All formats represent the same probability. Decimal odds are the base unit — the
cleanest form because they directly express payout-per-unit-staked including stake return.
Every other format converts through decimal.
American ↔ Decimal
Positive moneyline (underdog): decimal = american / 100 + 1.
At +200: 200 / 100 + 1 = 3.00.
Negative moneyline (favorite): decimal = 100 / |american| + 1.
At -150: 100 / 150 + 1 = 1.667.
Reverse (decimal → American): if decimal ≥ 2,
american = (decimal − 1) × 100 (positive).
If decimal < 2, american = −100 / (decimal − 1) (negative).
Fractional ↔ Decimal
Fractional odds express profit per unit staked. 5/1 means
$5 profit on $1 staked. To convert to decimal:
decimal = numerator / denominator + 1. So
5/1 → 5/1 + 1 = 6.0. And
10/11 → 10/11 + 1 = 1.909.
Reverse (decimal → fractional): subtract 1 to get the fraction value, then find the
nearest simple ratio with denominator ≤ 100. This is why the converter sometimes rounds
fractional odds slightly — UK bookmakers do the same.
Implied probability
probability = 1 / decimal × 100%. At 1.909 decimal:
1 / 1.909 × 100 = 52.38%. Reverse:
decimal = 1 / (probability / 100). At 40%:
1 / 0.40 = 2.50.
Implied probability is the bookmaker's embedded estimate of that outcome's chance of
occurring — inflated by the vig. Strip the vig with the
no-vig calculator
to find the true probability the market implies.
Quick reference table
| American | Decimal | Fractional | Prob |
| +500 | 6.00 | 5/1 | 16.67% |
| +200 | 3.00 | 2/1 | 33.33% |
| +150 | 2.50 | 3/2 | 40.00% |
| +110 | 2.10 | 11/10 | 47.62% |
| −110 | 1.909 | 10/11 | 52.38% |
| −150 | 1.667 | 2/3 | 60.00% |
| −200 | 1.500 | 1/2 | 66.67% |
| −400 | 1.250 | 1/4 | 80.00% |