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.
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