Implied probability, defined

Decimal odds of 2.50 imply 1 / 2.50 = 40%; 2.00 imply 50%; 1.25 imply 80%. Shorter odds mean a higher implied chance. The conversion is arithmetic, not opinion, and every format describes the same number: decimal 1 / odds, fractional denominator / (numerator + denominator), or American, taking the odds' absolute value, 100 / (odds + 100) for a positive price and odds / (odds + 100) for a negative one (so −150 is read as 150).

The catch is that across a whole market the implied probabilities sum to more than 100%. In a two-way match market you might see 55% and 50%, totalling 105%. That extra 5 points is the vig, the margin baked into the prices, so a raw implied probability always overstates the true chance. To recover an honest number the margin has to come out, which is what de-vigging does; only then can two markets be compared like for like, or against a model.

This matters because a price is a probability estimate, and estimates are only comparable once they sit on the same scale. Research on betting markets treats the de-vigged price as the market's genuine forecast (see Berkowitz et al., 2018, on the accuracy of the sports betting market). It is the same number the market line serves: across every live CS2 market, the de-vigged sides sum to exactly 100.0000%, with nothing left to strip out. How that aggregate is built is set out in the methodology.

Decimal, American and the stake

Decimal odds include the stake: 2.50 returns 2.5 times the stake in total. Fractional odds show profit alone: 3/2 pays 1.5 profit per 1 staked, so it returns 2.5 in total, the same as 2.50.

A price of 1.00 returns only the stake. 1 ÷ 1.00 is 100%, a certain outcome, so quoted prices sit above it. To go from a chance to a fair price, with no margin, use 1 ÷ probability. A 40% chance is 1 ÷ 0.40 = 2.50.

A positive American price is the profit on a 100 stake: +150 means 150 profit, so 250 back, which is decimal 2.50. A negative price is the stake needed to win 100: −200 means staking 200 to win 100, so 300 back, which is decimal 1.50.

To get the decimal price, use (odds ÷ 100) + 1 for a positive price and (100 ÷ odds) + 1 for a negative one, with odds as the number without its minus sign. Examples:

To go back to American, use (decimal − 1) × 100 at 2.00 or above, and −100 ÷ (decimal − 1) below it. Even money, decimal 2.00, is usually written +100, though −100 is also seen.

In the −110 row, the 52.38% comes from the full decimal price, about 1.909091, not from 1.91. Dividing 1 by 1.91 gives 52.36%, so round only for display.

Worked example: −150 and +130

Take an invented two-way market priced −150 and +130. Turn each price into a chance:

• −150: 150 ÷ (150 + 100) = 150 ÷ 250 = 60.00%
• +130: 100 ÷ (130 + 100) = 100 ÷ 230 = 43.48%

Together they total 103.48%, so the margin is 3.48 points. Dividing each chance by that total takes the margin out. This proportional method is one of several in de-vigging, and it leaves 57.98% and 42.02%. In decimal, the same prices are about 1.67 and 2.30.

More examples and the calculator

See how to convert odds to implied probability for worked examples across decimal, fractional and American formats.

Convert any single price with the free implied probability calculator, which also renders the same price in decimal, American and fractional odds.