Vig Calculator (Bookmaker Margin, Overround & No-Vig Fair Odds)

How it works

implied pᵢ = 1 ÷ decimal oddsᵢ · market % S = Σ pᵢ · overround = S − 1 · hold = 1 − 1/S · fair probability: multiplicative pᵢ/S; additive pᵢ − (S − 1)/n; power pᵢᵏ with k chosen so Σ pᵢᵏ = 1 · fair odds = 1 ÷ fair probability

A bookmaker builds its profit into the prices: the implied probabilities of every outcome add up to more than 100%. The excess is the overround; the hold (what the book expects to keep from balanced action) is 1 − 1/S — a standard -110/-110 line has a 4.76% overround and a 4.55% hold. Removing the margin gives "fair" or no-vig odds, the market's estimate of the true chances. The multiplicative method scales every outcome equally; the additive method subtracts the same amount from each; the power method takes more margin from long shots, matching the favourite–longshot bias seen in real markets.

Worked example

A point spread priced -110 on both sides is 1.91 decimal, a 52.38% implied chance each. The market adds to 104.76%, so the overround is 4.76% and the hold is 4.55% (a 95.45% payout rate). Removing the vig leaves 50% on each side — fair odds of 2.00 / 2.00, or +100.

Sources: Wikipedia — Vigorish · Wikipedia — Mathematics of bookmaking

Frequently asked questions