Guide · 6 min read
Implied probability: how to turn betting odds into percentages and back
Every price is a probability in disguise. Odds of 2.50 say 40%, odds of 1.25 say 80%. This guide shows the formula for every odds format, why the probabilities in one market add up to more than 100%, how to go back from a probability to a price, and how the same numbers reveal a sure bet.
Updated 22 October 2026
Contents
Odds converter and implied probability calculator
Pick the format you have, type in the price and see the same price in decimal, fractional and American odds, plus the implied probability; a comma or a full stop both work as the decimal mark.
Decimal odds above 1, e.g. 2.50
The formula: 1 / odds
For decimal odds, the format used by bookmakers across Austria, Germany and Slovakia, the implied probability is simply the reciprocal:
Implied probability = 1 / decimal odds
Odds 2.50 → 1 / 2.50 = 0.40 = 40%
Odds 1.25 → 1 / 1.25 = 0.80 = 80%
The logic: at odds of 2.50 a €10 stake returns €25. That is a fair deal if you win 40 times out of 100, because 40 × €25 = €1,000, exactly the 100 stakes of €10 you paid in. If you are new to odds, the betting basics guide explains stake, return and profit first.
Conversion table
| Decimal | Implied | Decimal | Implied |
|---|---|---|---|
| 1.01 | 99.0% | 2.50 | 40.0% |
| 1.25 | 80.0% | 3.00 | 33.3% |
| 1.50 | 66.7% | 4.00 | 25.0% |
| 1.80 | 55.6% | 5.00 | 20.0% |
| 2.00 | 50.0% | 10.00 | 10.0% |
The calculator inside the ArbVantage app does this for you: type in the prices and you see the stakes and the result for each outcome.
Why the sum is more than 100%
Add up the implied probabilities of all outcomes in one market at one bookmaker and you land above 100%. The excess is the bookmaker's margin.
Implied: 47.62% + 29.41% + 27.78% = 104.81%.
Normalised (divide each by 1.0481): 45.43% / 28.06% / 26.50%, together 100%. The fair odds without margin are the reciprocals: 2.20 / 3.56 / 3.77.
This simple normalisation spreads the margin evenly across all outcomes. In practice many bookmakers load more margin on to outsiders than favourites (the favourite-longshot bias), and more refined methods such as Shin's model account for that. How to calculate the margin itself is covered in bookmaker margin and overround.
Converting fractional and American odds
Fractional odds (UK and Ireland) show the net profit relative to the stake. For a/b:
Implied probability = b / (a + b)
6/4 → 4 / (6 + 4) = 40% (decimal 2.50)
1/4 → 4 / 5 = 80% (decimal 1.25)
American odds carry a sign. Plus means: this much profit on a 100 stake. Minus means: this much stake to win 100.
Positive (+X): 100 / (X + 100). Example +150 → 100 / 250 = 40%
Negative (−X): X / (X + 100). Example −200 → 200 / 300 = 66.7%
−110 → 110 / 210 = 52.4%
All formats side by side, plus Hong Kong and Malay odds, are in odds formats explained.
From probability back to odds
The way back is just as simple: fair odds = 1 / probability. If you rate an outcome at 60%, the fair odds are 1 / 0.60 = 1.667. If a bookmaker offers 1.75, the price is above your fair odds. Whether your estimate is right is a different question, and everything hinges on it.
- American: for p above 50% the price is −100 × p / (1 − p); below 50% it is +100 × (1 − p) / p. 60% gives −150; 40% gives +150.
- Fractional: (1 − p) / p as a fraction. 40% gives 0.6 / 0.4 = 3/2, usually written 6/4. 20% gives 0.8 / 0.2 = 4/1.
In practice you mostly use the way back to judge an offered price: turn your own estimate into fair odds and compare. If the offered price is below it, you are paying more margin than you think. How to remove the margin properly is shown in no-vig fair odds, and how to price an edge in expected value in betting.
Spotting a sure bet with implied probabilities
A tennis match, two outcomes. Bookmaker A offers 2.04 on player 1, bookmaker B offers 2.00 on player 2.
Implied: 1 / 2.04 = 49.02% and 1 / 2.00 = 50.00%, together 99.02%, so below 100%.
Split €1,000 in proportion to the implied probabilities: €495.05 at A and €504.95 at B. Either side then returns about €1,009.90, roughly €9.90 ahead whichever player wins, provided both bets are accepted at these prices and stand.
The formula behind it, plus three-way examples, is in sure betting explained.
Implied probability after Austria's 5% fee
If a bookmaker in Austria passes the 5% betting fee on to you, your effective odds are 5% lower. 2.50 becomes 2.50 × 0.95 = 2.375, and the implied probability rises from 40.0% to 42.1%. With such bookmakers always calculate with the net price. In the example above, a deduction at just one of the two bookmakers would push the sum above 100% and turn the sure bet into a loss.
Implied is not the true probability
The implied probability is the bookmaker's view plus margin, not a fact. Three things distort it:
- Margin: it shortens every price, so every outcome looks more likely than it is.
- Customer flows: bookmakers also move prices where a lot of money arrives, for example on popular teams.
- Information: just before kick-off, once line-ups are known, prices are usually more accurate than days earlier.
Even so, research shows that the prices of large, liquid betting markets are among the best available forecasts of sports results, which is why beating them consistently with your own estimates is hard. Sure bets need no estimate of your own: they rely only on price differences between bookmakers.
FAQ
Is the implied probability the true probability?
No. It includes the bookmaker's margin and its view of the market. Remove the margin and you get an estimate of the fair probability, but that can be wrong too.
How do I convert American odds into a probability?
For positive odds (+X) calculate 100 / (X + 100); for negative odds (−X) calculate X / (X + 100). +150 equals 40%, −200 equals 66.7%.
What do odds of 1.01 mean?
The implied probability is 99%. A €100 stake returns €101, so €1 profit. If you lose, the whole stake is gone: a large risk for a very small return.
How do I turn a probability into odds?
Divide 1 by the probability as a decimal. 60% gives 1 / 0.60 = 1.667, 25% gives 4.00. That is the fair price without margin; bookmakers usually offer a little less.
Why do all outcomes add up to more than 100%?
Because every price contains the bookmaker's margin. At 1.90 on both sides that gives 52.6% + 52.6% = 105.3%. The 5.3% above 100% is the mark-up.
Sources
- Steven D. Levitt: Why are gambling markets organised so differently from financial markets? The Economic Journal 114 (2004)
- Egidi, Pauli, Torelli: Combining historical data and bookmakers' odds in modelling football scores (arXiv, 2018)
- Unternehmensserviceportal (USP), Austria: Wettgebührenabrechnung
As of October 2026. Worked examples by ArbVantage, rounded.
Betting carries risk, sure bets included: odds change, bets get voided and accounts get limited. Only stake money you can afford to lose. Our responsible gambling page lists free, confidential help in Austria and Germany.
Not betting, legal or tax advice. 18+. As of October 2026.