Odds calculator: margin and fair odds
Enter the odds for every outcome of one market. The calculator works out the bookmaker margin, the implied probability of each price and the fair odds without the margin in four ways, and converts every price to fractional and American odds. Everything comes from the odds alone; it is not a prediction.
See statistics and probabilities for today's matches on StatsAIHow the bookmaker margin is calculated
Odds of 2.10 mean a probability of 1 / 2.10 = 47.62%. Do that for every outcome of one market and the total comes out above 100%. The excess is the bookmaker margin (overround, or vig): for odds of 2.10 / 3.40 / 3.60 the total is 104.81%, so the margin is 4.81%. The market payout is 1 / total, here 95.41%: for every 100 staked across all outcomes in proportion, the odds pay back 95.41 on average.
margin = Σ (1 / odds) − 1 · payout = 1 / Σ (1 / odds)
The same number is written in two ways. The total minus 100% (4.81%) says how far the probabilities are inflated; 100% minus the payout (4.59%) says how much of the stake the bookmaker keeps on average. One person quoting 4.81% and another quoting 4.59% can be describing the same market.
Explained in detail, with two-way markets and accumulators, in the StatsAI Academy: Bookmaker margin · Implied probability
Four ways to remove the margin
Fair probabilities add up to exactly 100%, but the bookmaker does not say how it spread the margin across outcomes. That is why there are several de-vig methods, and the calculator runs all four:
- Proportional: each implied probability is divided by the total. The margin is the same on every outcome. StatsAI uses this method when it compares its probabilities with the market.
- Additive: the same share of the margin is subtracted from every outcome. With a big longshot and a high margin it can give a negative probability.
- Power: the probabilities are raised to a power k until they add up to 100%. A small probability shrinks relatively more, so the longshot loses more margin.
- Shin: a model built on the observation that longshot odds are more often shorter than fair. It has to be solved iteratively, and the calculator does that for you.
The gap is largest when a market has a strong favourite. For odds of 1.30 / 5.50 / 11.00 the fair odds of the longshot are 11.46 with the proportional method, 13.00 with the additive, 12.71 with the power method and 12.55 with Shin's. The proportional method gives the longshot a fair probability of 8.72%, Shin's 7.97%: if you only look at the first, odds of 11.00 look closer to fair than they are under the other methods.
On a large sample of odds, Štrumbelj (2014) found that Shin's method gives more accurate probabilities than the proportional one. Still, no method reveals the true probability: each one is an assumption about how the bookmaker spread its margin.
Every method, step by step: How to de-vig odds · Value betting
Decimal, fractional and American odds
Decimal odds show the total return for a stake of 1, stake included. Fractional odds, common in the UK, show only the profit: 11/10 means a profit of 11 for a stake of 10, so the decimal price is 1 + 11/10 = 2.10. American odds with a plus (+150) are the profit on a stake of 100; with a minus (−150) they are the stake needed to win 100.
decimal = 1 + a/b · +A → 1 + A/100 · −A → 1 + 100/A
The table converts common odds into all three formats and into implied probability. For fractions it uses the form bookmakers usually quote, or the simplest fraction that gives the same price to two decimals.
| Decimal | Fractional | American | Probability |
|---|---|---|---|
| 1.20 | 1/5 | -500 | 83.33% |
| 1.25 | 1/4 | -400 | 80.00% |
| 1.40 | 2/5 | -250 | 71.43% |
| 1.50 | 1/2 | -200 | 66.67% |
| 1.80 | 4/5 | -125 | 55.56% |
| 1.91 | 10/11 | -110 | 52.36% |
| 2.00 | 1/1 | +100 | 50.00% |
| 2.20 | 6/5 | +120 | 45.45% |
| 2.50 | 6/4 | +150 | 40.00% |
| 3.00 | 2/1 | +200 | 33.33% |
| 3.50 | 5/2 | +250 | 28.57% |
| 4.00 | 3/1 | +300 | 25.00% |
| 5.00 | 4/1 | +400 | 20.00% |
| 7.00 | 6/1 | +600 | 14.29% |
| 11.00 | 10/1 | +1000 | 9.09% |
What the calculator does not know
- The true probability. Fair odds are the market's estimate at one moment, and prices keep moving until kick-off.
- Whether the odds belong to one market. The margin only makes sense for all outcomes of one market at one bookmaker; odds from different bookmakers can push the total below 100%.
- Whether a bet has value. Odds above your own fair price are only an estimate, and only a large number of bets shows whether your estimates hold up.
- Tax, deposit fees and the bookmaker's payout rules.
StatsAI measures the accuracy of its probabilities against margin-free odds, with the proportional method from this calculator: AI model performance
FAQ
How do you calculate the bookmaker margin?
Add up 1 / odds for every outcome of one market and subtract 100%. For odds of 2.10 / 3.40 / 3.60 the total is 104.81%, so the margin is 4.81%.
How do you convert odds to a percentage?
Divide 1 by the decimal odds: 1 / 2.50 = 40%. That probability still includes the margin; without it the number is a little lower and depends on the odds of the other outcomes.
What are fair odds?
Odds without the margin: 1 / fair probability. For odds of 2.10 / 3.40 / 3.60 the fair price of the home win is 2.20 with the proportional method.
Which de-vig method is the most accurate?
None of them knows the true probability. The proportional method is the most common and the simplest; in Štrumbelj's study (2014) Shin's method gave more accurate probabilities on a large sample of odds.
How do you convert American odds to decimal?
For +A the decimal price is 1 + A/100, so +150 = 2.50. For −A it is 1 + 100/A, so −150 = 1.67.