Three ways to write the same chance
Betting odds express a probability and a payout at the same time. In the United States, sportsbooks quote American odds such as −150 or +200. Europe, Canada and Australia use decimal odds such as 1.67 or 3.00, and the United Kingdom traditionally uses fractional odds such as 2/3 or 2/1. This calculator converts any of them to the others, shows the implied probability, and calculates the return on your stake.
The formulas
American to implied probability:
- Negative odds (favorite): p = −odds ÷ (−odds + 100). −150 → 60%
- Positive odds (underdog): p = 100 ÷ (odds + 100). +200 → 33.3%
Conversions:
- Decimal odds = 1 ÷ p, and the total return = stake × decimal odds
- Fractional odds (against) = (1 − p) ÷ p, so 2/1 means you win 2 for every 1 staked
- American odds = (decimal − 1) × 100 if decimal ≥ 2, otherwise −100 ÷ (decimal − 1)
Worked example
A team is listed at −150 and you consider a $100 bet.
- Implied probability: 150 ÷ 250 = 60%.
- Decimal odds: 1 ÷ 0.60 = 1.67; fractional odds: 0.4 ÷ 0.6 = 2/3.
- A winning bet returns $166.67: your $100 back plus $66.67 profit.
- The underdog at +200 has an implied probability of 33.3%: a $100 bet returns $300.
Odds conversion table
| American | Decimal | Fractional | Implied probability |
|---|---|---|---|
| −300 | 1.33 | 1/3 | 75.0% |
| −200 | 1.50 | 1/2 | 66.7% |
| −150 | 1.67 | 2/3 | 60.0% |
| −110 | 1.91 | 10/11 | 52.4% |
| +100 | 2.00 | 1/1 (evens) | 50.0% |
| +150 | 2.50 | 3/2 | 40.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +500 | 6.00 | 5/1 | 16.7% |
The bookmaker’s margin
Add up the implied probabilities of every outcome in a market and you get more than 100%. A game priced at −110 on both sides adds up to 104.8%; the extra 4.8% is the vig or juice, the sportsbook’s built-in margin. To estimate the market’s fair probability, divide each implied probability by the total: 52.4% ÷ 104.8% = 50%. To make money over time, a bettor must find prices whose true probability is higher than the implied one, after the margin, which very few manage.
Bet responsibly
Sports betting is legal in many but not all states, and only for adults, usually 21 and over. Set a budget you can afford to lose, never chase losses, and treat betting as paid entertainment rather than income. If gambling stops being fun, free and confidential help is available 24/7 at 1-800-GAMBLER.