Expectation of the Largest bet size in Labouchere System
Probability
2019-01-08 v3 Discrete Mathematics
Information Theory
Combinatorics
math.IT
Abstract
For Labouchere system with winning probability at each coup, we prove that the expectation of the largest bet size under any initial list is finite if , and is infinite if , 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.
Keywords
Cite
@article{arxiv.1807.11729,
title = {Expectation of the Largest bet size in Labouchere System},
author = {Yanjun Han and Guanyang Wang},
journal= {arXiv preprint arXiv:1807.11729},
year = {2019}
}