What is implied probability?
Implied probability is the chance of an outcome that is built into its odds. If a bet pays 2.50 (decimal), the price assumes a 1 ÷ 2.50 = 40% chance: a bet at that price breaks even if it wins 40% of the time. It is the bridge between odds and probability, and it works the same for every format.
The formulas
| Odds format | Implied probability | Example |
|---|---|---|
| Decimal | 1 ÷ odds | 2.50 → 1 ÷ 2.50 = 40.0% |
| Fractional (a/b) | b ÷ (a + b) | 3/2 → 2 ÷ 5 = 40.0% |
| American, positive (+x) | 100 ÷ (x + 100) | +150 → 100 ÷ 250 = 40.0% |
| American, negative (−x) | x ÷ (x + 100) | −200 → 200 ÷ 300 = 66.7% |
Odds and implied probability side by side
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.20 | 1/5 | −500 | 83.3% |
| 1.25 | 1/4 | −400 | 80.0% |
| 1.33 | 1/3 | −300 | 75.0% |
| 1.50 | 1/2 | −200 | 66.7% |
| 1.67 | 2/3 | −150 | 60.0% |
| 1.91 | 10/11 | −110 | 52.4% |
| 2.00 | 1/1 (evens) | +100 | 50.0% |
| 2.25 | 5/4 | +125 | 44.4% |
| 2.50 | 3/2 | +150 | 40.0% |
| 3.00 | 2/1 | +200 | 33.3% |
| 4.00 | 3/1 | +300 | 25.0% |
| 5.00 | 4/1 | +400 | 20.0% |
| 7.00 | 6/1 | +600 | 14.3% |
| 11.00 | 10/1 | +1,000 | 9.1% |
Need another price? The odds converter converts between all three formats and shows the implied probability instantly.
Implied probability is not the true probability
This is the key point. Implied probability comes from the bookmaker's price, and that price includes the bookmaker's margin. In a two-way market at −110 on both sides the implied probabilities are 52.38% + 52.38% = 104.76%. Two outcomes cannot both have more than 50% of the chances: the extra 4.76% is the vig.
To get a probability you can use, you remove the margin. At −110/−110, each side drops to 50%. With the football prices 2.10, 3.40 and 3.60 (implied 47.6%, 29.4%, 27.8%, total 104.8%), the margin-free probabilities are about 46.0%, 27.8% and 26.2%. The no-vig calculator does this for any market.
From odds to probability to value: one bet, three formats
The same price written three ways: 2.50 in decimal, 3/2 in fractional and +150 in American. All three imply 40%. If you believe the real chance is 45%, the bet is worth taking and the maths doesn't care which format you read it in:
EV = odds × true probability − 1 = 2.50 × 0.45 − 1 = +12.5%
A three-way market (1X2): implied vs margin-free
Football prices of 2.10, 3.40 and 3.60 imply 47.62%, 29.41% and 27.78%, a total of 104.81%. To remove the 4.81% margin there are two common methods, and they don't give the same answer:
| Outcome | Implied | Margin-free, proportional | Margin-free, power | Fair odds (power) |
|---|---|---|---|---|
| Home | 47.62% | 45.43% | 46.02% | 2.173 |
| Draw | 29.41% | 28.06% | 27.80% | 3.597 |
| Away | 27.78% | 26.50% | 26.18% | 3.819 |
The proportional method takes the same share off every outcome. The power method takes proportionally more from the long shots, where bookmakers hide more margin, so favourites end up with a slightly higher probability (46.0% rather than 45.4%). That 0.6-point difference is enough to turn a marginal bet into an apparent value bet, which is why we use the power method. Compare both in the no-vig calculator.
How a drop changes implied probability
Implied probability is also the clearest way to see what a drop means. When a price falls from 2.31 to 1.92, the implied probability rises from 43.3% to 52.1%: the market has moved almost 9 points toward that outcome. Not all of it is information (part is margin), but a move that big at a high-limit market is a real change of opinion. See dropping odds explained.
Implied probability and accumulators
In an accumulator the probabilities multiply, and so does the margin. Three legs at 2.00 (50% each) have a combined probability of 12.5% and a fair price of 8.00. If each leg is priced at −110 (1.909) the accumulator pays 1.909³ = 6.96, which is 13% less than fair: an effective margin of about 15%, against 4.76% on each single bet.
Why it matters for finding value
Why it matters for finding value
A bet has value when you believe the true probability is higher than the implied one. If your price implies 40% and the real chance is 45%, you are being paid for a 40% shot but getting a 45% one: EV = 2.50 × 0.45 − 1 = +12.5%. The whole practice of finding value bets is estimating the true probability better than the price does.
Common mistakes
- Treating implied probability as the real chance and forgetting the margin.
- Adding up probabilities across different bookmakers: the margin only makes sense inside one market at one bookmaker.
- Misreading American odds: −200 means you risk 200 to win 100, which implies 66.7%; +200 wins 200 on a 100 stake, which implies 33.3%.
- Comparing probabilities for different lines or periods.