The proportional bettor's return on investment
- 1 March 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (03) , 563-573
- https://doi.org/10.1017/s0021900200023822
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
This publication has 3 references indexed in Scilit:
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- Probability Inequalities for Sums of Bounded Random VariablesJournal of the American Statistical Association, 1963
- A New Interpretation of Information RateBell System Technical Journal, 1956