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Efficiency of the Market for Racetrack Betting


  • Donald B. Hausch

    (Northwestern University)

  • William T. Ziemba

    (University of British Columbia)

  • Mark Rubinstein

    (University of California, Berkeley)


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.

Suggested Citation

  • Donald B. Hausch & William T. Ziemba & Mark Rubinstein, 1981. "Efficiency of the Market for Racetrack Betting," Management Science, INFORMS, vol. 27(12), pages 1435-1452, December.
  • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:12:p:1435-1452
    DOI: 10.1287/mnsc.27.12.1435

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    Cited by:

    1. M. Sung & J. E. V. Johnson, 2010. "Revealing Weak‐Form Inefficiency in a Market for State Contingent Claims: The Importance of Market Ecology, Modelling Procedures and Investment Strategies," Economica, London School of Economics and Political Science, vol. 77(305), pages 128-147, January.
    2. Terrance Odean., 1996. "Volume, Volatility, Price and Profit When All Trader Are Above Average," Research Program in Finance Working Papers RPF-266, University of California at Berkeley.
    3. Fellner, Gerlinde & Maciejovsky, Boris, 2007. "Risk attitude and market behavior: Evidence from experimental asset markets," Journal of Economic Psychology, Elsevier, vol. 28(3), pages 338-350, June.
    4. Sathya Ramesh & Ragib Mostofa & Marco Bornstein & John Dobelman, 2019. "Beating the House: Identifying Inefficiencies in Sports Betting Markets," Papers 1910.08858,, revised Oct 2019.
    5. Bin Li & Steven C. H. Hoi, 2012. "Online Portfolio Selection: A Survey," Papers 1212.2129,, revised May 2013.
    6. Swidler, Steve & Shaw, Ron, 1995. "Racetrack wagering and the "uninformed" bettor: A study of market efficiency," The Quarterly Review of Economics and Finance, Elsevier, vol. 35(3), pages 305-314.
    7. Bjerksund, Petter & Stensland, Gunnar, 2017. "Profitable Robot Strategies in Pari-Mutuel Betting," Discussion Papers 2017/6, Norwegian School of Economics, Department of Business and Management Science.
    8. Jinook Jeong & Jee Young Kim & Yoon Jae Ro, 2019. "On the efficiency of racetrack betting market: a new test for the favourite-longshot bias," Applied Economics, Taylor & Francis Journals, vol. 51(54), pages 5817-5828, November.
    9. Brown, Lawrence D. & Lin, Yi, 2003. "Racetrack betting and consensus of subjective probabilities," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 175-187, April.
    10. Rablen, Matthew D., 2010. "Performance targets, effort and risk-taking," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 687-697, August.
    11. Steven D. Moffitt & William T. Ziemba, 2018. "A Method for Winning at Lotteries," Papers 1801.02958,
    12. Sung, Ming-Chien & McDonald, David C.J. & Johnson, Johnnie E.V. & Tai, Chung-Ching & Cheah, Eng-Tuck, 2019. "Improving prediction market forecasts by detecting and correcting possible over-reaction to price movements," European Journal of Operational Research, Elsevier, vol. 272(1), pages 389-405.
    13. Strumbelj, E. & Sikonja, M. Robnik, 2010. "Online bookmakers' odds as forecasts: The case of European soccer leagues," International Journal of Forecasting, Elsevier, vol. 26(3), pages 482-488, July.
    14. Mukhtar Ali, 1998. "Probability models on horse-race outcomes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 221-229.
    15. John Board & Charles Sutcliffe & William T. Ziemba, 2003. "Applying Operations Research Techniques to Financial Markets," Interfaces, INFORMS, vol. 33(2), pages 12-24, April.
    16. Hwang, Joon Ho & Kim, Min-Su, 2015. "Misunderstanding of the binomial distribution, market inefficiency, and learning behavior: Evidence from an exotic sports betting market," European Journal of Operational Research, Elsevier, vol. 243(1), pages 333-344.
    17. Bernardo, Giovanni & Ruberti, Massimo & Verona, Roberto, 2015. "Testing semi-strong efficiency in a fixed odds betting market: Evidence from principal European football leagues," MPRA Paper 66414, University Library of Munich, Germany.
    18. Erhan Bayraktar & Alexander Munk, 2016. "High-Roller Impact: A Large Generalized Game Model of Parimutuel Wagering," Papers 1605.03653,, revised Mar 2017.
    19. Bernardo, Giovanni & Ruberti, Massimo & Verona, Roberto, 2019. "Semi-strong inefficiency in the fixed odds betting market: Underestimating the positive impact of head coach replacement in the main European soccer leagues," The Quarterly Review of Economics and Finance, Elsevier, vol. 71(C), pages 239-246.
    20. Grant, Andrew & Johnstone, David & Kwon, Oh Kang, 2019. "The cost of capital in a prediction market," International Journal of Forecasting, Elsevier, vol. 35(1), pages 313-320.
    21. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2014. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 59292, London School of Economics and Political Science, LSE Library.
    22. Rosenbloom, E. S., 2003. "A better probability model for the racetrack using Beyer speed numbers," Omega, Elsevier, vol. 31(5), pages 339-348, October.
    23. Takahiro, Watanabe, 1997. "A parimutuel system with two horses and a continuum of bettors," Journal of Mathematical Economics, Elsevier, vol. 28(1), pages 85-100, August.
    24. MacLean, Leonard C. & Zhao, Yonggan & Ziemba, William T., 2016. "Optimal capital growth with convex shortfall penalties," LSE Research Online Documents on Economics 65486, London School of Economics and Political Science, LSE Library.

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