The Kelly Betting System for Favorable Games
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چکیده
It is an easy problem to find, by backward induction, the betting system that maximizes E(X20|X0), your expected fortune after the 20 days have passed. It is to bet all you have each day. On the last day, given you have fortune X19, to maximize E(X20|X19) you bet it all, b20 = X19, and your expected final fortune is (2/3)2X19 + (1/3)0 = (4/3)X19. Since E(X20|X18) = E(E(X20|X19)|X18) = (4/3)E(X19|X18) = (4/3)X18, the analysis by backward induction shows that E(X20|X0) = (4/3)X0 = 315.34X0. However, there is something disturbing about this solution. The distribution of X20 using the strategy of betting everything each time is
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تاریخ انتشار 2010