Implied probability is the single most useful number in betting. It turns any price, in any format, into a percentage that can be compared, added and reasoned about. This guide defines it, shows how to compute it from each odds format, explains why a market's probabilities sum to more than 100%, and then turns the idea around: given a probability you believe, what price is fair?
What "implied" means
A price implies a probability in the sense that there is exactly one win rate at which betting that price breaks even. Bet 100 at 2.00 over and over: if you win half the time you finish level, more than half you profit, less you lose. The break-even win rate for 2.00 is 50%. For 1.50 it is 66.7%: you need to win two bets in three, because each win only pays half a stake. For 4.00 it is 25%.
That break-even rate is the implied probability. It is a property of the price, not of the event. The bookmaker did not necessarily think the outcome was exactly that likely; they set a price at which they are happy to take bets, and the price contains their margin. But as a first reading of "how likely does the market think this is", the implied probability is the right number.
Computing it from each format
decimal d: p = 1 / d american +a: p = 100 / (a + 100) american −a: p = a / (a + 100) fractional
n/m: p = m / (n + m) polymarket q¢: p = q / 100
Some anchors worth memorising:
| Price | Decimal | Implied |
|---|---|---|
| -300 | 1.33 | 75.0% |
| -200 | 1.50 | 66.7% |
| -150 | 1.67 | 60.0% |
| -110 | 1.91 | 52.4% |
| +100 | 2.00 | 50.0% |
| +150 | 2.50 | 40.0% |
| +200 | 3.00 | 33.3% |
| +300 | 4.00 | 25.0% |
| +500 | 6.00 | 16.7% |
| +1000 | 11.00 | 9.1% |
The odds converter gives the implied probability of any price along with every other format.
Why a market adds up to more than 100%
Take a coin-flip market priced at -110 on both sides. Each side implies 52.38%. Together that is 104.76%. A real coin cannot land heads 52% of the time and tails 52% of the time, so the prices cannot both be true probabilities. The 4.76% excess is the bookmaker's margin, called the overround, vig or juice.
Every market works this way. A soccer match at 2.20 / 3.40 / 3.60 implies 45.5% + 29.4% + 27.8% = 102.6%. A tennis match at 1.30 / 3.60 implies 76.9% + 27.8% = 104.7%. A golf outright with fifty players can add up to 140% or more.
The overround tells you how expensive a market is to bet into. If you picked a side at random in a 104.76% market, you would lose 4.55% of your stakes over time (the margin as a share of turnover is 1 − 1/1.0476). Sharper bookmakers run 2–3% on major markets; recreational bookmakers 5–8%; exchanges, after commission, somewhere in between depending on the rate.
Removing the margin
To turn implied probabilities into fair probabilities you divide out the overround. The simplest method scales every outcome by the same factor:
fair_i = implied_i / Σ implied -110 / -110: 52.38% / 104.76% = 50.00% each 2.20 / 3.40 / 3.60:
44.3% / 28.7% / 27.1%
That method assumes the bookmaker spread the margin evenly, which they usually do not: longshots carry more of it. The devigging guide compares five methods. For symmetric two-way markets they all agree; for anything with a heavy favourite or a long outsider they differ by a point or two, which is enough to matter when deciding whether a price has value.
Turning it around: fair odds from a probability
If you have your own probability for an outcome — from a model, from a devigged sharp market, or from judgment — the fair price is its reciprocal.
fair decimal = 1 / p p = 55% → 1.818 decimal → −122 American p = 40% → 2.50 decimal → +150
American p = 25% → 4.00 decimal → +300 American
Any price longer than the fair price is value; any price shorter is not. The gap between the offered price and the fair price, expressed as expected value per unit stake, is p × offered − 1. At p = 55% and an offered price of 2.00, that is 0.55 × 2.00 − 1 = +10%. The EV & Kelly calculator does this and also suggests a stake.
Using implied probability day to day
To compare prices. Two prices are best compared as probabilities, because the scale is linear. A move from -110 to -120 is 52.4% to 54.5% (2.1 points); a move from +200 to +220 is 33.3% to 31.3% (2.1 points). Those are the same size, which neither the American nor the decimal numbers make obvious.
