报告题目：Expectation of the Largest Betting Size in Labouchère System

报告人：王冠扬 Stanford University

时间：8月13日周一10:00-11:00 

地点：五教5106

摘要： 

The Labouch\`ere system is one of the most well-known betting systems used in roulette. For a betting game with winning probability $p$,standard martingale argument shows the total betting size has infinite probability when $p\leq \frac {1}{2}$. In this talk, we will prove the expectation of maximum betting size is finite when $p>\frac{1}{2}$, and is infinite when $p \leq \frac{1{2}$, solving the open problem asked by Grimmett and Stirzaker. This is joint work with Yanjun Han. (No background more than undergraduate probability is required and everyone is welcome.)