Suppose that a casino introduces a game in which a player bets $1 and can either win $2 or lose it, both with equal chances. The game ends when the player runs out of money, or when he wins $4. (a) Build a transition matrix for the game, and show that it is not a regular transition matrix. (b) Find the long term expected payoff to the player, and explain why the game is proprofitable (or not) for the Casino. My Attempt: a) P = 0.5 0.5 0.5 0.5 I don't feel this is right because there is a lot of extra information in the question that seems wasted. My attempt to incorporate game ending at $4. P = 0.5 0.5 0 0.5 0.5 1 I can't even get to part B as im struggling at the transition matrix, if someone could guide me to a similar example because my textbook lacks here.