Subfair red-and-black with a limit
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- by David C. Heath, William E. Pruitt and William D. Sudderth PDF
- Proc. Amer. Math. Soc. 35 (1972), 555-560 Request permission
Abstract:
Suppose a gambler has an initial fortune in (0,1) and wishes to reach 1. It is known that, for a subfair red-and-black casino, the optimal strategy is always to bet $\min (f,1 - f)$ whenever the gambler’s current fortune is f. Furthermore, the gambler should likewise play boldly if there is a house limit z which is the reciprocal of a positive integer; i.e., he should bet $\min (f,1 - f,z)$. We show that if $1/(n + 1) < z < 1/n$ for some integer $n \geqq 3$ or if z is irrational and $\frac {1}{3} < z < \frac {1}{2}$, then bold play is not necessarily optimal.References
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J. L. Coolidge, The gambler’s ruin, Ann. of Math. 10 (1908/09), 181-192.
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- 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
- J. Ernest Wilkins Jr., The bold strategy in presence of house limit, Proc. Amer. Math. Soc. 32 (1972), 567–570. MR 292182, DOI 10.1090/S0002-9939-1972-0292182-2
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 35 (1972), 555-560
- MSC: Primary 90D99
- DOI: https://doi.org/10.1090/S0002-9939-1972-0309574-5
- MathSciNet review: 0309574