文章基本信息

标题：Expectation of the largest bet size in the Labouchere system
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作者：Yanjun Han ; Guanyang Wang
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2019
卷号：24
DOI：10.1214/19-ECP220
语种：English
出版社：Electronic Communications in Probability
摘要：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.