316
Cooperstown, New York, 571
Costa Rica, 134, 138, 139, 194
coupon, 146, 148, 151, 152, 154, 157, 159, 315
craps, 38, 39, 241, 247, 250, 372, 374, 375, 376, 377,
385, 387, 400, 534
cricket, 433
and betting motivation, 483
Galileo Managed Sports Fund, 140
gambling corruption in, 483, 486n
and longshot bias, 477
crime, xiv, 650, 654, 659, 662, 663
burglary, 119, 654
casino gambling and, xiv, 54, 59, 78, 108,
117–119, 122
conspiracy, 139
counterfeiting, 657
domestic violence, 657
fraud, 138, 139, 654, 657
and illegal gambling, 23, 132, 135, 139, 577, 657,
658
increase in, 118, 658
Internet, 141n
money laundering, 54, 75, 78, 135, 657
organized, 132, 617
and pathological gambling, 120
racketeering, 139
rates, 118, 119, 122, 685
theft, 5, 116, 117, 120, 657
voting fraud, 573, 574, 585n
white collar, 654
cross-price elasticities, 154, 657
for alternative forms of gambling, 24
of demand, 145
horse race betting, 255
of lottery tickets, xix, 673
lotto, 155
slot machine gambling, 651
traditional estimates, 44
Curb Exchange, 575, 587n
Curb Market, the, 576, 586
customer clustering, 129
Czech Republic, 210, 211, 212
D
Daily Express (newspaper), 567, 568
Daily Mail (newspaper), 567
daily numbers games, 508, 598, 602, 607n
Dallas, Texas, 139
dead-weight loss, xix, 683, 696, 702
Delaware, 44, 87, 88, 140n, 241, 242, 248, 249, 481
Democratic Party, 574, 575, 577, 585n
Denmark, 151
Department for Culture, Media, and Sport, 620,
621

---

## Page 728

general index
707
destination resort casinos, 4, 48
Detroit, Michigan, 26
Dewey-Roosevelt election contest, 587n
Diagnostic and Statistical Manual of Mental
Disorders 4e (DSM-IV), 120, 123n
difference in points, 176
disposition effect, 219, 220, 221, 228n, 446
dog racing
and betting behavior, 453, 463, 483, 509
betting volume, 122n
competition with other venues, 43, 112, 113,
123n, 240, 244, 246, 249, 255
and insider trading, xvi, 298, 301, 311n
legalization of, 3
longshot bias in, 182
pari-mutuel wagering, 5, 175, 241, 251n
at race tracks (racinos), 3, 242, 252n
state revenue from, 5, 114, 115
Double Exposure, 377
draw-based games, 617, 618, 619, 632, 635
duality of markets, 58
Dubai, 311
Dublin, Ireland, 580
Durbin-Watson values, 10, 11, 13
E
earned run average (ERA), 194
East Asia, 58, 62, 64, 65, 67
East Timor, 57
Eclipse Award, 269
economic downturn, 90
economic impact of gambling, xiii, xix, 695
assessment, 5
consumer choice, 5
displaced expenditure, 7
economic growth, 7, 55
employment, 5, 7, 14, 15
income, 5
increased revenue, 7
market saturation, 15
multiplier effects, 14
new investment, 5
pathological gambling, 5
policy issues, 4
regressive economic impact, 5
socio-economic impact analysis of gambling
framework, 656
state economies, 14
taxation, 55
effective odds, 173, 395
efﬁcient market hypothesis, 205, 293, 429
election betting
and Intrade, 211
and prediction markets, xviii, 546
and spread betting, 565, 566
election betting markets
in Asia, 570, 571, 579
in Australia, 570, 582n
demand for, 568
history of, xviii, 562, 563, 564, 568, 569, 572,
574, 575, 576, 578, 579, 579n, 585n
in Ireland, 583n
legality of, 562, 565, 573, 580n, 581n
and media, 563, 567, 578, 584n, 586n, 587n
microstructure, 562
and Wall Street, 577
electronic games of skill, 242
electronic gaming devices, 37, 38, 241, 641
English Football League, 161
English Premier League, 165, 361, 368
entry barriers, 131, 134, 698, 702
equilibrium takeout rate, 21
Era of Good Feelings (1815–1823), 573
ethics, 54, 57, 59, 74, 494, 512, 592, 606
EuroMillions, 606, 608n, 609n, 618, 628, 634, 635,
636n
European club, 164
European Lotteries, 151
European Union, 49
event studies, 443
exacta pools, 257, 261, 262, 268, 499
exchange betting, 272, 277, 278–280, 281, 291, 292,
293, 293n, 463, 513n
exit barriers, 131
expected returns
and betting motivation, 477, 479, 480, 485,
486n, 504
and betting strategies, 162, 166, 204, 216, 394,
399, 416, 602, 680
and betting volume, 264
and carryovers, 257, 261
and effective price, 674
and efﬁciency, 180, 189
and election betting, 550
and favorite-longshot bias, 218, 325
and forecasting model, 167, 168
and gambler’s fallacy, 508, 509
and insider trading, 300, 317, 320
and Kelly strategies, 360
and lotteries, 600, 675, 678, 679, 681, 682
and probability of winning, 179, 495, 593
and strong-form efﬁciency, 596
and trading strategies, 217
and weak-form efﬁciency, 219, 226
expected utility theory, 498, 499, 501, 524,
647
expected win percentage, 370, 371
expert analysis, 429, 430, 447, 454
F
FA Cup, 164
Facebook, 269
favorite-longshot bias
and baseball betting markets, 192, 193
and Betfair, 209
and betting behavior, 317, 455, 466, 471–473,
490, 496
and betting strategies, 416

