Question

B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the gambler has probability p of winning and q (1-p) of losing, show that the probability that the gambler attains a fortune of N starting from an initial sum of j is given by 1-(a/p) obtain a similar expression for φ, the probability that, starting from €, the gambler is ruined before reaching EN and show that dj+ ,-1 for all j 0,1, ,N. Explain the meaning of this result and what it says about the states of the associated Markov chain. Consider a game in which p - 1/3, N - 8 and the gambler starts with 2 and stakes 1 on each play (a) What is the probability that the gambler attains his fortune? (b) What is the probability that starting from his 2 the gambler wins having been nearly bankrupt (i.e. having only 1) once and once only?

Answer 1