Abstract
For the 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 [6]. 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.
Citation
Yanjun Han. Guanyang Wang. "Expectation of the largest bet size in the Labouchere system." Electron. Commun. Probab. 24 1 - 10, 2019. https://doi.org/10.1214/19-ECP220
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