---

## Page 729

708
general index
favorite-longshot bias (Cont.)
and bookmaker pricing, xvi, 303, 324–325, 335,
462
and ﬁnal odds pools, 272
and horse race betting, 268, 283, 302
and information efﬁciency, 217
and insider trading, 307
and market efﬁciency, 457
and pricing processes, 161
and probability of winning, 294n, 330
and weak-form information efﬁciency, 218, 227
Federal Electoral Act, 570
federal securities laws, 142n
Fianna Fáil Party, 563
ﬁeld data analysis, 185–187
ﬁeld size, 261, 294n, 437
FIFA World Cup, 221
Fifth Avenue Hotel, 575, 586n
ﬁnal wealth, xvii, 403, 406, 409, 415
ﬁnancial motives, 483, 484
Finland, 147, 151
ﬁsh tank phenomenon, 129
ﬁxed-odds betting, xv, 163, 315, 335, 448n
demand for, 241
and favorite-longshot bias, 161
informational efﬁciency of, 161, 162
and market makers, 545, 554
on match results, 165
and payoffs, 214
pricing, 162, 164, 169
and probabilistic forecasts, 162, 167
ﬁxed-odds betting markets, 161, 162, 169, 315, 335
horse racing, 334
ﬁxed-odds betting strategies, xv, 162, 163, 164
and insider trading, 300
ﬁxed-odds betting terminal, 242
ﬁxed-odds games, 485
ﬁxed-odds horse racing, xv, 162, 163, 164
ﬂat racing, 284, 286, 287, 288, 294n
Fleet Street press, 565
ﬂock of birds phenomenon, 129
Florida, 171, 242, 252n, 258, 270, 598, 676, 679
football (American)
and Galileo Fund, 140
gambling corruption in, 483
football (soccer) pools, xv, 145, 608n
coupon, 154, 156, 159
decline, 149, 150, 152
demand for, 149, 154
effective price, 151, 153, 154
entry fee, 147, 152
forecasting, 147, 158, 159
history, 145, 146
impact of lotteries, 149, 150, 154
jackpot prize, 146, 147
La Quiniela, 151, 152
Littlewoods, 147, 149
long-odds wagers, 146, 147, 150, 151
market, 146, 147, 150, 151, 156, 608n
marketing, 146
player demographics, 148, 149, 150, 152, 153
regulation, 150
revenue, 151, 152, 158
rollovers, 146, 147, 152, 154
rules, 146, 148, 152, 154
similarity to lotteries, 145, 147, 148, 156
Spanish vs. British market, 146
takeout rate, 148, 150, 153
taxation, 150
ticket price, 154
Vernons, 147, 149
Football League, U.K., 152, 161, 165, 368
forecast prices, 300, 301, 311n
forecasting models, 162
football (soccer) pools, 148
Foreign Intelligence Surveillance Act of 1978
(FISA), 133, 141n
Fortune Survey, 577
Foster v. Thackery, 580n
Fracsoft, 439, 440, 443, 444, 445, 448n
framing issues, 639, 648, 656
France, 151, 159, 170, 175, 209, 256, 580n
Fulham (football team), 361, 362, 363, 364–365,
366
G
G. B. de Chadenedes & Co., 576
Galileo Managed Sports Fund (Galileo Fund), 140
gambler behavior, 37, 50
Gamblers Anonymous, 116, 123n
Gambling Act. see Unlawful Internet Gambling
Enforcement Act of 2006
Gambling Act 2005, 616, 618, 636n
gambling dens, 58
gambling machines, xviii, 641. see also slot
machines; video poker machines
efﬁciency, 696
gross proﬁts tax, 696
market, 697
taxation, xix, 695, 701, 702
gambling markets, 3, 36, 216–217
efﬁciency, 195, 599, 682
ﬁxed-odds betting, 161, 162, 169, 315, 335
high frequency, xv, 217, 221
industry structure, 25
Major League Baseball, 204
match outcome, 210, 223
NFL, 193
order driven, xvi, 276, 277, 280, 282, 283
in play, xv, 207, 208, 227
quote driven, 275, 276, 282, 283
regulation, 25, 630
taxation, xiii
tote (totalizator), xv, 234, 238, 299
in the United Kingdom, 609n, 630
game denomination, 49
game design, 154, 155–157, 628
game shows, 454

---

## Page 730

general index
709
game theory, 396, 397, 400, 401
Gamebookers, 165, 166
games of chance, 400, 485, 486n, 641
Gaming Act of 1845, 567
Gangwondo Province, 73
general odds rule, 171, 177, 179, 180, 181, 183,
184, 188
Genoa, Italy, 563
Genting Club, 69
Genting Group, 71
Genting Highlands, 69, 77
Georgia (U.S.), 270, 598
Gluck’s second law, 466, 500
Goa Anti-Gambling Act, 73
Goliaths, 369n
goods and services tax, 23, 31
government subsidies, 254, 265, 266
Grand Slam tournaments, 138
Granger causality, 110
analysis, 5, 105, 109
testing, 109
gravitational pull effect, 281, 284, 291, 292, 293,
294n
Great Depression, 567
great investors, xviii, 420–423
Greece, 151, 678
Greek 6/49 lotto, 602
gross domestic product (GDP), 64, 256
gross gaming revenue (GGR), 31, 32, 55, 60, 81n,
644
in Asian casino gambling, 64, 65, 66, 67, 68, 69,
71, 72, 73, 74, 75
gross gaming yield, 150, 617, 618
gross proﬁts, xiii, 279, 695, 696, 698
gross proﬁts tax (GPT), 696, 697, 698, 699, 700,
701, 702, 702n
gross win, 695
Guildhall, 614
Gulley-Scott model, 153, 154
H
halo effect, 601, 681
Han Dynasty, 673
handicap races, 284, 285, 286, 287, 288, 289, 467,
468, 470
Hanson market maker, 546, 554, 556
Happy Valley (Hong Kong racetrack), 307, 308,
309
harness, 242, 264
horse breeds, 240
races, 252n, 256, 298
racing markets, 301, 481
wagering, 247
Harrah’s, 92, 96
Hart-Agnew Act, 575, 576
heavy favorites, 535, 536, 539n
hedging strategies, xv, 171, 188, 189, 433, 434, 447
Heinz, 369n
herding behavior, 304, 503, 504, 505, 506, 512
Herﬁndahl index, 262
High Street, 161, 162, 165, 166, 209
high-frequency data, xv, 207, 208, 210, 219
Hinduism, 57, 62
hockey, 192, 193, 483
Hoffman House, 575
hold percentage, 38, 40, 370, 371
Holland, 49
Hollywood Park, 269
home country bias, 478
home favorite, 197, 199, 200, 201
home team underdog bias, 477
home win, 146, 158, 159, 161, 163, 164, 165, 198,
213, 214, 222, 353
homogeneous agents, 234–235
Hong Kong, 56, 57, 67, 80n, 175, 307, 308, 309
Horseplayers Association of North America, 257
hot hand fallacy, 490, 506, 507, 508, 512, 513n,
514n, 533, 534, 535, 536, 539n, 648
in betting markets, 509–510, 511
house edge, 370, 371, 372, 374, 375, 376, 387
House of Commons, U.K., 695
House of Representative, U.S., 574
Hurricane Katrina, 110–111, 121
I
IG Markets, 546
illegal gambling, 23, 132, 135, 139, 577, 657, 658
Illinois
casino gambling, 41
casino legalization, 30
casino revenue, 47, 48
casinos in, 8, 96
competition, 9
election betting, 572
employment impacts of gambling, 6
gambling regulation in, 86
gambling revenue, 45
riverboat casinos, 5, 378
riverboat casinos legalization, 16n
riverboat casinos regulation, 50n, 85
slot handle, 100, 103
slot machine wagering, 242
smoking ban effects, xiv, 44, 87, 89, 90, 91, 92,
93, 94, 95, 97, 98
table drop, 101, 103
Illinois Supreme Court, 573
immediacy, 275, 284, 293n
implicit options, xvi, 335
implied odds, 280, 395
India, 54, 57, 64, 65, 66, 67, 70, 73, 76, 483, 582n
Indian casinos, 94, 95
and betting volume, 112, 122n
competition with other venues, 44, 113, 663
data collection, 9, 122n
earnings, 3
growth of, 3
nontaxable revenue, 26
regulation of, 88, 139

