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May, 1974 Red-and-Black with Unknown Win Probability
Donald A. Berry, David C. Heath, William D. Sudderth
Ann. Statist. 2(3): 602-608 (May, 1974). DOI: 10.1214/aos/1176342724

Abstract

A gambler seeks to maximize his probability of reaching a goal in a game where he is allowed at each stage to stake any amount of his current fortune. He wins each bet with a certain fixed probability $w$. Lester E. Dubins and Leonard J. Savage found optimal strategies for a gambler who knows $w$. Here strategies are found which are uniformly nearly optimal for all $w$ and, therefore, also for a gambler with an unknown $w$.

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Donald A. Berry. David C. Heath. William D. Sudderth. "Red-and-Black with Unknown Win Probability." Ann. Statist. 2 (3) 602 - 608, May, 1974. https://doi.org/10.1214/aos/1176342724

Information

Published: May, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0285.90085
MathSciNet: MR423507
Digital Object Identifier: 10.1214/aos/1176342724

Subjects:
Primary: 60G35
Secondary: 62C10 , 93E99

Keywords: dynamic programming , gambling theory , optimization , primitive casinos , red-and-black

Rights: Copyright © 1974 Institute of Mathematical Statistics

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Vol.2 • No. 3 • May, 1974
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