Question

Consider a game of tennis from deuce onward. Starting at the state of deuce, if the server wins, the score is ad-in. If the server then loses the next point, the game is back to deuce. However, if the server wins two points in a row, he wins the game. Similarly, starting at the state of deuce, if the returner wins, the score is ad-out. If the returner then loses the next point, the game is back to deuce. But if the returner wins two points in a row, he wins the game.

Let the probability of winning a point be 0.2. Moreover, the winner gets $10, and the loser pays $10.

1. Is this game recursive?
2. Draw and properly label the game tree. If there is a state that recurs, do not go beyond that state.
3. What is the probability of winning the game in the state of deuce?
4. What is the probability of winning the game for the server given that he wins the first point after deuce?
5. What is the value of the game at the state of deuce?

Answer 1

thank you

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Answer 2

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