---

## Page 731

710
general index
Indian casinos (Cont.)
revenue, 8, 9, 47, 48
slot machines at, 242, 662
state tax revenue from, 6, 27, 112
tribes operating, 3, 30, 271
Indian Gaming Regulatory Act of 1988, 3, 16n
Indiana
casino legalization, 30
casino revenue, 47
casinos in, 41
economic impacts of gambling in, 119
and election betting history, 572
horse racing subsidies in, 255
racinos in, 242
riverboat casino competition, 9
riverboat casino demand, 45
riverboat casino gambling in, 662
riverboat casino legalization, 16n
riverboat casinos in, 48, 663
smoking ban effects in, 89
social impacts of gambling in, 119
Indonesia, 56, 57
industry structure, 25, 48, 49, 147
inﬂation, 240, 244, 247, 249, 260, 288
information aggregation, 268, 433
information arrival, 212, 226
information efﬁciency. see market efﬁciency
Inkling Markets, 546
in-play betting, xv, 138, 207, 208, 210, 213, 214,
227
in-running betting. see in-play betting
instants (lottery game), 599, 607n, 609n
International Tennis Federation, 138
Internet gambling. see online gambling
Interwetten, 165, 166
Intrade, 211, 221, 222, 223, 228n, 562
intrade.com, 211
investor behavior, 292, 520, 521, 522, 524, 525,
531, 534, 536
Iowa, 3, 6, 8, 16n, 30, 41, 45, 47, 48, 50n, 85, 89,
241, 242, 247, 248, 250
Iowa Political Stock Market, 562
Ireland, xviii, 300, 563, 569, 570, 583, 628, 677
Irish Free State, 563
Irish Lottery, 608n
Islam, 56, 62, 85
Italy, xvii, 141n, 170, 209, 562, 563, 564
J
J. S. Fried & Co., 576
jackpot fatigue, 600, 601, 681
jai alai, 171, 172, 175, 176, 188, 242, 252n
Jockey Club, 300, 301
jockeys, 258, 259, 298, 308, 311n, 318, 484, 502
joint hypothesis problem, 222, 223, 478
Joint Stock Act, 636n
Journal of Economic Behavior and Organization,
457
jumps racing, 286, 288
K
Kangwon Land, 69, 73, 77
Kansas, 242
Kazakhstan, 57, 59, 65, 66, 67, 70, 75, 76
Keeneland Race Track, 269
Kefauver Committee, 132
keno, 39, 245, 375, 377, 387
Kentucky, 41, 255, 258, 260, 264, 572, 597
Kentucky Cabinet for Economic Development,
267
Kentucky Derby, 258
Kyrgyzstan, 57, 59, 66, 67, 107
L
La Primitiva, 152, 154
La Quiniela, 156
entry fee, 154
Gulley-Scott model, 153
prize structure, 154
sales, 158
La Rioja, Spain, 170, 172, 176
Labour Party, 566, 567
Lacaussade v. White, 580n
Ladbrokes, 165, 166, 212, 226, 369n, 567, 568,
582n, 583n
Lake Tahoe, Nevada, 46
Laos, 57, 59
Las Vegas, Nevada, 245
betting boards in, 191
blackjack in, 412, 413
and casino gambling, 67, 379
casino gambling economic impacts in, 55
and casino gambling taxation, xiv
comparative gross gaming revenue, 73
as gambling location, 15, 24
gambling revenue, 44, 46
and gambling taxation, 18, 30
gaming machines in, 66
gaming tables in, 66
pathological gambling in, 116
and social impact of gambling, 119
sports betting in, 192
sports betting markets in, 176
sportsbooks in, xiv, 130
law of one price, 211
Lee County, Iowa, 6
Liberal Party, 566, 567
license fees, 30, 31, 621, 695, 696, 698
Liga Portuguesa, 134
limit orders, 276, 278, 279, 281, 284, 293n, 294n
Literary Digest, 577, 578
Littlewoods, 146, 147, 149
Lloyds Coffeehouse, 564
Lloyd’s of London, 565, 582n
LMAX, 209
lobbying, 123n
London, 140, 416, 429, 439, 442, 564, 614
bookmakers, 567, 568–569
insurance ﬁrms, 581n, 636n

