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Favorable red and black on the integers with a minimum bet

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Kevin Ruth
Kevin Ruth*
Affiliation:
University of Miami
*
∗Postal address: Dept. of Math & Computer Science, College of Arts & Sciences, Coral Gables, FL 33124–4250, USA. Email address: kruth@cs.miami.edu
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Abstract

In a superfair red and black gambling house where the player must bet at least 2 units at each stage, a gambler wishes to maximize the probability of reaching a goal integer N before reaching zero. For win probability p > 1/2, when N is even, an optimal strategy is to bet 3 units when you have 3 units or N − 3 units and to bet 2 units otherwise. When N is odd, there are two strategies which are optimal depending on the value of the win probability p. When p is smaller than a certain value, p*, the above strategy is optimal, and when p is larger than this value, the timid strategy is optimal.

Keywords

Superfair red and black gambling housetimid strategyexcessivenessgambler's ruin

MSC classification

Secondary: 90C40: Markov and semi-Markov decision processes 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 3 , September 1999 , pp. 837 - 851
Copyright
Copyright © Applied Probability Trust 1999 

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References

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