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The dependence of betting strategies on the probability of winning

Published online by Cambridge University Press:  14 July 2016

Eduardo J. Subelman
Eduardo J. Subelman*
Affiliation:
University of California, Los Angeles
*
∗Postal address: Department of System Science, School of Engineering and Applied Science, University of California, Los Angeles, CA 90024, U.S.A.
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Abstract

We consider the optimal wagers to be made by a gambler facing cointossing games who desires to maximize the expected value of the utility of his final fortune in a fixed number n of plays. In the case of fixed probability of a win, the optimal bet is shown to be increasing in the probability. In the case of unknown probability of a win, the wager is shown to be monotone in the prior distribution under the monotone likelihood ratio ordering of these distributions.

Keywords

GAMBLING THEORYBETTING STRATEGIESMONOTONE POLICIESADAPTIVE BETTINGBAYESIAN DECISIONS
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 855 - 866
Copyright
Copyright © Applied Probability Trust 1979 

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Footnotes

Partially supported by the U.S. Army Research Office under Grant DAAG29–77–0040 with the University of California.

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