---

## Page 732

general index
711
investors, 567, 568
sportsbooks, xiv, 138
London 2012 Olympic and Paralympic Games,
621
London Aqueduct lotteries, 636
London Stock Exchange, 133, 139, 207, 565
long-run elasticity, 42, 45, 48
Los Angeles Dodgers, 269
losing streaks, 164, 507, 509, 510, 539n
loss limits, 41, 42, 85, 86, 95
Lotterie Generall, 613, 635
lotteries
and betting behavior, 679
demand for, 674, 677
effective price, 674
efﬁciency, 683
and income elasticity, 675
and market efﬁciency, 682
microeconomics, 674, 677
revenue from, 683, 684
structure, 677
lottery markets, xviii, 28, 628, 673, 674, 676, 680
design, 628
efﬁciency, xiv, xix, xviii, 591, 595, 596, 605,
682–683
rationality, 605
lottery ticket sales, 115, 122n, 597, 609n, 620, 621,
673, 674, 675, 676, 677, 679, 680, 681
demographics, 676
lotto games, 145, 146, 152, 153, 154, 157, 606. see
also 6/49 lotto games
abnormal proﬁts in, 600
addiction to, 601, 681
advertising, 605
and betting motivation, 601, 604
and betting strategies, 416–418, 602, 603
competition among, 676, 677
demand for, 595, 675
efﬁciency, 592, 593, 594, 597, 598, 599
entry fee, 156
and gambler’s fallacy, 609
jackpots, 607, 609, 676, 678, 681
long-odds wagers, 155
misconceptions about, 609
prize levels, 608
publicity, 601
revenue, 156
scams related to, 609
structure, 605
and ticket prices, 609
and ticket sales, 680
weak form efﬁciency of, 596
Louisiana, 8, 15, 16n, 30, 45, 47, 48, 89, 110, 242
Louisville, Kentucky, 260
lowball (poker variant), 388
luck, 40, 261, 370, 388, 400, 423, 507, 526
lucky store effect, 680
Lumiere Place, 86, 90, 91, 92, 93, 96
lump sum, 609n, 682
M
M Resort, 130, 138
Macao. see Macau
Macau, 3, 68, 80–81n
casino business organization, 67, 68, 74,
75
casino fees, 19
casino jurisdictions, 56
casino monopoly, 59, 65, 72
casino taxation, 18, 30, 31–32
casinos in, xiv, 66, 67, 69, 71, 73, 122
economic impact of gambling, 77
gambling expansion in, 3, 55
gross gaming revenue, 36, 64, 65, 68, 71, 74
internal governance structure, 59
oligopolistic competition, 70, 71
visitor volume, 67–68
world’s casino capital, 58
Machine Games Duty, 696, 701
Maine, 242, 577
Major League Baseball, 193, 195, 197, 202, 204,
205
Makropoulou-Markellos framework, 306, 315,
334, 335
Malaysia
casino jurisdictions, 57
casinos in, 58, 66, 67, 69
competition, 70, 71
economic impact of gambling, 77
election betting in, 570, 571
gross gaming revenue, 64, 65
internal governance structure, 59
Maldives, the, 57
Mann-Whitney-Wilcox U test, 91
marginal odds, 307, 312n
Maricopa County, Arizona, 26
Marina Bay Sands, 31, 71
market efﬁciency, xv, xvi, 216–217, 228n, 235,
682–683
in baseball betting, 192
in betting markets, 161, 162, 169, 208, 217,
226–227, 227
and betting strategies, 430, 445, 447, 455, 456,
457, 478
in betting systems, 175
and favorite-longshot bias, 218, 227
and FIFA World Cup, 221, 222
in ﬁnancial markets, 596, 597, 599, 605
and Intrade, 221
levels of, 217
in lotteries, 674, 679
in lotto games, 598
media forecasters, xvii, 429, 431
in online soccer wagering, 137
in order-driven markets, 276, 277
in person-to-person betting, 171
in point spread wagering, 533
in quote-driven markets, 276
in soccer betting, 162

---

## Page 733

712
general index
market makers, 170, 175, 188, 275, 276, 282, 283,
284, 293n, 294n, 432, 478, 486, 530
for prediction markets, xviii, 546
market odds, 180, 193, 201
and betting behavior, 481, 482
and betting strategies, 368, 438
and election betting, 564
and the general odds rule, 177, 180, 181
and horse race betting, 272
and the hot hand fallacy, 511
and probability, 177, 183, 184, 185, 186, 187, 189
and probability of winning, 179, 182, 429
and relative risk, 465
and risk taking behavior, 467
market orders, 276, 278, 281, 294n
market power, 36, 140, 615, 654
market simulation games, xviii
Markowitz portfolio theory, 216
Maryland, 92, 96, 242, 250, 256, 508, 598, 659, 660,
662, 664
Maryland Jockey Club, 256
Massac County, Illinois, 6
Massachusetts, 41, 88, 597, 602, 681
Massachusetts State Lottery, 609n
Meadowlands, 270
media forecasters, xvii, 429
Mega Millions, 606
Melbourne, Australia, xvii, 305, 312, 570
Melbourne Cup, 297, 298
Metcalfe’s law, 129
Metropol, 575
Metropolitan Turf Association, 576
Mexico City, 171
MGM, 70
Michigan, 8, 30
Microsoft, 546
microstructure analysis, xvi, 277, 293
Middle East, 310n, 387
middle prices, 316, 318
Million Adventure game, 614
mining town casinos, 47, 48
Minnesota, 8, 88, 242
Mississippi, 6, 8, 15, 16n, 24, 30, 44, 45, 47, 48, 89,
110, 378, 572
Mississippi River, 86, 96
Missouri, 111, 242
casino gambling in, 8
casino regulation, 50n
casino revenue, 47
casinos in, 45, 48, 86, 92–93, 95, 96, 100
competition, 6, 9, 27, 42
economic impacts, 6, 26
legalization of casinos, 16n, 30, 85
slot machine demand, 41
smoking ban in, 87, 89, 90, 101, 103
mobile devices, 454
mobile phones. see cell phones
money laundering, 54, 75, 78, 135, 657
Montana, 140, 242
Monte Carlo simulations, xvi, 213, 214, 306, 324,
329, 331, 354, 507, 508, 664
Montreal, Canada, 571
Moore’s law, 129, 209
Morning Line (racing program), 429
Morocco, 151
Mountaineer, 43, 242, 243, 244, 245, 246, 247, 250,
251, 252n
multicorners spread bet, 215
N
National Basketball Association (NBA), 202, 485,
532, 534, 535, 539n
National Collegiate Athletic Association (NCAA),
483
National Council of Sports, 152
National Football League (NFL), 193, 202, 219,
368, 529, 532, 533, 534, 538, 538n
National Gambling Impact Study Commission
(NGISC), 3, 132
National Government coalition, 567
National Hockey League (NHL), 193, 202
national hunt racing, 277, 286, 287, 289, 291
National Indian Gaming Commission, 3, 9
National Lottery Commission, 616, 618, 619, 620,
630
National Lottery Distribution Fund (NLDF), 617,
620, 621
National Lottery, United Kingdom, xviii, 149, 600,
602, 603, 604
cannibalization, 607n, 608n
cultural impact, 463
demand for, 22, 601
efﬁciency, 597
launch, 148, 154, 613
portfolio, 151
price elasticity of demand, 609n
regulation, 616, 617
rollovers, 155
takeout rate, 675
Native American casinos. see Indian casinos
natural disasters, 107. see also Hurricane Katrina
Navarra, Basque Country, xv, 170, 172, 176
NBA, 193
Nepal, 57, 66, 67, 70
Netherlands Antilles, 133
New Hampshire, 133, 254, 686
New Jersey, 8, 30, 31, 45, 47, 48, 49, 107, 109, 140n,
240, 258, 509, 576, 598
New Mexico, 27, 242
New Orleans, Louisiana, 387
New South Wales, Australia, 42
New York, 242, 264, 271, 571, 572, 574, 575, 576,
577, 578, 584n
New York Breeders’ Awards, 264
New York City, xviii, 131, 574, 587n
New York Curb Association, 576, 586n, 587n
New York Herald (newspaper), 577
New York lottery, 617, 678

