Efficiency of Racetrack Betting Markets

The following sections are included:

• Contents

• Preface to 2008 Edition

• Preface in 1994 Edition

• List of Contributors

• Acknowledgments

Gambling is decision making under risk. On the surface, it seems a simple exercise, of gaining a profit or losing one's wager. While that is, of course, the essence of the exercise, a closer inspection reveals great complexity and scope. Indeed, this simplicity veiling a complex and general process is what has attracted academics from a variety of disciplines to consider gambling as a forum for investigating matters of wider importance than simply wagering. For instance, psychologists have used gambling to illustrate and inform about fundamental behavior in the face of uncertainty, and numerous behavioral biases have seen support. Economists bring a more rational, utility-based perspective to decision making under uncertainty, and wagering has provided an opportunity to test numerous theories and has generated new theories as well. Financial experts view gambling markets as possessing many of the intricacies of financial markets; however, the repeated and short-lived reduced form of gambling markets allows cleaner analysis than is generally possible in most financial markets. Thus, starker views of aggregate investor behavior are sometimes possible, including investigations of market efficiency. Statisticians have used gambling to motivate improved estimates of complicated probabilistic events. Mathematicians and management scientists have developed useful gambling strategies that have drawn on and extended efforts in other domains (e.g., Kelly betting and information transmission). While gambling is of academic interest in its own right, it has clearly been demonstrated to enhance our understanding of more farranging environments…

Just as the racetrack market has many features that make it an interesting setting in which to study market efficiency, it likewise provides an excellent forum for a psychological investigation of investor risk behavior. As Metzger (1985)¹ notes, the racetrack offers at least four advantages over laboratory studies: 1) data is plentiful and there is considerable variation in locale, track size, race characteristics, etc.; 2) the level of dollars wagered are of economic significance to most bettors; 3) a vast amount of information is available to bettors from a variety of sources; and 4) there are several betting possibilities — straight and exotic wagering — in each race. A downside of the racetrack forum is that the odds aggregate bettors' decisions, and so individual actions are usually indiscernable; however, numerous aggregate effects have been documented that a psychological perspective provides some insights to. Foremost among these is the strong and stable favorite-longshot bias in the win market, first documented by psychologists Griffith (1949)¹ and McGlothlin (1956)¹…

In horse-race betting, 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…

The following sections are included:

• Problem

• Procedure

• Results

• Discussion

• Summary

In an early note Griffith (1949) showed that horse race bettors put too much money on horses which have little chance of winning and too little on those most likely to win. McGlothlin (1956) repeated the study, confirming the results and revealing many further potentialities in the data by considering the position of the race in the day's program. An obvious extension of the analysis—one which McGlothlin picked up but brushed over lightly—is to turn from win betting to “show” betting. The person who would like to bet on a surer thing than even the heavy favorite to win the race may bet that he will “place,” that is, finish first or second, or, what is more likely yet, that he will “show,” finish third or better. The tendency to under-bet the most probable event should appear in its most marked degree in show betting…

Three experimentally established biases away from optimality that result from misconceptions of chance, variations in the framing of outcomes, and the illusion of validity are of detectable dysfunctional consequence in the natural world of the gambler. A study of the public's betting in 12,316 horse races shows that the gambler's fallacy, increasing risk preference within a day, and insensitivity to actual contingencies contradicting expert opinion, principles derived from the results of laboratory experiments, can be meaningfully applied in the practical setting.

Racetrack betting is a classic example of decision making under uncertainty. The options available to a bettor - they types of wagers possible - are clearly understood. A bettor's probabilities are, of course, only subjective, not objective. Considerable data is available to refine one's probabilities and the parimutuel method aggregates these individual assessments to arrive at the public's assessment which, as was discussed in the previous sections, roughly approximates objective probabilities. The papers in this section attempt to describe the risk-taking behavior of the representative bettor by evaluating this bettor's utility function and by comparing reactions to different wagers that have similar risk characteristics…

For portfolio problems with joint normally distributed asset returns, the risk aversion measure R = −w₀ (Eu″(w)/Eu′(w)), where w₀ is initial wealth can be used to characterize optimality. Comparisons between the global measure R and local measures based on R_A = −u″(w)/u′(w) are explored. Simulations for several utility function classes are described.

