OME 1993 Problem 6
A game in a casino uses the diagram shown. At the start a ball appears at . Each time the player presses a button, the ball moves to one of the adjacent letters with equal probability. The game ends when one of the following two things happens: (i) The ball returns to , the player loses. (ii) The ball reaches , the player wins. Find the probability that the player wins and the expected duration of a game.
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