Probability of a deuce in tennis?

In a game of tennis, if one player gets 4 points and the other has 2 or fewer, the game is over. However, if both players get 3 points, this is called a Deuce and the game continues until one player has 2 more points than the other.

Suppose two players are equally skilled (i.e. have an equal chance of winning each round), Find \(10000p\), where \(p\) is the probability of them reaching a deuce.

Details and Assumptions:

  • Both players start with 0 points.

  • The winner of each round gets 1 point added to their score when the round is over. There are no draws in tennis.


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