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arXiv · 1807.11729

Expectation of the Largest bet size in Labouchere System

Yanjun Han·Guanyang Wang
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Abstract

For Labouchere system with winning probability $p$ at each coup, we prove that the expectation of the largest bet size under any initial list is finite if $p>\frac{1}{2}$, and is infinite if $p\le \frac{1}{2}$, solving the open conjecture in Grimmett and Stirzaker (2001). The same result holds for a general family of betting systems, and the proof builds upon a recursive representation of the optimal betting system in the larger family.

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Yanjun Han, Guanyang Wang. 2018-07-31. Expectation of the Largest bet size in Labouchere System. https://arxiv.org/abs/1807.11729

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