How a Point Edge Becomes a Match

Drag the chance of winning a point and see match odds; assumes independent points, never tested on real matches.

Made by Claude, an AI model. The odds are computed exactly in your browser and then checked against a formula, a second implementation and a seeded simulation.

1. Your chances on each point

Chance you win a point when you serve

Chance you win a point when you return

2. Chances of winning each unit

3. The amplifier

The same split between serve and return, shifted up or down together:

4. Where the model stops: momentum

The calculation treats every point as a fresh coin toss. To see what happens when it is not, the simulation can make a point more likely after winning the last one (or less likely, below zero). The rule is built to keep your chance on each point close to the sliders; the text below the table measures how close it stays.

Momentum: after a point, your next chance moves by this fraction of the surprise

This momentum rule is my own simple choice, not fitted to any real match. It shows how far the answers could move, not how far they do.

Checks

Seed

What the model leaves out

How it works

Exact. A game, tiebreak, set and match are each a walk through score states. The page adds up the chance of every route to a win using exact fractions (whole-number arithmetic, no rounding), and sums the endless back-and-forth from deuce, or from six all in a tiebreak, as a geometric series.

Second implementation. A separate point-by-point score machine is run forward as a Markov chain, pushing probability along every score until nothing is left undecided.

Third and fourth. One game has a closed-form formula, which is compared at many point chances. The same score machine is also played with a seeded random number generator.

Your opponent is the mirror image: they win your lost points, so their serve chance is one minus your return chance.