Odds and probability
Convert between probability, decimal odds, fractional odds and American odds.
Percent, 0–100
European format, e.g. 2.50
UK format, e.g. 3/2
Moneyline, e.g. +150 or −200
For : against, e.g. 2 : 3
How it works
Probability is the share of all outcomes that are favourable. Odds instead compare favourable outcomes with unfavourable ones. A probability of 25% corresponds to odds of 1 to 3, meaning one favourable outcome for every three unfavourable ones.
Decimal odds are the total payout per unit staked, including the stake. The probability is 1 divided by the decimal odds, so odds of 4.00 correspond to 25%.
Fractional odds show the profit relative to the stake. 3/1 means three units of profit per unit staked and corresponds to 25%.
American odds show how much you win on a 100 stake for positive numbers, and how much you must stake to win 100 for negative numbers. +300 corresponds to 25%, and −300 corresponds to 75%.
Note that bookmakers include a margin, so the sum of their implied probabilities across all outcomes exceeds 100%.
How the tool calculates
Everything is converted through the probability. Decimal odds below 10 are shown with two or three decimal places, between 10 and 100 with one or two, and from 100 with at most one: the odds for 50% show as 2.00, for 30% as 3.333, for 7.5% as 13.33 and for 0.75% as 133.3. The third decimal place below 10 lets 1.909 be read back as 10/11. American odds are rounded to whole numbers.
Fractional odds and the Odds (for : against) field show a fraction with a denominator of 100 or less, found with continued fractions: the tool takes the last approximation before the denominator would pass 100, which is not always the nearest fraction. A probability of 30% gives fractional odds of 7/3. Decimal odds of 1.91 give 91/100, while 1.909 gives 10/11. A value below 1/100 is written as 1/n instead: decimal odds of 1.005 give fractional odds of 1/200, and decimal odds of 151 give 1 : 150.
Edge cases and common mistakes
American odds never lie between −100 and +100, and the tool marks such values as invalid. Both +100 and −100 mean 50%, and every probability above 50% gives a negative number.
The fractional field and the for : against field read numbers the opposite way round. In the fractional field, 2/3 means winning 2 for a stake of 3, which is 60%. In the for : against field, 2/3 means two favourable outcomes against three unfavourable ones, which is 40%. Fractional odds can also be typed with a hyphen, as in 3-2.
Example: removing the bookmaker’s margin
A football match is priced at 2.10 for a home win, 3.40 for a draw and 3.60 for an away win. The tool gives 47.62%, 29.41% and 27.78%, which add up to 104.81%. Everything above 100% is the bookmaker’s margin.
The simplest way to get probabilities that add up to 100% is to divide each by the total, which the research literature calls basic normalisation. Here that gives 45.43%, 28.06% and 26.50%, or, rounded, fair decimal odds of 2.20, 3.56 and 3.77. Egidi, Pauli and Torelli describe the method and report that Štrumbelj found Shin’s method, based on a model in which some bettors already know the outcome, gives better forecasts than basic normalisation.