Timid Play when Large Bets are Profitable

David Gilat; William Sudderth

doi:10.1214/aop/1176995764

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Home > Journals > Ann. Probab. > Volume 5 > Issue 4 > Article

August, 1977 Timid Play when Large Bets are Profitable

David Gilat, William Sudderth

Ann. Probab. 5(4): 573-576 (August, 1977). DOI: 10.1214/aop/1176995764

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Abstract

The total variation of a simple, symmetric random walk with absorbing barrier at zero, is stochastically larger than the total variation of any other nonnegative, integer-valued supermartingale with the same initial position. This strengthens a result of David Freedman on the optimality of timid play for maximizing the time to bankruptcy in certain gambling situations.

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David Gilat. William Sudderth. "Timid Play when Large Bets are Profitable." Ann. Probab. 5 (4) 573 - 576, August, 1977. https://doi.org/10.1214/aop/1176995764