The following sections are included:

• INTRODUCTION

• THE EXPECTED-UTILITY HYPOTHESIS

• EXPERIMENTAL BACKGROUND: THE RACE TRACK AND PARIMUTUEL BETTING

• THE EXPERIMENTAL PROBABILITY CURVE

• FORMULATION OF THE MODEL MR. AVMART

• AVMART'S INDIFFERENCE CURVE

• AVMART'S UTILITY OF MONEY CURVE

• CONCLUSION

The following sections are included:

• INTRODUCTION

• PARI-MUTUEL BETTING

• BETTING COMBINATIONS

• THE THEORETICAL RELATION BETWEEN RETURNS AND PROBABILITIES

• RACE-TRACK DATA

• THE EMPIRICAL RELATION BETWEEN RETURN AND THE PROBABILITY OF WINNING

• CONCLUSIONS

• APPENDIX A LIMITS ON THE p − R RELATION

• APPENDIX B THE PARLAY RELATION

• APPENDIX C THE MARTINGALE RELATION

Subjective and estimated objective winning probabilities are obtained from 20,247 harness horse races. It is shown that subjectively a horse with a low winning probability is exaggerated and one with a high probability of winning is depressed. Various hypotheses characterizing the bettors' behavior to explain the observed subjective-objective probability relation are explored. Under some simplified assumptions, a utility of wealth function of a decision maker is derived, and a quantitative summary measure of his risk attitude is defined. Attitude toward risk of a representative bettor is examined. It is found that he is a risk lover and tends to take more risk as his capital dwindles.

The earlier sections of this book have primarily dealt with positive analysis contributions to the horseracing literature. This section begins our discussion of normative analysis. We start with the original paper in this area, Isaacs (1953)¹, where our bettor is assumed to know the true win probabilities in the horserace and wishes to maximize expected profit. Isaacs accounted for our bettor's effect on the odds and developed an ingenious algorithm to determine the optimal wagers. The remainder of the papers in this section consider three extensions of Isaacs model. First, Isaacs assumed risk neutrality while Breiman (1961)² (extending Kelly (1956)²) showed that the rate of growth of wealth is maximized, asymptotically, by assuming a logarithmic utility function. Second, Isaacs' model takes win probabilities as given; estimating these probabilities can involve fundamental methods (which are discussed here and in many popular trade publications) and technical schemes (which are considered in Section 4). Third, Isaacs' restriction to win betting can be extended to place, show and exotic wagering with ordering probability estimates. These three important extensions are now discussed in some additional detail…

The following sections are included:

• Introduction

• The problem

• The solution

• Some ramifications

Suppose in a given horserace there are n horses and the ith horse's chances of winning is qi. Let W₁ be the amount bet on i by the crowd, W ≡ ∑W₁ and 1–Q be the percentage track take…

Models of optimal betting in pari-mutuel systems, using a general utility function, are discussed. A theorem showing the relative attractiveness of each outcome (“horse”) is given. Some special cases of the linear utility model are considered. An algorithm is presented for the logarithmic utility. The case where the public bets are random random variables is also analyzed.

This paper concerns the problem of optimal dynamic choice in discrete time for an investor. In each period the investor is faced with one or more risky investments. The maximization of the expected logarithm of the period by period wealth, referred to as the Kelly criterion, is a very desirable investment procedure. It has many attractive properties, such as maximizing the asymptotic rate of growth of the investor's fortune. On the other hand, instead of focusing on maximal growth, one can develop strategies based on maximum security. For example, one can minimize the ruin probability subject to making a positive return or compute a confidence level of increasing the investor's initial fortune to a given final wealth goal. This paper is concerned with methods to combine these two approaches. We derive computational formulas for a variety of growth and security measures. Utilizing fractional Kelly strategies, we can develop a complete tradeoff of growth versus security. The theory is applicable to favorable investment situations such as blackjack, horseracing, lotto games, index and commodity futures and options trading. The results provide insight into how one should properly invest in these situations.

This paper investigates fundamental investment strategies to detect and exploit the public's systematic errors in horse race wager markets. A handicapping model is developed and applied to win-betting in the pari-mutuel system. A multinomial logit model of the horse racing process is posited and estimated on a data base of 200 races. A recently developed procedure for exploiting the information content of rank ordered choice sets is employed to obtain more efficient parameter estimates. The variables in this discrete choice probability model include horse and jockey characteristics, plus several race-specific features. Hold-out sampling procedures are employed to evaluate wagering strategies. A wagering strategy that involves unobtrusive bets, with a side constraint eliminating long-shot betting, appears to offer the promise of positive expected returns, even in the presence of the typically large track take encountered at Thoroughbred racing events.

