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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The bold strategy in presence of house limit

Author: J. Ernest Wilkins
Journal: Proc. Amer. Math. Soc. 32 (1972), 567-570
MSC: Primary 60J15; Secondary 90D05
MathSciNet review: 0292182
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Abstract: It is known that an optimal strategy for a gambler, who wishes to maximize the probability of winning an amount $ a - x$ in a subfair red-and-black casino if his initial capital is x, is the bold strategy in which the gambler wagers at each opportunity the minimum of his entire current capital $ x'$ and the amount $ a - x'$ required to reach the goal a if he wins the bet. If the casino imposes an upper limit L on wagers, we shall prove that the modified bold strategy of wagering $ \min (x',a - x',L)$ is optimal, at least in the important special case in which the goal a is an integral multiple of the house limit L.

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Keywords: Gambler's ruin, bold strategy, red-and-black casino
Article copyright: © Copyright 1972 American Mathematical Society