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An optimal betting strategy for repeated games

  • Gary Gottlieb (a1)

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.

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Corresponding author

Postal address: Department of Quantitative Analysis, College of Business and Public Administration, New York University, Washington Square, New York, NY 10003, USA.

References

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Breiman, L. (1961) Optimal gambling systems for favorable games. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 6578.
Ethier, S. and Tavare, S. (1983) The proportional bettor's return on investment. J. Appl. Prob. 20, 563573.
Ferguson, T. (1965) Betting systems which minimize the probability of ruin. J. SIAM 13, 795818.
Finklestein, M. and Whitley, R. (1981) Optimal strategies for repeated games. Adv. Appl. Prob. 13, 415428.
Friedman, J. (1981) Understanding and applying the Kelly Criteria. Fifth Conference on Gambling and Risk Taking, University of Nevada.
Gottlieb, G. (1985) An analytic derivation of win rates at blackjack. Operat. Res.
Karlin, S. and Taylor, H. M. (1981) A Second Course in Stochastic Processes. Academic Press, New York.
Kelly, J. Jr. (1956) A new interpretation of information rate. IRE Trans. Inf. Theory. IT-2 (3); Bell System Tech. J. 35, 917926.
Wong, S. (1981) What proportional betting does to your win rate. Blackjack World 3, 162168.

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An optimal betting strategy for repeated games

  • Gary Gottlieb (a1)

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