---

## Page 734

general index
713
New York Racing Association, 271
New York Sire Stakes, 264
New York Stock Exchange, 586n
New York Times (newspaper), 575, 578
New Zealand, 41, 42, 300, 482, 497, 569, 570, 581n,
617
Newcastle (football team), 361, 362, 363, 364–365,
366
nonhandicap races, 284, 285, 286, 287, 288, 289
non-rollover drawing. see rollover drawing
North America, 55, 58, 63, 68, 175, 202, 257, 499
North American Industry Classiﬁcation System
(NAICS), 8, 9
North American (newspaper), 572
North Korea, 57, 59
Norway, 151
O
Oaklawn Park, 258
Oceania, 56
odds movements, 429, 430, 437, 446, 447
odds range, 294n, 462, 467
odds scale, 170, 188
oddschecker.com, 162
off-course betting, 299, 305, 306, 460, 463, 466,
467, 469
offshore sportsbooks, xiv, 138
off-track betting (OTB), 23, 89, 132, 240, 255, 256,
260, 263, 264, 267, 268
Ohio, 41, 112, 255, 597
Oklahoma, 242
Olympic Lottery Distribution Fund, 621
Omaha (poker variant), 388, 398
online betting exchanges, 138, 162, 176, 188, 207,
209
online gambling, xiii, 15, 49, 132, 133, 134, 136,
138, 139, 141n, 208, 210, 647
opening prices, 303, 311, 316, 318, 320, 321, 323,
329, 332, 546
opening spread, 529, 532, 535, 537, 538n, 539n
optimal commodity taxation, 28
optimal takeout rate, 23, 25, 675, 679
option markets, xvi, 335
option values, xvi, 329, 330, 331, 332, 335
option-pricing framework, 315, 318
ordinary least squares (OLS) regression analysis,
88, 196, 251, 261, 288, 531
Oregon, 140, 242
ostrich racing, 310n
overlays, 429
P
Paddy Power, 355
pai gow poker, 39, 375
Pakistan, 57
papal succession betting, 562, 563, 564, 570
PaperofRecord.com, 573
Papua New Guinea, 57
pari-mutuel markets, 255, 299, 462, 477, 478, 482,
485, 545, 547, 551
betting behavior, 463, 473
betting motivation, 484
competition with other forms of gambling, xv,
416
favorite-longshot bias, 268
and information presentation, 233, 268, 272
legalization of, 309n, 310n
mathematics of, 234, 235, 236, 237, 238
systems, 131, 175, 188, 233, 256, 258
pari-mutuel racetracks, xvi
casino gambling at, xvi, 239, 241, 242, 244
competition with other forms of gambling, 247,
248, 249
demand for, 243, 244, 245, 247, 248, 250
handle, 240
herding behavior, 504, 505
history of, 239–240
revenue, 240, 247, 250, 252n
pari-mutuel wagering, 15n, 37, 259
and betting behavior, 460, 463, 498
and betting strategies, 430
competition with other forms of gambling, 44,
112, 258
decline of, 43, 243, 244, 246, 247, 248, 249, 251,
269, 641
demand for, 246, 250
dog racing, 251n
and election betting, 574
and football pools, xv, 145
increase in, 244
jai alai, 252n
legalization of, 270
and lotteries, 509, 593, 594, 598, 615, 617, 618,
621, 622, 624, 680
and odds betting, 521
price of, 40, 44, 248
regulation of, 245
revenue, 243, 244, 250, 251
takeout rate, 243, 245, 261
tax revenue from, 43, 244, 250, 251
Paris Mutual wagering. see pari-mutuel wagering
parlays. see accumulator bets
parliament, Canada, 571, 583n
parliament, Irish, 583n
parliament, Italy, 563
parliament, U.K., 562, 565, 566, 567, 569, 570,
580n, 581n, 582n, 583n, 613, 614
past-posts, 132
pathological gambling, 7, 77, 78, 644
and casino gambling demand, 20
and crime, 108
degrees of, 123n
and gambling demand, 23
and gambling legalization, 120, 123n
and gambling motivation, 479
and slot machines, 21, 642, 662
and social costs, 115, 116, 119, 121, 122

---

## Page 735

714
general index
pathological gambling (Cont.)
treatment of, 117, 119
pelota, 170
pelota betting market, 172–173
efﬁciency, 171
pelota betting system, 170, 188
compared with betting exchanges, 176, 188
efﬁciency, 180, 183, 185, 189
general odds rule, 171, 177, 179–180, 183, 188
hedging, 188
and inconsistent beliefs, 177
longshot bias, 189
odds, 174, 188
odds scale, 170
probability of winning, 177–178, 181–182, 184,
187, 189
rules, 170, 172, 176
Penghu Islands, Taiwan, 107
Pennsylvania, 114, 241, 242, 248, 250, 255, 272, 585
per capita income, 5, 7, 9, 41, 42, 48, 109, 110, 158,
623, 675
percentage bet, 194, 195, 197, 199–201, 202, 203,
204, 205
person-to-person betting. see betting exchanges
Philippine Amusement and Gaming Corporation
(PAGCOR), 68, 69
Philippines, the, 57, 58, 64, 65, 66, 67, 68, 69, 70,
71, 77
Phoenix, Arizona, 26
Pigouvian tax, 29
pitchers, baseball, xv, 191
Cy Young Award, 194, 197, 204, 205, 206n
Cy Young voted, 194, 198, 201, 202, 203
player loyalty programs, 49
Players Boycott, 257
player-versus-player game, 387
plunging, 303, 310n, 312n, 330, 333, 334, 335
point spread betting
and betting behavior, 523, 528, 532
and bookmakers, 530
data, 536
on football games, 176
in sports, xvii, 176, 537
point spread betting markets, 520, 521, 523, 528,
529, 530, 532, 533, 537
mechanics of, 521
for NFL games, 532, 533, 536
point spread wagering. see point spread betting
Poisson processes, 213, 214, 216, 327, 329
poker
and artiﬁcial intelligence, 397
and Betfair, 209
blufﬁng in, 396, 397, 398
expected odds, 395
expected value, 393–394, 400
and game theory, 396–397, 400, 401
hand probabilities, 389, 390, 397
hand rankings, 389–390, 391
history of, 131, 387
hold percentages, 371
house-banked, 387, 398–399
implied odds, 395
and Internet sportsbooks, 136
mathematics of, 387, 388, 389, 393, 394, 395,
396, 397, 400
odds, 388, 393, 399, 400
player versus player games, 387, 388, 398
popularity of, 387
pot odds, 394, 395, 396, 398
at Prairie Meadows, 247
probability, 390, 391, 393, 400
revenue, 387
reverse-implied odds, 395
and skill, 387, xvii, 388, 395, 397, 398, 399, 400,
401
and strategy, 396, 397, 398, 399, 400, 401
winning odds, 394
Polaris, 398
political corruption, xiv, 570
pool impact, 234, 236, 237
pools sales, 153, 154, 155, 158
portfolio betting strategy, xvii, 341
pot odds, 394, 395, 396, 398
Powerball, 601, 606, 676
Prairie Meadows Racetrack and Casino, 247
Prais-Winstein method, 11, 13
Premier League, 165, 361, 368, 369n
Premiership matches, 223
premium players. see VIP players
President Casino, 92
price elasticity of demand, 23, 36, 37–40, 41, 42,
257, 609n, 626, 627, 628, 644, 675, 679
price-based overrounds, xvi
Pricewise, 429, 430, 431, 432, 433, 436, 437, 438,
439, 443, 444, 445, 446, 447, 448n
pricing structure, 162
Princeton Newport Partners, 422
prize ﬁghts, 576
probability judgments, 495, 496, 512
Professional and Amateur Sports Protection Act of
1992 (PASPA), 140n, 141n
proﬁt margins, 54, 304, 323
proﬁt maximization, 48, 137, 218, 319, 699, 700
Profumo Affair, 568
prospect theory, 446, 498–500, 523, 524, 536, 603
public choice, xix, 55, 57, 73, 80, 81, 266, 673,
686–687
public ﬁnance, xix, 673, 683–684, 684–685,
685–686, 688
public information, 211
and betting behavior, 481, 485
and horse race betting, 305, 306, 308, 315, 316,
317, 318, 319, 320, 325
and illegal trading, 210
and insider trading, 284
and sports betting markets, 192
and trader opinions, 280, 281

