For the gambler’s ruin model of Section 4.5.1, let Mi denote the mean number of games that must be played until the gambler either goes broke or reaches a fortune of N, given that he starts with i, i = 0, 1, . . . , N. Show thatMi satisfies

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Mo= MN = 0; Mi=1+pMi+1+qMi-1, i = 1,..., N-1 Solve these equations to obtain M = i(N-i), if p = i N 1-(q/p)i = 9-P q-p1-(q/p) N if p