Odds and probability

How odds and probability relate

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%.

Formulas

• Decimal odds = 1 / p
• Fractional odds = (1 − p) / p
• American odds = 100 · (1 − p) / p when p ≤ 0.5, otherwise −100 · p / (1 − p)
• Odds ratio = p : (1 − p)