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2019 Expectation of the largest bet size in the Labouchere system
Yanjun Han, Guanyang Wang
Electron. Commun. Probab. 24: 1-10 (2019). DOI: 10.1214/19-ECP220

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

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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

Information

Received: 7 January 2019; Accepted: 18 February 2019; Published: 2019
First available in Project Euclid: 22 February 2019

zbMATH: 1412.60062
MathSciNet: MR3916343
Digital Object Identifier: 10.1214/19-ECP220

Subjects:
Primary: 60C05 , 60G40

Keywords: combinatorics , gambling theory , Labouchere system , martingale

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