# Clash of the Tennis Titans

**Discrete Mathematics**Level pending

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.