Question: Two gamblers play a game in which in each play gambler A beats B with probability p, 0 < p < 1, and loses to

Two gamblers play a game in which in each play gambler A beats B with probability p, 0 < p < 1, and loses to B with probability q = 1−p. Suppose that each play results in a forfeiture of $1 for the loser and in no change for the winner. If player A initially has a dollars and player B has b dollars, what is the probability that B will be ruined?

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