The Bolton and Chapman (1986) multinomial logit modeling approach to handicapping horse races is extended to a new setting with much more sophisticated handicapping factors and a larger database. Applying a 20-variable pure fundamental multinomial logit handicapping model to 2,000 Hong Kong races yields clear evidence of positive returns to win betting with a simple single unit bets strategy in holdout sample predictions. By eliminating extreme longshots with estimated win probabilities less than 0.04, expected returns in excess of 20% are observed.

This paper examines the elements necessary for a practical and successful computerized horse race handicapping and wagering system. Data requirements, handicapping model development, wagering strategy, and feasibility are addressed. A logit-based technique and a corresponding heuristic measure of improvement are described for combining a fundamental handicapping model with the public's implied probability estimates. The author reports significant positive results in five years of actual implementation of such a system. This result can be interpreted as evidence of inefficiency in pari-mutuel racetrack wagering. This paper aims to emphasize those aspects of computer handicapping which the author has found most important in practical application of such a system.

This paper presents the results of a two year cross-validation of a fundamental handicapping system. Harness race performance data from a single season's entire racing meet were subjected to a discriminant analysis and classification criteria were developed. The Year 1 discriminant function and classification criteria were applied to Year 2 data. The classification techniques are evaluated in terms of percent correct classification and return on investment.

The problem discussed is one of assessing the probabilities of the various possible orders of finish of a horse race or, more generally, of assigning probabilities to the various possible outcomes of any multi, entry competition. An assumption is introduced that makes it possible to obtain the probability associated with any complete outcome in terms of only the ‘win’ probabilities. The results were applied to data from 335 thoroughbred horse races. where the win probabilities were taken to be those determined by the public through pari-mutuel betting.

Some properties of models for the outcomes of races are described, these properties being consequences of a stochastic ordering of the permutations which define the outcomes of a race. Order statistics models which lead to stochastic ordering are also discussed — particular cases of these are the first-order model of Plackett (1975) and the normal model of Upton and Brook (1974). An approximation for the normal model is suggested.

The following sections are included:

• Introduction

• The racetrack betting market

• The Harville Formulas

• Alternatives to the Harville formulas

• Comparing the models

• Conclusions

• References

To predict the the ordering probabilities such as the probability that horse i wins and j finishes second), the Harville (1973) model has been the most popular. The model assumes the running time distribution is independent exponential. However, a recent empirical study shows that the Henery (1981) model has a better fit. In this paper, we consider the Stern (1990) model in addition to the two models above. We fit the Stern model in a Japanese data set and conclude that the Stern model with a particular value of the shape parameter is superior to the others. Under the assumption of the Stern model, we show that the Harville model has a systematic bias in predicting the ordering probabilities.

Economists have long shown interest in racetrack betting as a source for investigating attitudes to risk and the efficiency of markets. Thaler and Ziemba (1988)¹, surveying research in both racing and lotteries, point that racetrack betting is an interesting application of efficient markets and rational expectations hypotheses since it possesses the usual characteristics of financial markets; namely, large numbers of investors/bettors with access to rich information sets. An advantage for testing financial theories that the racetrack has over most financial markets, though, is that there is a well-defined termination point at which final payoffs are determined…

The following sections are included:

• Introduction

• Racetrack Betting Markets
  • Betting Strategies
  • Cross Track Betting

• Lotto Games

• Commentary
  • Racetrack betting
  • Lotteries

• References

The following sections are included:

• Parimutuel Betting

• The Weak Form

• The Semi-strong Form

• The Strong Form

• Conclusion

• REFERENCES

In a 1978 article [10] in this journal, Wayne W. Snyder makes an analogy between security markets and pari-mutuel betting on horse races, suggesting that similarities between the two markets form a basis for the application of the theory of efficient markets to pari-mutuel betting. Snyder's analogy is apt, and his weak form test based on his own findings and similar findings by other researchers [4, 6, 7, 8, 11], is a reasonable test of the weak form efficient markets hypothesis. Furthermore, Snyder's discussion of a strong form test provides a useful basis for the formulation of a test of market efficiency; and with further refinement, it can be transformed into a more powerful test that also provides additional insight as to the influence of handicappers' quoted odds on publicly determined odds. This note further clarifies the applicability of the efficient markets model to pari-mutuel betting markets, and defines and implements a strong form test¹ of the efficiency of pari-mutuel betting markets which is a logical extension of Snyder's work…