---

## Page 736

general index
715
punters, 212, 275, 278, 279, 302, 306, 368, 369, 462,
699
pure gambling, 297, 298
Q
Quantum, 421, 422
Quay Financials, 140
R
race quality, 261
Raceform, 293
Racing Post, the, 429, 441, 442, 447, 448n
racinos, 3, 241, 249–251, 271
characteristics of, 239
demand for, 239
as entertainment complex, 484
impact on pari-mutuel racing, xvi, 239,
243–245, 247–249
to increase demand for racing, 43, 240, 246,
249–251
launch dates, 241, 242, 249
layout, 245
legalization, 3, 87, 239, 240, 241, 251n
locations, 241, 249
Mountaineer Racetrack and Gaming Resort,
243, 244
Prairie Meadows, 247
revenue, 88, 241, 246, 247, 252n
simulcast races, 252n
smoking ban at, 88, 249
types, 241
rafﬂes, 614, 617, 642
rake, 387
Ramsey rule, 28
Razz, 388
Real Madrid (football team), 158
real-world environments, 491, 492, 493, 502, 503,
512
recession, xiv, 49, 106, 621, 622
red dog (poker variant), 372
regression analysis, 4, 5, 7, 89, 90, 93, 288, 289, 291,
531
regression models
and betting market outcomes, 196, 201, 202,
204, 222
and betting volume, 197, 199
and employment impacts, 9, 11
and lotteries, 622, 626, 627
and racetrack gambling demand, 261, 288
and smoking ban impacts, 88, 93
remonte, 172, 172–174, 174
Renaissance Medallion, 422, 423
Reno-Sparks, Nevada, 46
representative agents, 235, 525
representativeness, 507, 510, 512, 522, 524, 525,
526, 532, 533, 534, 536, 537n
Republic of Ireland, 563, 569, 570
Resorts World Manila, 69, 71
Resorts World Sentosa, 31, 71
return on investment, 399, 473
Reuters, 570
reverse-implied odds, 395
Rhode Island, 171, 242, 622
risk aversion index, 404, 410
risk aversion index, Arrow-Pratt, 411, 423
risk management, 468
Ritz Club, 58
River City Casino, 86, 96
riverboat casinos, 3, 5, 6, 9, 15, 16n, 22, 30, 41, 43,
45, 47, 48, 49
cannibalization, 607n
cruising requirements, 50n, 85
economic displacement effects, 26
pricing, 378
slot machines, 242, 641, 662, 663
smoking ban, xiv, 86, 87, 89, 94
St. Louis, Missouri, 96
table games, 44
road favorite, 193, 196, 197, 198, 199, 200, 201, 204
road win, 198, 199
robot market makers, xviii, 545
rollover drawing, 597, 608n, 609n
roulette, 387, 486n
and betting behavior, 49
and betting market operations, 297, 298
and casino taxation, 18
and gambler’s fallacy, 507, 509, 511
and gambling motivation, 479, 484
and game price, 37, 40, 378, 380, 485
and the hot hand fallacy, 534
and house advantage, 38, 39, 371, 375
legalization of, 241, 250
and player skill level, 400
and player value, 381, 382
and probability of winning, 372, 373, 374, 384
and volatility benchmarks, 383
and wagering demand, 247
Royal Ascot, 429
Royal Jewel Lottery, 636n
S
Saar plebiscite, 570
sales tax revenue, 37, 115
Salisbury, U.K., 433, 446
Santa Anita Park, 259
Saratoga, 131
scaled commission fee, 387
Scorecast, 368
scratchcards, 617, 618, 619, 621, 630, 632, 635,
636n, 677
Seaham, 567
Second Great Awakening, 573
security price, xviii, 546, 548, 579n
seemingly unrelated regression analysis (SUR), 88,
113
Senate, U.S., 132
Senate Special Committee to Investigate Crime in
Interstate Commerce, 132

