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Optimal Betting Strategies for Simultaneous Games

Author

Listed:
  • Andrew Grant

    (Discipline of Finance H69, The University of Sydney, Sydney NSW 2006, Australia)

  • David Johnstone

    (Discipline of Finance H69, The University of Sydney, Sydney NSW 2006, Australia)

  • Oh Kang Kwon

    (Discipline of Finance H69, The University of Sydney, Sydney NSW 2006, Australia)

Abstract

In this paper we consider the problem of optimal betting on simultaneous games when the bookmaker accepts bets on the joint outcome of subsets of any combination of those events, called parlays, accumulators, or multibets. When the bookmaker's take is a fixed proportion of the wager, multibetting on all n games replicates any other betting strategy and dominates separate (simultaneous) bets on individual games. When, more typically, the bookmaker quotes multiplicative payouts, and hence takes a higher percentage on multibets than bets on single games, the optimal betting strategy depends on the bettor's utility function. We consider the special case of a Kelly (log utility) bettor, and the more general case of a (lambda)-Kelly bettor who wagers a fixed fraction (lambda) (le) 1 of the full-Kelly bet. Our main result is that when the bookmaker offers multiplicative payouts, a Kelly or (lambda)-Kelly bettor realizes the same monetary outcome by multibetting as would have been achieved by sequential betting on single games (were sequential bets possible). It follows, therefore, that even when games are sequential, a Kelly or (lambda)-Kelly bettor should only bet sequentially when there is an expectation of the bookmaker's odds becoming more favorable nearer to game time.

Suggested Citation

  • Andrew Grant & David Johnstone & Oh Kang Kwon, 2008. "Optimal Betting Strategies for Simultaneous Games," Decision Analysis, INFORMS, vol. 5(1), pages 10-18, March.
    • Handle: RePEc:inm:ordeca:v:5:y:2008:i:1:p:10-18
    DOI: 10.1287/deca.1080.0106
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    References listed on IDEAS

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    Cited by:

    1. D. J. Johnstone, 2011. "Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score," Management Science, INFORMS, vol. 57(2), pages 308-314, February.
    2. L. Robin Keller, 2008. "From the Editor..," Decision Analysis, INFORMS, vol. 5(1), pages 1-4, March.
    3. Xiaogang Ma & Chunyu Bao & Jizi Li & Wandong Lou, 2022. "The impact of dual fairness concerns on bargaining game and its dynamic system stability," Annals of Operations Research, Springer, vol. 318(1), pages 357-382, November.
    4. Rakesh K. Sarin, 2013. "From the Editor —Optimal Betting, Reducing Unnecessary Mammography in Breast Cancer Diagnosis, Product Line Design, and Value of Information," Decision Analysis, INFORMS, vol. 10(3), pages 187-188, September.
    5. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Philippe Delquié & Kenneth C. Lichtendahl & Jason R. W. Merrick & Ahti Salo & George Wu, 2011. "From the Editors ---Probability Scoring Rules, Ambiguity, Multiattribute Terrorist Utility, and Sensitivity Analysis," Decision Analysis, INFORMS, vol. 8(4), pages 251-255, December.
    6. L. Robin Keller, 2011. "Investment and Defense Strategies, Heuristics, and Games: From the Editor ..," Decision Analysis, INFORMS, vol. 8(1), pages 1-3, March.
    7. Andrew Grant & David Johnstone & Oh Kang Kwon, 2019. "A Probability Scoring Rule for Simultaneous Events," Decision Analysis, INFORMS, vol. 16(4), pages 301-313, December.
    8. Joseph B. Kadane, 2011. "Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics," Decision Analysis, INFORMS, vol. 8(1), pages 4-9, March.

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