Clash of the Tennis Titans

Discrete Mathematics Level pending

Roger Federer and Rafael Nadal are playing a tennis match.

It is Roger's serve.

Because he is serving (and the server have an edge over the reciever), Roger's odds of winning a point are \(2:1\) in his favour.

Find the probability that Roger wins his service game. Round your answer off to 3 decimal places.

\(\textbf{Details about Tennis Scoring}\)

  • For those who are not acquainted with tennis, the scoring is explained on this page. Briefly, the game scoring (the scoring that concerns us in this problem) is as follows

  • \(0\) is also called "love" in tennis.

  • Examples of scores - \(0-0, \ 0-30, \ 40-15\) etc.

  • \(40-40\) is called Deuce.

  • Once at deuce, a player must win \(\textbf{2 consecutive}\) points to take the game.

  • If Player \(A\) \(\textbf{wins the deuce point}\), then the score is \(\textbf{Advantage Player A}\).

  • If, after gaining advantage, the player \(\textbf{looses the next point}\), then the score comes \(\textbf{back to deuce}\).

  • In all the points that concern us, Roger serves as they are all part of the same Federer service game.

  • This is a completely hypothetical scenario.


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