Implied probability calculator
Implied probability is the chance of winning at which a price breaks even: 1 divided by the decimal odds. −110 implies 52.38%, +150 implies 40.00%. It includes the sportsbook’s margin, so it is not the true chance of the result. Turned around, a probability gives fair odds: 1 divided by the probability, with no margin.
Odds to implied probability
Probability to fair odds
Fair odds are the price at which a bet on a result with that probability would break even. A sportsbook’s price for the same chance is shorter, because it includes the margin.
The formulas
Implied probability = 1 ÷ decimal odds.
From American odds: negative odds −A: A ÷ (A + 100). Positive odds +A: 100 ÷ (A + 100).
From fractional odds a/b: b ÷ (a + b).
Fair decimal odds = 1 ÷ probability; then convert to American or fractional as usual.
−110: 110 ÷ (110 + 100) = 52.38%. +150: 100 ÷ (150 + 100) = 40.00%. In reverse, a 55% probability has fair decimal odds of 1 ÷ 0.55 = 1.818, which is −122 in American odds and 9/11 in fractional.
Worked examples
| American | Decimal | Implied probability |
|---|---|---|
| −300 | 1.333 | 75.00% |
| −200 | 1.50 | 66.67% |
| −150 | 1.667 | 60.00% |
| −110 | 1.909 | 52.38% |
| +100 | 2.00 | 50.00% |
| +150 | 2.50 | 40.00% |
| +200 | 3.00 | 33.33% |
| +300 | 4.00 | 25.00% |
| +500 | 6.00 | 16.67% |
| Probability | Fair American | Fair decimal | Fair fractional |
|---|---|---|---|
| 10.00% | +900 | 10.00 | 9/1 |
| 20.00% | +400 | 5.00 | 4/1 |
| 25.00% | +300 | 4.00 | 3/1 |
| 33.33% | +200 | 3.00 | 2/1 |
| 40.00% | +150 | 2.50 | 3/2 |
| 50.00% | +100 | 2.00 | 1/1 |
| 55.00% | −122 | 1.818 | 9/11 |
| 60.00% | −150 | 1.667 | 2/3 |
| 66.67% | −200 | 1.50 | 1/2 |
| 75.00% | −300 | 1.333 | 1/3 |
| 80.00% | −400 | 1.25 | 1/4 |
| 90.00% | −900 | 1.111 | 1/9 |
Why implied probabilities add up to more than 100%
A sportsbook prices both sides of a market so that their implied probabilities add up to more than 100%. At −110 on both sides, each side implies 52.38%, 104.76% together. The extra is the sportsbook’s margin (also called the vig or juice). To estimate the probabilities with the margin taken out, use the no-vig calculator.
Questions
Is implied probability the real chance of winning?
No. It is what the price says, margin included. The real chance of a sporting result is unknown; implied probability is the market’s price for it, not a measurement of it.
What are fair odds?
The odds at which a bet would break even over the long run if the probability you entered were exactly right. They contain no margin, so real sportsbook prices for the same chance are shorter.
Why does a 50% probability show +100?
Fair odds for 50% are decimal 2.00, which is even money. +100 and −100 are the same price; the calculator shows it as +100.
Why can I not enter 0% or 100%?
A certainty or an impossibility has no price. The calculator accepts probabilities from 0.01% to 99.99%.
Arithmetic, not advice
These calculators do arithmetic on the numbers you enter. They do not know the true chance of any result, they do not predict outcomes, and using them does not make betting profitable. Betting involves financial risk, and no research or model makes gambling safe or removes that risk.
StatsNext is for people 18 and older. Being 18 or older does not mean sports betting is legal for you: follow the laws and legal gambling age requirements where you live. Never wager money you cannot afford to lose, and do not chase losses. If gambling stops feeling like it is within your limits, free and confidential help is available 24/7 from the National Problem Gambling Helpline: 1-800-MY-RESET (1-800-697-3738). More resources are on the Responsible Gambling page.
StatsNext is a research platform, not a sportsbook; it does not accept wagers or guarantee results (Research Disclaimer, Responsible Gambling).
Continue in StatsNext
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