Expectation of the largest bet size in the labouchere system

Yanjun Han; Guanyang Wang

doi:10.1214/19-ECP220

Expectation of the largest bet size in the labouchere system

Yanjun Han, Guanyang Wang

Mathematics

Research output: Contribution to journal › Article › peer-review

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 >¹ ₂, and is infinite if p ≤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.

Original language	English (US)
Article number	11
Journal	Electronic Communications in Probability
Volume	24
DOIs	https://doi.org/10.1214/19-ECP220
State	Published - 2019

Keywords

Combinatorics
Gambling theory
Labouchere system
Martingale

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

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10.1214/19-ECP220

Cite this

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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 >1 2, and is infinite if p ≤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.",

keywords = "Combinatorics, Gambling theory, Labouchere system, Martingale",

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AB - 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 >1 2, and is infinite if p ≤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.

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KW - Martingale

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Expectation of the largest bet size in the labouchere system

Abstract

Keywords

ASJC Scopus subject areas

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