Odds and probability
Probability compares favourable outcomes with all outcomes; odds compare favourable outcomes with unfavourable ones. If an event has probability p, the odds for it are p : (1 − p) and the odds against it are (1 − p) : p. Odds of A:B for an event mean p = A ÷ (A + B).
Betting markets quote the same idea in three formats. Fractional odds are odds against, read as profit per unit staked. Decimal odds are the total return per unit staked, 1 ÷ p. American odds are +100(1 − p)/p for an underdog and −100p/(1 − p) for a favourite.
| Probability | Odds against | Fractional | Decimal | American |
|---|---|---|---|---|
| 25% | 3 : 1 | 3/1 | 4.00 | +300 |
| 50% | 1 : 1 | 1/1 | 2.00 | +100 |
| 60% | 2 : 3 | 2/3 | 1.67 | −150 |
| 80% | 1 : 4 | 1/4 | 1.25 | −400 |
Worked example
Fractional odds of 3/1 mean a 1-unit stake wins 3 units profit. The implied probability is 1 ÷ (3 + 1) = 25%, the decimal odds are 4.00 and the American odds are +300. A 10 stake returns 40: 30 profit plus the 10 staked.
American odds of −110 mean you stake 110 to win 100. The implied probability is 110 ÷ 210 = 52.38% and the decimal odds are 1.91.
Implied probability is not the true chance
Bookmakers build a margin into their prices, so the implied probabilities of all outcomes in a market add up to more than 100%. The converted figure is the break-even probability at those odds, not an estimate of how likely the event really is.
This calculator converts one price at a time and does not remove the margin or account for fees, taxes or exchange commission.