How to use the tennis probability calculator
- Set the percentage of points player A wins on their own serve.
- Set the percentage of points player B wins on their own serve.
- Choose best of 3 or best of 5.
The calculator shows the chance that A holds serve, wins the set, wins the match, and the fair odds for A, with B's numbers in the line underneath.
How it works
- Game. If a player wins a point on serve with chance p (and q = 1 − p), they win the game with chance p⁴ (1 + 4q + 10q²) + 20 p³q³ × p² ÷ (p² + q²). The last term covers deuce.
- Set. The set is a race to six games, won by two, with a tie-break at 6-6. Serve alternates every game. In the tie-break the first server serves one point, then each player serves two.
- Match. If a player wins each set with chance s, a best-of-3 is won with s² (3 − 2s) and a best-of-5 with s³ (10 − 15s + 6s²).
The calculator averages over who serves first, so the result does not depend on the toss.
Example
Player A wins 66% of points on serve and player B wins 64%, in a best-of-3.
| Player A | Player B | |
|---|---|---|
| Holds serve | 84.6% | 81.3% |
| Wins the set | 56.5% | 43.5% |
| Wins the match | 59.8% | 40.2% |
| Fair odds | 1.67 (−148) | 2.48 |
How the serve edge changes the match
Player B stays at 65% of points on serve. Best of 3.
| Player A on serve | A holds | A wins the set | A wins the match | Fair odds A |
|---|---|---|---|---|
| 60% | 73.6% | 33.7% | 26.3% | 3.80 |
| 63% | 79.5% | 43.4% | 40.1% | 2.49 |
| 65% | 83.0% | 50.0% | 50.0% | 2.00 |
| 68% | 87.5% | 59.6% | 64.2% | 1.56 |
| 70% | 90.1% | 65.6% | 72.6% | 1.38 |
A 5-point difference in points won on serve moves the match from a coin flip to roughly a 2-to-1 favourite.
Using it for betting
- Compare fair and market odds with the no-vig calculator so you compare like with like.
- Check the surface. Serve numbers differ a lot between grass, hard and clay.
- Size the stake with the Kelly calculator and keep it modest.
Read our tennis betting guide for markets such as sets, games and tie-breaks, and value betting for the theory.
