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Fortune's Formula or the Road to Ruin? The Generalized Kelly Criterion With Multiple Outcomes

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  • Whelan, Karl

Abstract

You can bet on an event where there are multiple possible winners but only one will actually win. At the odds offered, you think there may be multiple bets worth taking. How much do you place on each bet to maximize your expected utility? We describe how this problem can be solved for concave utility functions and illustrate the properties of the solution. The optimal betting strategy is more aggressive than strategies derived from considering each outcome separately such as the Kelly criterion. The strategy also recommends sometimes placing bets with negative expected returns because they act as hedges against losses on other bets. While this strategy maximizes the bettor's subjective expected utility, if betting odds incorporate a profit margin and reflect underlying probabilities correctly, then this more aggressive approach loses more money and results in lower realized utility.

Suggested Citation

  • Whelan, Karl, 2023. "Fortune's Formula or the Road to Ruin? The Generalized Kelly Criterion With Multiple Outcomes," CEPR Discussion Papers 18060, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:18060
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    References listed on IDEAS

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    1. Chris Whitrow, 2007. "Algorithms for optimal allocation of bets on many simultaneous events," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(5), pages 607-623, November.
    2. Whelan, Karl & Hegarty, Tadgh, 2023. "Forecasting Soccer Matches With Betting Odds: A Tale of Two Markets," MPRA Paper 116925, University Library of Munich, Germany.
    3. 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.
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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