A game in a casino uses the diagram shown. At the start a ball appears at S. 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 S, the player loses.
(ii) The ball reaches G, the player wins.
Find the probability that the player wins and the expected duration of a game. probabilitycombinatoricsgame