Optimal Proportional Play

  • Stewart N. Ethier
Part of the Probability and its Applications book series (PIA)


This chapter is concerned with a betting system for superfair games, known as optimal proportional play or the Kelly system, that maximizes the long-term geometric rate of growth of the gambler’s fortune. Section 10.1 considers the case in which a single superfair betting opportunity is available at each coup. Section 10.2 assumes that multiple betting opportunities, at least one of which is superfair, are available at each coup. Finally, Section 10.3 establishes several optimality properties of the Kelly system.


Prediction Interval Optimality Property Common Distribution Strict Concavity True Odds 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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