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Tennis Service Game Hold Probability Calculator

Closed-form probability of winning a game given per-point win probability p.

Given the server's per-point win probability p, compute the probability of holding the game (closed form): G(p) = p⁴(15 − 34p + 28p² − 8p³) + p⁴(1−p)⁴ · 70 · p² / (1 − 2p(1−p)). Reports both the winning probability and its complement.

Marcus Laurent By Marcus Laurent
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

G(p) = direct game probabilities + deuce series geometric sum.

In depth

Given the server's per-point win probability p, compute the probability of holding the game (closed form): G(p) = p⁴(15 − 34p + 28p² − 8p³) + p⁴(1−p)⁴ · 70 · p² / (1 − 2p(1−p)). Reports both the winning probability and its complement.