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Consider a gambler who, at each play of the game, either wins $1 with probability 1/2, draws with probability 1/6, loses $1 with probability

Consider a gambler who, at each play of the game, either wins $1 with probability 1/2, draws with probability 1/6, loses $1 with probability 1/3. If we suppose that our gambler quits playing either when he goes broke or he attains a fortune of $3, then the gambler's fortune is a Markov chain. Suppose that his current fortune is 1 Find the probability that his fortune reaches 3 before 0. Given that his fortune will reach 3 before 0, find the probability that he wins next bet. Find the expected duration of the game using conditional expectation.

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