Absorbing markov chain with states

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A gambler plays a game in which on each play he wins one dollar with probability p and loses one dollar with probability q = 1 - p. The Gambler's Ruin problem is the problem of finding the probability wx of winning an amount T before losing everything, starting with state x. Show that this problem may be considered to be an absorbing Markov chain with states 0, 1, 2, . . . , T with 0 and T absorbing states. Suppose that a gambler has probability p = .48 of winning on each play. Suppose, in addition, that the gambler starts with 50 dollars and that T = 100 dollars. Simulate this game 100 times and see how often the gambler is ruined. This estimates w50.

Reference no: EM13983569

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