Much of the information available to participants in speculative markets is in the nature of expert opinion, analysis, professional advice, and so on. Markets discount widely held factual information very well; this paper studies market efficiency with respect to subjective information. We examine the “market” for bets on thoroughbred horse races to determine whether the published forecasts of professional handicappers are completely discounted. A multinomial logit probability model is used to measure the information content of the forecasts, and we find that they do contain considerable information but that the track odds generated by betting discount almost all of it. Within the population of bettors, those betting at the track appear to discount the handicapper information fully, but those betting through New York's off-track betting system do not.

Horse racing data permit interesting tests of attitudes toward risk. The present paper studies a new sample of racetrack results from Atlantic City, New Jersey. The questions examined are: (1) Are the market odds the best data for predicting the order of finish? (2) Do horses go off at odds that reflect their true probability of winning? (3) Is there any evidence that late bettors have better information than early bettors? It is found that market odds predict the order of finish well, but that ‘favorites’ are good bets and ‘long shots’ are poor ones. The data suggest that there does exist an ‘informed’ class of bettors and that bettors are on the whole neither risk neutral nor risk averse.

Recent studies in racetrack market often deal with analyses of bet fractions, estimations of win probabilities and ordering probabilities. The logit model is a common way of statistical modelling of probabilities. This paper discusses and summarizes the possible applications of logit models in racetrack market analyses with win bet and exotic bets. In addition, we illustrate the application of logit model and how to apply the likelihood-based arguments to compare the accuracies of different sources of information using a real data set. The logit model may be more extensively used in racetrack market analyses.

The following sections are included:

• Introduction

• The Efficient Locus

• Conclusion

• References

The following sections are included:

• Introduction

• The Horseacing Market
  • Behavior of Bettors
  • Determination of Market Odds
  • Track Take and Optimal Bets

• Races with 2 Horses

• Races with J Horses
  • Risk Loving with Homogeneous Beliefs
  • Heterogeneous Beliefs with Risk Neutral Bettors
  • Risk Loving Bettors with Heterogeneous Beliefs

• Illustration with Log–Normal Distribution

• Estimation Technique

• Description of Data

• Results

• Conclusion

• References

The following sections are included:

• THE MODEL

• DERVIATION OF EQUILIBRIUM PRICES

• A MORE GENERAL ARGUMENT

• CONCLUDING REMARKS

• APPENDIX

• References

Most of the research on racetrack efficiency has focused on the win bet market, and the general conclusion has been that there exists a favorite-longshot bias but it is not sufficiently strong to allow positive profits (e.g. Snyder (1978)¹). Extreme favorites of odds 3-10 and shorter are an exception, allowing a small positive return, but they are so uncommon that for practical purposes the win market is weak form efficient, see Ziemba and Hausch (1986)². Inefficiencies in the place and show markets, however, have been reported as early as Griffith (1961)¹. There are several explanations: 1) their pools are smaller; 2) place and show wagers are more complicated than win bets since many different payoffs are possible depending on which horses are the first two or three finishers; and 3) extrapolating the win market's bias for favorites to higher probability place and show bets on favorites suggests a potential for inefficiencies…

The following sections are included:

• Introduction

• Data and Definitions
  • The Data set
  • Some Definitions

• Models and Results
  • Simulations Using Only Win Bets
  • Simulations Using Place Bets and Show Bets

• Conclusions

• References

We recently reported (Asch, Malkiel, and Quandt 1984) the results of simulated betting strategies based on logit analysis of racetrack betting data. Morning line odds, final odds, and marginal odds (defined as the odds implied by the moneys wagered during the last few minutes prior to each race) were used to predict the winning probability of each horse in a race; and a variety of strategies involving bets on the highest-probability horses was attempted. Our main conclusions were that we were unable to devise profitable strategies for win betting but that such strategies could be employed in place and show betting.

