Red-and-Black with Unknown Win Probability
Donald A. Berry, David C. Heath, William D. Sudderth
The Annals of Statistics · 1974 · Volume 2 · Issue 3
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 $w$.
Keywords
60G35, 62C10, 93E99, dynamic programming, gambling theory, optimization, primitive casinos, red-and-black
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