Analyze a Tennis Game

In a game of tennis between two players, suppose the probability of the server winning a point is . Visualize the random walk graph for , with 17 states.

    
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Find the probability of the server winning the game for :
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Find the mean time to absorption, that is, the number of points played:
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Find the mean number of states visited:
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Find the average number of times the score will be tied at deuce:
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