Many racetrack bettors have systems. Since the track is a market similar in many ways to the stock market one would expect that the basic strategies would be either fundamental or technical in nature. Fundamental strategies utilize past data available from racing forms, special sources, etc. to “handicap” races. The investor then wagers on one or more horses whose probability of winning exceeds that determined by the odds by an amount sufficient to overcome the track take. Technical systems require less information and only utilize current betting data. They attempt to find inefficiencies in the “market” and bet on such “overlays” when they have positive expected value. Previous studies and our data confirm that for win bets these inefficiencies, which exist for underbet favorites and overbet longshots, are not sufficiently great to result in positive profits. This paper describes a technical system for place and show betting for which it appears to be possible to make substantial positive profits and thus to demonstrate market inefficiency in a weak form sense. Estimated theoretical probabilities of all possible finishes are compared with the actual amounts bet to determine profitable betting situations. Since the amount bet influences the odds and theory suggests that to maximize long run growth a logarithmic utility function is appropriate the resulting model is a nonlinear program. Side calculations generally reduce the number of possible bets in any one race to three or less hence the actual optimization is quite simple. The system was tested on data from Santa Anita and Exhibition Park using exact and approximate solutions (that make the system operational at the track given the limited time available for placing bets) and found to produce substantial positive profits. A model is developed to demonstrate that the profits are not due to chance but rather to proper identification of market inefficiencies.

In a previous paper (Management Science, December 1981) Hausch, Ziemba and Rubinstein (HZR) developed a system that demonstrated the existence of a weak market inefficiency in racetrack place and show betting pools. The system appeared to make possible substantial positive profits. To make the system operational, given the limited time available for placing bets, an approximate regression scheme was developed for the Exhibition Park Racetrack in Vancouver for initial betting wealth between $2500 and $7500 and a track take of 17.1%. This paper: (1) extends this scheme to virtually any track and initial wealth level; (2) develops a modified system for multiple horse entries; (3) allows for multiple bets; (4) analyzes the effects of the track take and breakage on profits; (5) presents recent results using this system; and (6) considers the extent of the inefficiency, i.e., how much can be bet before the market becomes efficient?

The following sections are included:

• Introduction

• Efficiency of the Various Betting Markets

• Inefficiency of the Win Market and the Risk-free Hedging Model

• The Optimal Capital Growth Model

• Testing the One-Track Capital Growth Model

• Final Discussion

• References

The following sections are included:

• Our lock concentrates on the show market

• The show payoff on Arbor Hoggart is thought to be the highest show payoff of any sort

• Acknowledgments

• References

A model of racetrack betting behavior is set forward, and its implications tested, albeit with a small sample size. The model is consistent with risk-loving on the part of bettors. A simple betting rule [essentially a crude version of the Dr. Z system, describd by Ziemba and Hausch (1984)] is then tested, with evidence put forward that an unexploited profit opportunity may exist. When uncertainty is introduced, however, it is found that the profits vanish, a result consistent with the joint hypothesis of market efficiency and the model of betting behavior described in the paper.

Exotic bets are wagers involving two or more horses, and a variety of them are offered by tracks. Quinellas require one to predict the first two finishers in a race. Exactas (or perfectas) also require one to predict the first two horses in a race, but additionally one needs to predict their order of finish. The trifecta involves naming the first three finishers in the correct order. In a double (or daily double) bet, one must select the winner of two consecutive races. The double concept has been extended to predicting winners of three, four, six, and more consecutive race, providing the public extremely low probability but high payoff wagers. This section is concerned with the efficiency of these markets…

It is well known that the returns on various betting opportunities at a racetrack are determined by a competitive bidding of the bettors in a natural environment of their decision making. In this paper, two simple bets of unknown but identical winning probabilities are identified. An analysis of 1,089 observations shows the data are consistent with the hypothesis that both bets are identically priced, an implication of an efficient speculative market.

The efficiency and profitability of exotic racetrack bets such as exactas and daily doubles are examined. Efficiency is understood to mean that above average returns cannot be made in the long run once risk is appropriately controlled for. The markets in question are found not to be efficient; the inefficiencies, however, are insufficient to permit simple strategies to show a consistent profit. Some evidence of “smart money” exists in that holders of inside information may bet on exactas rather than equivalent standard bets in order to avoid signalling their actions to the betting public.

