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SummaryIn a version of gambler's ruin, players start with x and y dollars respectively, and flip coins for one dollar per flip until one player runs out of money. This is a random walk with two absorbing barriers. We consider the number of ways for the first player to lose on the nth flip, for n=x,n+2. We use probabilistic arguments to construct generating functions for these quantities along with explicit methods for computing them. This paper builds on the paper by Hirshon and De Simone, Mathematics Magazine 81 (2008) 146–152.
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