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The proportional bettor's return on investment

Published online by Cambridge University Press:  14 July 2016

S. N. Ethier  and
S. Tavaré
S. N. Ethier*
Affiliation:
Michigan State University
S. Tavaré*
Affiliation:
Colorado State University
*
∗ Postal address: Department of Statistics and Probability, Michigan State University, East Lansing, MI 48824, U.S.A.
∗∗ Postal address: Department of Statistics, Colorado State University, Fort Collins, CO 80523, U.S.A.
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Abstract

Suppose you repeatedly play a game of chance in which you have the advantage. Your return on investment is your net gain divided by the total amount that you have bet. It is shown that the ratio of your return on investment under optimal proportional betting to your return on investment under constant betting converges to an exponential distribution with mean as your advantage tends to 0. The case of non-optimal proportional betting is also treated.

Keywords

CONVERGENCE IN DISTRIBUTIONGAMMA DISTRIBUTIONBETTING SYSTEMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 563 - 573
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

Supported in part by NSF Grant MCS-8102063.

References

Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.Google Scholar
Breiman, L. (1961) Optimal gambling systems for favorable games. Proc. 4th Berkeley Symp. Math. Statist. Prob. 1, 65–78.Google Scholar
Finkelstein, M. and Whitley, R. (1981) Optimal strategies for repeated games. Adv. Appl. Prob. 13, 415–428.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series, and Products. Academic Press, New York.Google Scholar
Griffin, P. A. (1981) The Theory of Blackjack, 2nd edn. GBC Press, Las Vegas.Google Scholar
Hoeffding, W. (1963) Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30.Google Scholar
Kelly, J. L. Jr. (1956) A new interpretation of information rate. 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