Paper 1, Section II, H
A coin-tossing game is played by two players, and . Each player has a coin and the probability that the coin tossed by player comes up heads is , where . The players toss their coins according to the following scheme: tosses first and then after each head, pays one pound and has the next toss, while after each tail, pays one pound and has the next toss.
Define a Markov chain to describe the state of the game. Find the probability that the game ever returns to a state where neither player has lost money.
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