IDEAS home Printed from https://ideas.repec.org/a/inm/ordeca/v5y2008i1p10-18.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/deca.1080.0106
    Download Restriction: no
    File URL: https://libkey.io/10.1287/deca.1080.0106?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Leonard Maclean & William Ziemba & Yuming Li, 2005. "Time to wealth goals in capital accumulation," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 343-355.
    2. L. C. MacLean & W. T. Ziemba & G. Blazenko, 1992. "Growth Versus Security in Dynamic Investment Analysis," Management Science, INFORMS, vol. 38(11), pages 1562-1585, November.
    3. Justin Wolfers & Eric Zitzewitz, 2004. "Prediction Markets," Journal of Economic Perspectives, American Economic Association, vol. 18(2), pages 107-126, Spring.
    4. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    5. Ali, Mukhtar M, 1979. "Some Evidence of the Efficiency of a Speculative Market," Econometrica, Econometric Society, vol. 47(2), pages 387-392, March.
    6. repec:bla:econom:v:54:y:1987:i:215:p:289-98 is not listed on IDEAS
    7. MOSSIN, Jan, 1968. "Optimal multiperiod portfolio policies," LIDAM Reprints CORE 19, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Robin Insley & Lucia Mok & Tim Swartz, 2004. "Issues Related to Sports Gambling," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 46(2), pages 219-232, June.
    9. Steven D. Levitt, 2004. "Why are gambling markets organised so differently from financial markets?," Economic Journal, Royal Economic Society, vol. 114(495), pages 223-246, April.
    10. Thaler, Richard H & Ziemba, William T, 1988. "Parimutuel Betting Markets: Racetracks and Lotteries," Journal of Economic Perspectives, American Economic Association, vol. 2(2), pages 161-174, Spring.
    11. Tim Kuypers, 2000. "Information and efficiency: an empirical study of a fixed odds betting market," Applied Economics, Taylor & Francis Journals, vol. 32(11), pages 1353-1363.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. L. Robin Keller, 2008. "From the Editor..," Decision Analysis, INFORMS, vol. 5(1), pages 1-4, March.
    2. D. J. Johnstone, 2011. "Economic Interpretation of Probabilities Estimated by Maximum Likelihood or Score," Management Science, INFORMS, vol. 57(2), pages 308-314, February.
    3. L. Robin Keller, 2011. "Investment and Defense Strategies, Heuristics, and Games: From the Editor ..," Decision Analysis, INFORMS, vol. 8(1), pages 1-3, March.
    4. 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.
    5. 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.
    6. Joseph B. Kadane, 2011. "Partial-Kelly Strategies and Expected Utility: Small-Edge Asymptotics," Decision Analysis, INFORMS, vol. 8(1), pages 4-9, March.
    7. 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.
    8. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alexis Direr, 2013. "Are betting markets efficient? Evidence from European Football Championships," Applied Economics, Taylor & Francis Journals, vol. 45(3), pages 343-356, January.
    2. Nikolaos Vlastakis & George Dotsis & Raphael N. Markellos, 2009. "How efficient is the European football betting market? Evidence from arbitrage and trading strategies," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(5), pages 426-444.
    3. Raphael Flepp & Stephan Nüesch & Egon Franck, 2013. "Liquidity, Market Efficiency and the Influence of Noise Traders: Quasi-Experimental Evidence from the Betting Industry," Working Papers 341, University of Zurich, Department of Business Administration (IBW).
    4. Sathya Ramesh & Ragib Mostofa & Marco Bornstein & John Dobelman, 2019. "Beating the House: Identifying Inefficiencies in Sports Betting Markets," Papers 1910.08858, arXiv.org, revised Oct 2019.
    5. Kai Fischer & Justus Haucap, 2022. "Home advantage in professional soccer and betting market efficiency: The role of spectator crowds," Kyklos, Wiley Blackwell, vol. 75(2), pages 294-316, May.
    6. Erik Snowberg & Justin Wolfers, 2010. "Explaining the Favorite-Long Shot Bias: Is it Risk-Love or Misperceptions?," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 723-746, August.
    7. Angelini, Giovanni & De Angelis, Luca & Singleton, Carl, 2022. "Informational efficiency and behaviour within in-play prediction markets," International Journal of Forecasting, Elsevier, vol. 38(1), pages 282-299.
    8. David Forrest & Robert Simmons, 2008. "Sentiment in the betting market on Spanish football," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 119-126.
    9. Sagara Dewasurendra & Pedro Judice & Qiji Zhu, 2019. "The Optimum Leverage Level of the Banking Sector," Risks, MDPI, vol. 7(2), pages 1-30, May.
    10. Angelini, Giovanni & De Angelis, Luca, 2019. "Efficiency of online football betting markets," International Journal of Forecasting, Elsevier, vol. 35(2), pages 712-721.
    11. Grant, Andrew & Johnstone, David, 2010. "Finding profitable forecast combinations using probability scoring rules," International Journal of Forecasting, Elsevier, vol. 26(3), pages 498-510, July.
    12. Guy Elaad, 2020. "Home-field advantage and biased prediction markets in English soccer," Applied Economics Letters, Taylor & Francis Journals, vol. 27(14), pages 1170-1174, July.
    13. Nicos Zafiris, 2016. "Is There Such A Thing As A Safe Bet ?," Journal of Gambling Business and Economics, University of Buckingham Press, vol. 10(1), pages 40-65.
    14. Gross, Johannes & Rebeggiani, Luca, 2018. "Chance or Ability? The Efficiency of the Football Betting Market Revisited," MPRA Paper 87230, University Library of Munich, Germany.
    15. Montone, Maurizio, 2021. "Optimal pricing in the online betting market," Journal of Economic Behavior & Organization, Elsevier, vol. 186(C), pages 344-363.
    16. Ziemba, William, 2016. "A response to Professor Paul A. Samuelson's objections to Kelly capital growth investing," LSE Research Online Documents on Economics 119002, London School of Economics and Political Science, LSE Library.
    17. Oliver Merz & Raphael Flepp & Egon Franck, 2019. "Does sentiment harm market efficiency? An empirical analysis using a betting exchange setting," Working Papers 381, University of Zurich, Department of Business Administration (IBW).
    18. Egon Franck & Erwin Verbeek & Stephan Nüesch, 2013. "Inter-market Arbitrage in Betting," Economica, London School of Economics and Political Science, vol. 80(318), pages 300-325, April.
    19. Kai Fischer & Justus Haucap, 2020. "Betting Market Efficiency in the Presence of Unfamiliar Shocks: The Case of Ghost Games during the Covid-19 Pandemic," CESifo Working Paper Series 8526, CESifo.
    20. Merz, Oliver & Flepp, Raphael & Franck, Egon, 2021. "Sonic Thunder vs. Brian the Snail: Are people affected by uninformative racehorse names?," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 93(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ordeca:v:5:y:2008:i:1:p:10-18. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.