The bold strategy in presence of house limit
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- by J. Ernest Wilkins PDF
- Proc. Amer. Math. Soc. 32 (1972), 567-570 Request permission
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.References
- Lester E. Dubins and Leonard J. Savage, How to gamble if you must. Inequalities for stochastic processes, McGraw-Hill Book Co., New York-Toronto-London-Sydney, 1965. MR 0236983 Georges de Rham, Sur certaines équations fonctionnelles, Ecole Polytechnique de L’Université de Lausanne, Centenaire 1853-1953, Ecole Polytechnique, Lausanne, 1953, pp. 95-97. MR 19, 842.
- R. Salem, On some singular monotonic functions which are strictly increasing, Trans. Amer. Math. Soc. 53 (1943), 427–439. MR 7929, DOI 10.1090/S0002-9947-1943-0007929-6
- William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley & Sons, Inc., New York; Chapman & Hall, Ltd., London, 1957. 2nd ed. MR 0088081
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 32 (1972), 567-570
- MSC: Primary 60J15; Secondary 90D05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292182-2
- MathSciNet review: 0292182