Previous studies in the analysis of double bets in racetrack markets compared the payoffs resulting from a double bet with a parlay contructed by the bettors. We compare the accuracy of implied winning probabilities between double bet and bets based on a single race and suggest that bettors bet on doubles less accurately. We also report the analysis based on payoff comparisons for a new data set.

Numerous authors have found that the win market at racetracks is essentially weak-form efficient. The relative amounts wagered at various odds levels provides a fairly accurate estimate of the true chances of winning. However, the accuracy of this estimate can be improved by adjusting for the favorite-longshot bias. This is the tendency for bettors to significantly overvalue low probability high payoff wagers on longshots and significantly undervalue high probability low payoff favorites. The resulting pricing equation coupled with a probability model for running time distributions generates accurate probabilities of all possible finishes. This allows us to price exotic wagers such as the exactor, triactor, quinella and daily double, and to identify when such bets have a positive expected return.

This paper proposes a system for double betting at a racetrack, The proposed method utilizes Harville's (1973) formulas to reduce the -dimensional space of empirical odds for double Bets to a (k−1)-dimensional space (k is the number of horses in a race). A novel feature of our betting system, compared with earlier work e.g. by Ziemba and Hausch, is that win market efficiency is not assumed since it is not supported by the Finnish data. The Kelly criterion is utilized for determining die amount of money to be wagered on each bet. The system is tested on data from 111 races at a Finnish racetrack and found to produce positive profits.

Biases that reflect the economic worth of uncertain contingent claims occur in many financial markets. Parimutuel betting at racetracks is one such market with ample data to investigate such biases. The total wagering market is about $10 billion per year in North America. The configuration of racetracks leads to an advantage for horses breaking from post positions near the rail, especially for tracks with small circumferences. Can the bettor make profits with knowledge of this bias? To investigate, we utilize data from 3,345 races involving over $300 million in wagers from 1982, 1983 and 1984 on win and exotic bets at Exhibition Park in Vancouver where this bias should be strong. The results indicate that the bias exists but the prices adjust to fully negate the potential gains from the bias.

This paper investigates the existence of a post position bias during the 1987 racing season at Exhibition Park. The econometric techniques of Probit and Pooled Cross-sectional Time Series analysis were used to analyze the relationship between the odds ranking, post position, and final position of a horse. The length of the race does not significantly improve the fit of any of the models. The results of this analysis indicate that the post position significantly adds to the information reflected in the odds rankings. The significance of the post position bias tends to increase as the number of horses taking part in the race increases.

The parimutuel betting system utilizing electric tote boards is the dominant method of betting at Noah American racetracks. Under the parimutuel system, the win bet fractions may be interpreted as consensus subjective win probabilities provided by the public. In England, and in other Commonwealth countries, such as Australia and New Zealand and other European countries, such as Italy and France, the dominant system is the fixed-odds system where it is bookies who establish and offer the odds…

Confident in the belief that vital resource allocation decisions depend on well functioning capital markets, economists over the last two decades have spent a good deal of their time, and not a little of the computer's, studying the behaviour of stock market prices. Their main aim has been to discover the extent to which capital markets, and in particular markets in equity shares, are “efficient”. Perhaps surprisingly to the layman, their answer has usually been “very efficient”, and despite the amount of effort devoted to attempts at refutation, Fama was able to conclude that “the evidence in support of the efficient market's model is extensive and (somewhat uniquely in economics) contradictory evidence is sparse” (Fama, 1970, p. 416)…

In an earlier paper (Crafts, 1985) I examined the relationship of the racecourse odds at the start of a horserace in Britain to the odds forecast in the morning racing press. The results showed that there is considerable potential for profitable insider trading in British horserace betting but that the adjustment of the odds to the starting prices is “weakly efficient” in the sense that bettors at starting price could not share in the exploitation of profitable opportunities. I also demonstrated the existence of “mug bets”, a class of particularly poor value bets where horses listed in the morning as fancied runners lengthen markedly in the betting during pre-race trading. In other words I argued that insiders are able to profit at the expense of outsiders, a situation which appears to be acceptable to or regarded as inevitable by the authorities…

The nature of the British racetrack betting market provides a distinctly different opportunity for testing market efficiency. On the basis of data from a single racing season, we compare the returns to two similar forms of betting: (1) starting price bets placed with bookmakers and (2) pari-mutuel tote bets. Our analysis indicates that tote returns are consistently higher than starting price returns, even though both betting forms are of similar risk and the payoffs are widely reported. The persistently higher tote returns suggest that the British racetrack betting market does not satisfy the conditions of semistrong efficiency. Our results also provide indirect support that the market fails to meet the conditions for strong efficiency.

