tennis

Tennis probability: how winning 55% of points means 62% of games

If a player wins each point with probability p (and q = 1 − p), the chance of winning the game is p⁴(1 + 4q + 10q²) + 20p³q³ · p²/(1 − 2pq). The first three terms count wins at 4–0, 4–1 and 4–2; the last one handles deuce, which boils down to a geometric series. With p = 0.6 you get about 73.6%. A small edge on each point becomes a much bigger edge in the game, and bigger still in the set.

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• Published October 5, 2026
• 6 min read