(Answered) Problem gamblers ruina gambler repeatedly plays a game

Statistics

Problem: GAMBLER'S RUIN

A gambler repeatedly plays a game where in each round, he wins a dollar with probability 1/3 and loses a dollar with probability 2/3. His strategy is "quit when he is ahead by $2", though some suspect he is a gambling addict anyway. Suppose that he starts with a million dollars. Show that the probability that he'll ever be ahead by $2 is less than 1/4.

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