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Best-of-seven series: from game price to series price

A series contract pays if a team wins four games before its opponent does. A small edge in each game becomes a much bigger edge over seven.

Game chance to series chance

Chance of winning each gameChance of winning the series
50%50.0%
55%60.8%
60%71.0%
65%80.0%
70%87.4%

Assumes the same chance every game and games independent of each other. Home court and injuries change the real per-game chance.

The series at every score

For a team that wins each game 60% of the time:

Wins ↓ · Losses →0123
071.0%54.4%33.7%13.0%
182.1%68.3%47.5%21.6%
291.3%82.1%64.8%36.0%
397.4%93.6%84.0%60.0%

Which games swing the most

At 2–2, a win takes the series to 84.0% and a loss to 36.0%, a 48-point swing. At 2–3, a win means 60.0% and a loss ends it: a 60-point swing. At 3–3, game 7 decides everything.

Hedging one game's swing

Holding 100 series contracts at 2–2, buying about 48 of the opponent's game 5 contracts evens out the two outcomes, because the opponent contract pays 100¢ exactly when the series value drops. At 42¢, both outcomes move the position by about −$0.96 before fees.

Game 7

At 3–3, the series contract and the game 7 contract are the same bet. Buying as many of the opponent's game 7 contracts as you hold locks the result in one trade, if your entry price plus the opponent's price is under 100¢.

Plan a game 7 hedge

At 3–3, enter your series contracts and the opponent's game 7 price in the hedge calculator.

Open the hedge calculator

Questions

How do you convert game odds to series odds?

Add up the chances of every way a team can win four games first. A team that wins each game 60% of the time wins a best-of-seven series about 71% of the time.

Why do favorites win series more often than single games?

Seven games give the better team more chances for its edge to show. A 55% per-game edge becomes about 61% over a series.

Which game of a series is the biggest swing?

Late games. At 2–3 the swing is 60 points for a 60% team, and at 3–3 the series is decided by one game.

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