Shortly after the publication of our paper in this Journal (Gabriel and Marsden 1990), we received a kind letter with several informational questions from Paddy Waldron, a graduate student at Wharton and long-time “punter” (bettor) in his native Ireland. One of Waldron's questions caused us to recheck the original source (The Sporting Chronicle Handicap Book, 1978) from which our data were gathered by research assistants. As his questions suggested to us, we discovered that a footnote had been overlooked and that the tote returns on Irish races included in the flat season (about 27 percent of all such races) are quoted as returns on a 20-pence bet (their minimum bet) rather than as returns on the 10-pence minimum used for reporting the other flat races. Thus we found that we had overstated the tote returns. We completely recollected all our data, making the necessary adjustments for Irish races and adding in eight races that had been reported out of sequence in the Handicap Book…

The betting strategy proposed in Hausch, Ziemba and Rubinstein (1981) and Ziemba and Hausch (1984, 1987) has had considerable some success in North American place and show pools. The place pool is England is very different. This paper applies a similar strategy with appropriate modifications for places bet at British racetracks. The system or minor modifications also applies in a number of other countries such as Singapore with similar betting rules. The system appears to provide positive expectation wagers. However, with the higher track take it is not known how often profitable wagers will exist or what the long run performance might be.

The following sections are included:

• Introduction

• Gambling in Australia

• Australian Evidence
  • Utility Preferences of Racetrack Bettors
  • Efficiency of Win Markets and the Favourite-Longshot Bias
    • The Movements in Bookmaker Odds
    • Tipsters Information
    • Insider Information
    • Two Markets, Bookmakers and the Totalisator
  • Prices vs. Handicapping: Place and Show Anomalies

• New Zealand Evidence

• Other Issues

• Endnotes

• References

Apparent irregularities between the win and the place betting markets in Australian horseracing are examined. Win odds are used to predict win probabilities from which place probabilities are estimated and compared with the place odds on offer. It is concluded that anomalies do in fact exist and are capable, in theory at least, of profitable exploitation.

The objective of this study is to evaluate the informational efficiency of the market for betting on horse races. Whereas the price data used in previous studies have been drawn largely from totalizator (parimutuel) odds, the data used in this study are derived from bookmaker odds. The availability of a series of prices throughout betting facilitates the use of filter tests to evaluate market efficiency. We conclude that this gambling market is efficient in the use of information supplied via both the movements in odds during the course of betting and the selections of newspaper tipsters. However, there is evidence to suggest that those with access to private information can earn positive returns from gambling.

The following sections are included:

• Introduction

• Risk Preference?

• The Data

• Revealed “Risk Attitudes” Assuming True Win Probabilities

• The Empirical Case For and Against Risk Preference: Inferred Win Probabilities
  • Grouping by Pari-mutuel Odds
  • Grouping by Favorite Position

• The Classification Problem

• A Final Note

• References

Researchers concerned with efficiency of racetrack betting seem agreed on the existence of market inefficiency or risk preference among gamblers. However, Busche and Hall (1988) found an anomaly: they analyzed 2,653 races run in Hong Kong from 1981 to 1986, and could not reject a hypothesis of equal average returns across groups of horses. I present evidence that the above result is not unique. I find virtually identical results when I examine a sample of 2,690 new Hong Kong races, pool all 5,343 Hong Kong races (Table 1), or examine 1,738 races run in Japan during 1990 (Table 2)…

This paper reports he results of an empirical study on cross-mck betting based on a sample of about 10,000 horses from 867 races in Singapore and Malaysia. Statistical test shows that the usual favorite-longshot bias exists at both the home and cross tracks. Arbitrage profit was possible in 13 races. The paper also shows that by employing a stylized version of the Kelly criterion as suggested by Hausch and Ziemba (1990a). Using simultaneous home and cross mck information on dividends, positive returns can be made. Implications of these results are discussed and directions for future research suggested.

The following sections are included:

• Annotated Additional Bibliography

• Annotated Bibliography of Handicapping Books

• Index