Question 40
A casino gaming machine has a screen that displays a layout like the one in the figure. When the game starts, a ball appears at point $S$.
With each impulse of the player, the ball moves to one of the immediate circles, with the same probability for each of them. The game ends when the first of the following two events occurs: The ball returns to $S$, and the player loses. (2) The ball reaches $G$, and then the player wins. The probability of the player winning, and the average duration of the games, is requested.
With each impulse of the player, the ball moves to one of the immediate circles, with the same probability for each of them. The game ends when the first of the following two events occurs: The ball returns to $S$, and the player loses. (2) The ball reaches $G$, and then the player wins. The probability of the player winning, and the average duration of the games, is requested.