---

## Page 737

716
general index
sequential betting, 341, 359, 360
seven-card stud, 388, 398, 400
Sha Tin, 307, 308, 309
Shelby County, Tennessee, 44
Shin measure, 303, 505
Shinnecock, 271
short-run elasticity, 46–48
sic bo, 378
simulcast betting, 242, 270
simulcasting, 240, 247, 254, 257, 262, 271, 272
simultaneous events, xvi, 341
Singapore, 146, 569, 570, 579
election betting, xviii
Singapore casinos, xiv, 18, 30, 57, 69, 70, 71, 72, 73,
75, 78
expansion, 36, 55, 58, 67
gambling legalization, 59, 65
gross gaming revenue (GGR), 65
market structure, 65, 66
regulation, 59
taxation, 31
Singapore’s National Council of Churches, 78
slot machines, 9, 10, 12, 46, 47, 48, 136, 485, 486n,
640–641
and Asian preferences, 62
beneﬁts and costs, xviii, 659, 662, 665
demand for, 22, 41, 250, 251
effect on lottery games sales, 24, 44, 608
effects of smoking ban, 87, 90, 91, 92, 93, 94, 97,
98, 99–103
as a ﬁxed-odds games, 38, 242
growth of, 26, 58, 68
house advantage, 371
motivation, 479
and pathological gambling, 642, 643, 646
performance, 69
player demographics, 659
and price elasticity of demand, 37, 39
price of, 248, 375
proﬁtability, 68
at race tracks (racinos), 43, 241, 242, 243–245,
247, 248, 250, 251, 254
regulation, 22, 24, 248, 249, 251
revenue, 21, 42, 44, 248, 249, 250, 251, 255, 266,
641, 642, 646
taxation and fees, 18, 31, 32
video slot machines, 245
wagering, 248, 249, 250, 251
smart money wager, 267, 268, 307
smoking restriction, 86, 87, 88
social impact of gambling, xiv, 4, 37, 55, 77, 79, 106
bankruptcy, 5, 108, 403, 578, 655, 662, 663, 666
casinos, 4, 78, 121
commercial sex, 59
crime, 59
divorce, 5, 117, 662, 663
drug abuse, 59
moral objections, 107
perceptions of, 79
religious objections, 107
social services, 117, 656, 658
Societdade de Turismo e Diversões de Macao, 32
South Africa, 50n, 569, 583n
South Asia, 57, 62, 63, 582n
South Dakota, 16n, 30, 45, 47, 48, 242
South Korea, 57, 58, 59, 64, 65, 66, 67, 69, 70, 73, 77
South Oaks Gambling Screen (SOGS), 120, 123n
Southeast Asia, 58, 64, 65, 67
Soviet Union, former, 75
Spain, xv, 628, 642, 678
football (soccer) pools, 145, 151–153
Spanish 21, 377
Spartak Moscow (football team), 210, 211
Sportech, 147
Sportingbet (bookmaker), 165, 166, 355
sports betting
football (soccer) pools, 148
legalization, 153
sports gambling market, 130, 529
Sports Insights, 193, 194, 196, 537
Sportsbook.com, 194, 537
SportsbookReview.com, 135
sportsbooks, 133, 138, 141n
and baseball, 192, 195, 201
bet size limits, 538n
betting odds, 204
bookmakers, 192, 193, 194, 196, 205, 528
corruption, 132–133
demand elasticity, 136
economic environment, 133–134
economies of scope, 136
efﬁciency, xiv, 137
and the efﬁcient market hypothesis, 205
entry barriers, 134
and the Galileo Fund, 140
Las Vegas based, 130
legal status, 130, 131, 133–134
local bookmakers, 132
market shares, 135
in the NFL, 193
objectives of, 131
in point spread markets, 528, 529, 538n
point spreads, 529
product differentiation, 135–136
and set point spreads, 193
taxation, 23
and the Unlawful Internet Gambling
Enforcement Act of 2006, 139
sportsbooks markets, 129
Sri Lanka, 57, 58, 65, 66
St. Could County, Illinois, 6
St. Louis, Missouri, xiv, 6, 42, 86, 87, 89–94, 96–99,
102, 103
St. Paul’s Cathedral, 613
St. Petersburg paradox, 402, 403
Stamp Act, 580n
Stan James (bookmaker), 165, 166
Standard & Poor’s (S&P), 8

---

## Page 738

general index
717
Standard Industrial Classiﬁcation (SIC), 8, 9
starting price
and betting motivation, 458, 461, 465, 477, 478
and betting strategies, 430, 437, 438
in horse race betting, 318, 323, 448n
and insider trading, 329
and overrounds, xvi, 276, 277, 291, 293n
and the Shin measure, 303
and totes, 299
Starting Price Regulatory Commission, 279, 293n
state lotteries, 15n, 146
accessibility, 592
auspices of, 241, 242, 243, 249, 641, 678, 682
competition from, 239, 240, 249, 608
competition with other venues, xvi, 6
efﬁciency of, 598
in Great Britain, 148, 613, 614, 615, 616, 636
jackpot fatigue, 601
legalization of, 94, 254, 687
nature of, 617
regulation, 616
revenue, 26, 27, 43, 685
social impacts, 684, 685
taxation of, 23, 114, 683
in United States, 621–623
State Lottery, the, 614, 615, 616, 636
state-sponsored wagering, 233
stock markets, 140, 267, 293, 420, 422, 456, 530,
534, 545, 567, 579n. see also Iowa Political
Stock Market
Strait Times (newspaper), 570
Street Betting Act of 1906, 565
substitution effect, 27, 44, 607n, 608n, 677
sum of prices, 283, 287, 288, 289, 323
decrease with time, 331
efﬁciency, 279, 280
last race effect on, 285
number of horses effect on, 302
in sensitivity analysis, 290, 293n
trading volume, 282
unpredictable factors effect on, 286
sumo, 482
Super Bowl, 263, 484
Super Heinz, 369n
superstition, 62
supply and demand, 20, 174, 252n, 276, 473, 476,
485, 642
Surabaya, Indonesia, 56
Sweden, 151
Sydney, Australia, xvi, xviii, 570, 582
syndicates, 140, 258, 308, 416, 418, 478, 481, 503,
608n
systematic biases, xvii, 490, 512
T
table drop, 90, 91, 92, 93, 94, 97, 98, 99, 101, 102,
103
table games, 32, 42, 49, 69, 87, 131
competition with other venues, 247, 248
demand for, 22, 62
hold percentage, 371
income elasticity, 47
legalization, 266
let it ride, 371
market, 54, 58, 68
poker, xviii
price, 37
price elasticity, 41
at race tracks (racinos), 44, 241, 242, 247, 250,
251
regulation, 22, 24
revenue, 249
table drop, 38, 39, 90
taxation, 18
Taiwan, 41, 56, 57, 80–81n, 107, 675
Tajikistan, 57
takeout, track, 257, 260, 262
Tammany Hall, 577
Tashkent, Indonesia, 56
taste-for-gambling function, 539n
Tea Act, 564
telephones, 133, 152, 240, 305, 458, 460, 463, 467,
577. see also cell phones
television, 223, 454
advertising, 150
election news, 568
sports viewing, 176, 387
tennis, 140, 141, 141n, 433, 477
betting markets, 137
Tennis Integrity Unit, 138
terrestrial gambling, 129, 130, 135, 136
Texas, 622, 680
Texas hold ’em, 388, 389, 390, 392, 393, 397, 398,
399, 400
Thailand, 57, 59
theoretical probability of winning, 177, 178, 181,
184
theoretical win percentage, 370, 371, 382
thoroughbred
horse breeds, 240, 256
races, 252n, 257, 258, 259, 260, 265, 268, 269,
271, 272
racetracks, 22, 243, 244, 258, 262, 416
racing markets, 301
wagering, 247, 260
Thoroughbred Racing Association, 255
three-card poker, 371, 372, 375, 377,
398
Tioga Downs, 270
tipsters, 429, 481
Tobit model, 107
Toronto, Canada, 63, 571
Toronto Star (newspaper), 571
Toronto World (newspaper), 571
Tory Party, 566
total return, 169
total stakes, 207, 699
totals betting, 192, 193, 194, 195, 202

