MathDB

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.

Problem Statement