Market maths
Implied probability calculator
Implied probability is the chance a price corresponds to. A decimal price of 2.50 is the same statement as "this happens 40% of the time": divide one by the price and you have the probability that price implies. This calculator runs the conversion in both directions — a price into the probability behind it, and a probability of your own into the price that would be fair for it.
What comes back is the probability implied by the price as quoted, not the true chance of the outcome. Every bookmaker price carries margin, and margin pushes the implied probability above the underlying chance. Add up the implied probabilities of every outcome in a market and the total exceeds 100%; that excess is spread through the individual prices, so a single price always overstates. Stripping it out needs the complete outcome set, which is what the overround calculator does.
Inputs
Both directions are the same relation rearranged. Pick whichever figure you already have.
Decimal (European) format: 2.50 means a winning bet returns 2.5 times the stake, stake included.
Result
- Implied probabilityThe chance a price of 2.50 corresponds to, margin included
- 40.00%
- Break-even strike rateThe same figure read differently: how often a selection at this price would have to win for level stakes on it to come out even
- 40.00%
- The same chance written as "1 in N"Round-trip check: converting the probability back returns the price you entered
- 1 in 2.50
This is the probability the price you entered corresponds to, with the bookmaker margin still in it — not an estimate of the true chance. Removing the margin needs every price in the market, and the price you actually get can differ from the one you converted: prices shorten, exchange commission lowers the effective price, and rule deductions change what a bet settles at.
How this is calculated
implied probability = 1 / decimal odds decimal odds = 1 / probability
Decimal odds are the multiplier on your stake when the bet wins, stake included: a EUR 1 bet at 2.50 returns EUR 2.50. Betting that price repeatedly breaks even when what comes back equals what goes out, and that happens when the chance of winning is 1 / 2.50 = 0.40. That is the whole derivation, and it is why the two directions are one equation rearranged — convert a price to a probability and back and you land on the price you started with, which is what the round-trip row checks. To verify any figure on this page by hand, divide 1 by the price and multiply by 100 for the percentage; to go the other way, divide 1 by the probability written as a decimal. What the formula does not do is remove margin. Sum 1 / price across every outcome of a real market and the total is above 1, and that excess is already inside each individual price, so the percentage shown here sits above the de-vigged chance for the same outcome.
Worked example
A three-way football market, converting one price and then checking it against the rest of the book.
- 01The market is priced 2.50 on the home win, 3.50 on the draw and 3.00 on the away win.
- 02Home win: 1 / 2.50 = 0.4000, so that price implies a 40.00% chance.
- 03Going back the other way: 1 / 0.40 = 2.50, the price you started with. That agreement is the round-trip check.
- 04The other two prices imply 1 / 3.50 = 28.57% and 1 / 3.00 = 33.33%.
- 05Adding all three: 40.00 + 28.57 + 33.33 = 101.90%. The 1.90 points above 100 are the margin built into the prices.
- 06Removing that margin proportionally: 40.00 / 1.0190 = 39.25%, which corresponds to a price of about 2.55.
- 07So the 40.00% this calculator reports for 2.50 sits about 0.75 percentage points above the de-vigged figure for the same outcome. A single price cannot show you that gap on its own — it takes the full outcome set, which is the overround calculator.
Questions
Is the implied probability the real chance of the outcome?
No. It is the chance the quoted price corresponds to, with the bookmaker margin still included, so it sits above the de-vigged figure for the same outcome. How far above depends on the market and cannot be read off one price: you need every outcome in the market to measure it.
Why do the implied probabilities in a market add up to more than 100%?
Because the prices are shortened to build in the bookmaker margin. A three-way market priced 2.50, 3.50 and 3.00 implies 40.00%, 28.57% and 33.33%, a total of 101.90%. The 1.90 points above 100 are the margin, which is why summed implied probabilities never come to exactly 100% at a real book.
How do I convert this into a fair probability?
Take the implied probability of every outcome, add them up, and divide each one by that total. That is proportional de-vigging, and the overround calculator does it for you. Be aware it assumes margin is spread evenly across the outcomes, whereas in practice longshots usually carry more of it than favourites, so a proportional split tends to understate the true chance of a favourite relative to the power and Shin methods.
Why does the price I end up with imply a different probability?
The conversion describes the number you typed in, and that is often not the number your bet settles on. Prices shorten between the screen and the bet being accepted, an exchange takes commission from winnings so the effective price is lower than the quoted one, enhanced prices can cap the payout, and non-runner or rule deductions cut the price after the fact. Convert the price on the settled bet, not the one you were looking at.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.