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Optimal betting strategies for favorable games

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  • Eduardo J. Subelman

Abstract

We examine the problem of a gambler interested in maximizing the expected value of a convex utility function of his fortune after n plays of a game. We allow any probability distribution to rule the outcome of each play, and this distribution may change from play to play according to a Markov process. We present results regarding the existence of an optimal policy and its structural dependence on the gambler's fortune. The well‐known results of Bellman and Kalaba for exponential and logarithmic utility functions and coin‐tossing games are generalized. We also examine the situation of general stale spaces and show that the same structural results hold.

Suggested Citation

  • Eduardo J. Subelman, 1979. "Optimal betting strategies for favorable games," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(2), pages 355-363, June.
    • Handle: RePEc:wly:navlog:v:26:y:1979:i:2:p:355-363
    DOI: 10.1002/nav.3800260215
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