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In each game a gambler wins the dollars he bets with probability p and looses with probability 1 p. If he has less than $3,
In each game a gambler wins the dollars he bets with probability p and looses with probability 1 p. If he has less than $3, he will bet all that he has. Otherwise, since his goal is to have $5, he will only bet the difference between $5 and what he has. He continues to bet until wither he has either $0 or $5. Let Xn denote the amount he has right after the n-th bet. Draw the transition graph.
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