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Explicit Optimal Strategy for the Vardi Casino with Limited Playing Time

Part of: Game theory Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Yi-Ching Yao
Yi-Ching Yao*
Affiliation:
Academia Sinica and National Chengchi University
*
∗ Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan, ROC. Email address: yao@stat.sinica.edu.tw
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Abstract

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The Vardi casino with parameter 0 < c < 1 consists of infinitely many tables indexed by their odds, each of which returns the same (negative) expected winnings -c per dollar. A gambler seeks to maximize the probability of reaching a fixed fortune by gambling repeatedly with suitably chosen stakes and tables (odds). The optimal strategy is derived explicitly subject to the constraint that the gambler is allowed to play only a given finite number of times. Some properties of the optimal strategy are also discussed.

Keywords

Gambling theorybold playprimitive casinofinite horizon

MSC classification

Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory 91A60: Probabilistic games; gambling

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 831 - 837
Copyright
Copyright © Applied Probability Trust 2007 

References

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