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An optimal betting strategy for repeated games

Published online by Cambridge University Press:  14 July 2016

Gary Gottlieb
Gary Gottlieb*
Affiliation:
New York University
*
∗ Postal address: Department of Quantitative Analysis, College of Business and Public Administration, New York University, Washington Square, New York, NY 10003, USA.
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Abstract

We consider the problem of finding a betting strategy for an infinite sequence of wagers where the optimality criterion is the minimization of the expected exit time of wealth from an interval. We add the side constraint that the right boundary is hit first with at least some specified probability. The optimal strategy is derived for a diffusion approximation.

Keywords

GAMBLING SYSTEMSKELLY CRITERIAOPTIMALITY CRITERIADIFFUSION APPROXIMATIONREPEATED GAMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 787 - 795
Copyright
Copyright © Applied Probability Trust 1985 

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References

Breiman, L. (1961) Optimal gambling systems for favorable games. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 65–78.Google Scholar
Ethier, S. and Tavare, S. (1983) The proportional bettor's return on investment. J. Appl. Prob. 20, 563–573.Google Scholar
Ferguson, T. (1965) Betting systems which minimize the probability of ruin. J. SIAM 13, 795–818.Google Scholar
Finklestein, M. and Whitley, R. (1981) Optimal strategies for repeated games. Adv. Appl. Prob. 13, 415–428.Google Scholar
Friedman, J. (1981) Understanding and applying the Kelly Criteria. Fifth Conference on Gambling and Risk Taking, University of Nevada.Google Scholar
Gottlieb, G. (1985) An analytic derivation of win rates at blackjack. Operat. Res. Google Scholar
Karlin, S. and Taylor, H. M. (1981) A Second Course in Stochastic Processes. Academic Press, New York.Google Scholar
Kelly, J. Jr. (1956) A new interpretation of information rate. IRE Trans. Inf. Theory. IT-2 (3); Bell System Tech. J. 35, 917–926.Google Scholar
Wong, S. (1981) What proportional betting does to your win rate. Blackjack World 3, 162–168.Google Scholar