To spot a bad market. Add the implied probabilities. Over 108% on a two-way market is expensive; a sharper book will be cheaper.
To sanity-check a favourite. A -400 favourite implies 80%. Ask whether the outcome really happens four times in five. If your answer is "more like three in four", the price is too short.
To size a bet. Kelly staking needs a probability and a price. The implied probability of the sharpest available market, with the vig removed, is the standard estimate.
Worked examples
A two-way market
An NBA moneyline is -150 / +130. Implied: 60.0% and 43.5%, sum 103.5%. Fair (multiplicative): 58.0% and 42.0%. Fair prices: 1.72 (-138) and 2.38 (+138). If another book offers +145 on the underdog, the implied probability there is 40.8%, below the fair 42.0%: the price is longer than fair, so it has value. Check it in the
devig calculator
.
A three-way market
A soccer 1X2 is 2.20 / 3.40 / 3.60. Implied: 45.5% / 29.4% / 27.8%, sum 102.6%. The overround is small, typical of a sharp book on a major league. Fair (multiplicative): 44.3% / 28.7% / 27.1%. Fair prices: 2.26 / 3.49 / 3.70. A book offering 3.80 on the away side is above fair; at 3.60 it is exactly the sharp book's price with the margin still in it.
A prediction market
A Polymarket YES share at 64¢ implies 64%. The NO side at 38¢ implies 38%. Sum: 102%. The 2¢ excess is the spread, and the fair probability of YES is about 64 / 102 = 62.7%. The
Polymarket converter
shows both sides as odds and reports the spread.
Probability and the long run
An implied probability describes an average, not a sequence. A 52.38% bet loses four in a row about one time in twenty, and a 25% bet can lose ten in a row without anything being wrong with the price. That variance is why implied probability is a poor guide to what will happen next and a good guide to what will happen over many bets. Over 500 bets at a true 55% win rate, the observed rate lands between 50.5% and 59.5% about 95% of the time; over 50 bets the range is 41% to 69%. A bettor who judges a price by the last few results is reading noise. Judge it by the probability, and judge the probability by comparing with sharper prices and closing lines.
The same variance sets the stakes. Kelly staking, covered in the EV and Kelly guide, uses the probability and the price to choose a fraction of bankroll that survives the losing runs the probability implies. A 55% edge at even money suggests 10% of bankroll at full Kelly; most bettors use half that, precisely because the probability is uncertain and the runs are long.
Reading a probability from one price versus a pair
Given only one side of a market, the implied probability is the best available estimate, margin included. Given both sides, you can do better: the margin is visible as the amount by which the two sum over 100%, and dividing it out gives a fair probability for each side. For a -110 / -110 market the answer is 50% each. For -150 / +130 it is 58.0% / 42.0% under the multiplicative method, and the devigging guide shows how the answer shifts under methods that put more of the margin on the underdog.
The pair also tells you something the single price cannot: how sharp the book is. A two-way market at 103% is a low-margin book whose prices are close to fair; one at 108% is a recreational book whose implied probabilities overstate both sides by several points. When you compare a price across books, compare it against the fair probability from the sharpest pair you can find, not against the other book's single price. That is what "value" means in practice: a price whose implied probability is below the fair probability from the sharpest market, after the sharpest market's margin has been removed.
Two habits make the number useful. Convert every price you see into its implied probability before forming an opinion, so that the format never colours the judgement. And when a price surprises you, find the sharpest pair on the same market, devig it, and compare: the difference between your reaction and the fair probability is either your edge or your mistake, and the arithmetic will not tell you which.
What implied probability is not
It is not the true probability. The bookmaker's price includes margin and reflects money flows as much as opinion; the crowd can be wrong. It is also not your probability: if you have a reason to think an outcome is 60% likely and the market implies 52%, the market may be mispriced, or you may be. The implied probability is the market's price expressed as a chance. Everything else — devigging, comparing books, modelling — is about deciding whether to believe it.