---

## Page 739

718
general index
tourism, 64, 663, 687
and casinos, 4, 26, 72, 73, 76, 77, 94, 108, 111,
115, 118
and crime, 119
economic impact of gambling, 658
employment impact, 15
gambling motivation, 479
industry structure, 49
and racetracks, 267
and racinos, 240, 246, 249
as social impact, 79
track conditions, 261, 286
TradeSports, 211, 219, 220, 228n
TradeSports.com, 219, 220
trading volume, 256, 277, 280, 282–283, 287, 288,
289, 291, 292, 294n, 432, 444, 447, 596, 597
transaction costs, 129, 155, 276, 319, 328, 355, 363,
494, 497, 535, 595, 599, 601, 605, 608n, 683
transaction privilege, use, and severance tax, 26
treble chance, 146, 147, 148, 151, 153
trifecta wagers, 257, 261, 262
Trixies, 369n
Tunica County, Mississippi, 6, 44
Turkey, 210, 211, 212, 222
turnover, 54, 71, 145, 234, 355, 432, 433, 634, 651
of bet suppliers, 485
horse race wagering, 239
turnover (amount wagered), 38, 50n
turnover, betting, 429, 568
turnover, business, 66, 67, 72, 73, 74
turnover, cash, 59
turnover, pools, 149, 151
turnover-based tax, xiii
TVG (betting service), 209
TVH (TV station), 209
U
U.K. National Lottery. see National Lottery,
United Kingdom
under betting, xv, 192, 202, 236, 268, 283, 457, 500,
599
under proposition, 192
underdog, 176, 192, 193, 195, 201, 205, 477, 528,
529, 535, 538n
United Nations (UN), 56, 80n, 502
United Press International, 570
Unlawful Internet Gambling Enforcement Act of
2006, xiii, 139, 141n
urban casinos, 3
U.S. Census Bureau, 9
user interface, 210
utility function, 61, 62, 410, 523, 530, 545, 629, 646
of baseball bettors, 195
bettors’, 457, 473
concave, 523, 539n
consumers’, 61
entertainment component of, 601
for gains, 446
rationality based, 524
utility function, Bernoulli, 523
utility function, concave, 403
utility function, Friedman-Savage, 64, 594, 674,
679
utility function, logarithmic, 342
utility function, negative power, 404
utility function, power, 341, 342
utility-of-wealth function, 523, 539n
Uzbekistan, 56, 57
V
value added tax (VAT), 696, 701, 702
Value Line, 418, 429
vector autoregressive system (VAR), 109, 226, 227
Venetian, the, 70
Venice, Italy, 563
Vernon Downs, 270
Vernons, 147, 149
Victoria, Australia, 87, 88, 305, 306, 312n
Victorian era, 565, 569
video lottery terminals (VLTs), 43, 44, 241, 242,
243, 249, 258, 641, 660, 685
growth of, 246
Mountaineer, 244
price of, 244, 245
regulation of, 245
revenue from, 244, 246, 247, 250, 251
wagering volume of, 244, 246, 247, 251
video poker, 38, 39, 40, 242, 377, 399
video poker machines, 37, 641
and house advantage, 375, 387, 398
payback percentages, 399
Vietnam, 57, 59, 63, 65, 66
vigorish, 131, 136, 141n, 674
VIP players, 31, 32, 54, 74
Virginia, 598, 636n
Virginia City, Nevada, 310n
Virginia lotto, 683
Von Neumann-Morgenstern expected utility
function, 523, 539n
W
W. L. Darnell & Co., 576, 587n
wagering asymmetry, 275
wagering taxes, xiv, 18, 25, 30
wagering venues, 272
off-track, 260
Waldorf Astoria, 575
Warren County, Mississippi, 6
Washington Post (newspaper), 575, 577, 578
Washington State, 88, 598, 678
weak-form efﬁciency hypothesis, 161
wealth paths, 404, 421, 423
weather, 110–111, 121, 146, 263, 286, 495
West Asia, 56, 67, 73, 75
West Brom (football team), 361, 362, 363,
364–365, 366
West Virginia
casinos in, 43
lotteries, 44, 50n, 622

---

## Page 740

general index
719
racinos in, 241, 242, 243, 248, 249, 250, 641
video lottery in, 685
West Virginia Lottery, 243, 244
West Virginia Video Lottery Act of 1994, 244, 246
Western Europe, 146
Western Union, 132
Whig Party (U.K.), 564, 585n
Whig Party (U.S.), 571, 573, 574
White-Huber “sandwich” correction, 196
White’s Club, 564
William Hill (bookmaker), 130, 165, 166, 212, 568,
583n
win percentages, 42, 193, 196, 197, 198, 201, 202,
243, 252n, 382
and betting volume, 199, 204
and house advantage, 371, 376
in price elasticity, 40, 41
in slot machine gambling, 244, 245, 248, 371
as win rate metric, 370
win/draw/away win probabilities, 164
winning streaks, 507, 509, 510, 511, 533, 534, 539n
Wire Act of 1961, 132, 133, 138, 141n
Wisconsin, 663, 664
Women’s Tennis Association, 138
Woodbine Entertainment Group, 258
World Cup, 223, 263
World Series, 576
World Series of Poker, 388, 399
World War II, 146
worst cases, 233, 236, 237, 363, 554
www.soccer-data.co.uk, 165
Wynn Resorts, 70
Y
Yahoo!, 546
Yankees (baseball team), 205
Yankees (betting type), 369n
Z
Zenyatta, 269
zero-proﬁt condition, 302, 316, 332, 335, 431, 435