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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


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.


Published: August, 1977
First available in Project Euclid: 19 April 2007

zbMATH: 0367.60051
MathSciNet: MR458577
Digital Object Identifier: 10.1214/aop/1176995764

Primary: 60G45
Secondary: 62L99

Keywords: decision theory , dynamic programming , gambling theory , martingale , Simple random walk , timid play , variation

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 4 • August, 1977
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