At time 0, John has $2. At times 1, 2, . . ., he independently plays a game in which he bets $1. With probability p = 0.49, he wins the game and with probability 1 − p = 0.51, he loses the game. His goal is to increase his capital to $3, and as soon as he does, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbing Markov chain and answer the following questions. • What is the expected duration of the game? •

What is the probability that he goes broke?