Foundations · Odds & betting
Implied Probability Calculator
What probability is a set of odds really claiming? Convert decimal, fractional or American (moneyline) odds into the implied probability — and back into every format. Then enter all the outcomes of an event to see the overround: why the implied chances add up to more than 100%, how big the bookmaker's margin is, and what the "fair" probabilities would be without it.
Implied probability is the break-even win rate: bet at these odds and you only profit long-term if the real chance beats it.
For example the home win, draw and away win — or both sides of a coin-toss market. The format chip above applies to these too.
Result
In plain English
Odds are just a probability in disguise, plus a margin. The implied probability strips off the disguise — it is the chance an outcome would need for the bet to be a fair, break-even gamble. Add up the implied probabilities for every outcome of a real event and they come to more than 100%; that surplus is the bookmaker's built-in edge.
- decimal odds
- The total return per 1 staked, including the stake (2.50 returns 2.50). Implied probability = 1 ÷ decimal odds.
- fractional odds
- Profit-to-stake, the traditional UK form (3/2 means win 3 for every 2 staked). Implied probability = denominator ÷ (numerator + denominator).
- American odds
- Moneyline. A positive number is the profit on a 100 stake (+150 wins 150); a negative number is the stake needed to win 100 (−200 risks 200 to win 100).
- overround (vig, juice)
- The amount by which the implied probabilities of all outcomes exceed 100%. A book set to 105% has a 5-point overround.
- bookmaker's margin
- The share of all stakes the book expects to keep: 1 − (1 ÷ total implied probability). It is the house edge, the same idea as a casino's.
- fair (de-vigged) probability
- Each implied probability rescaled so they sum to 100% — the book's own estimate with the margin stripped out.
Frequently asked
How do you convert odds to implied probability?
For decimal odds, implied probability = 1 ÷ the odds (so 2.50 implies 1 ÷ 2.50 = 40%). For fractional odds a/b, it is b ÷ (a + b) (3/2 implies 2 ÷ 5 = 40%). For American odds, a positive figure +A implies 100 ÷ (A + 100), and a negative figure −A implies A ÷ (A + 100). All three describe the break-even win rate for a bet at those odds.
Why do the implied probabilities add up to more than 100%?
Because the odds are shortened to build in the bookmaker's margin. If a fair coin toss were priced fairly, both sides would be 2.00 (50% each, summing to 100%). In practice you might see 1.90 each — 52.6% apiece, summing to 105.3%. That extra 5.3 points is the overround: the book's edge, and the reason the average bettor loses over time regardless of any system.
What is the difference between implied and "true" probability?
Implied probability is what the odds assert; true probability is the real chance, which nobody knows exactly. Removing the margin (de-vigging) gives the book's estimate of the true probability, but it is still an estimate, and a sharp bettor is looking for cases where their own estimate of the true chance is higher than the implied one — that, not a staking pattern, is the only edge there is.
What is a “value” bet?
A value bet is one where your own estimate of the true probability is higher than the implied probability the odds are offering — so the bet has positive expected value. The fair price is the de-vigged figure with the bookmaker’s margin stripped out; you only have an edge when your estimate beats that, not merely the headline odds. Finding genuine value is hard precisely because bookmakers price carefully, and no staking system can manufacture it where it does not exist.