Every odds line contains a probability estimate — the sportsbook's view of how likely each outcome is. Once you can extract that number, you can compare it to your own probability estimate and decide whether the bet has an edge.
Decimal odds — the easiest formula
Implied probability = 1 / decimal odds
That's the whole formula. Examples:
- Decimal 2.00 → 1 / 2.00 = 0.5000 = 50%
- Decimal 1.91 → 1 / 1.91 = 0.5236 = 52.36% (the standard −110 line)
- Decimal 2.50 → 1 / 2.50 = 0.4000 = 40% (equivalent to +150)
- Decimal 3.50 → 1 / 3.50 = 0.2857 = 28.57%
- Decimal 1.50 → 1 / 1.50 = 0.6667 = 66.67% (equivalent to −200)
If you only remember one formula, remember this one. Convert any other format to decimal first, then take 1 / decimal.
American odds — two formulas
American odds use a + or − sign and you need a different formula for each:
Positive (+) American: implied probability = 100 / (odds + 100)
- +100 → 100 / 200 = 50%
- +150 → 100 / 250 = 40%
- +200 → 100 / 300 = 33.33%
- +500 → 100 / 600 = 16.67%
Negative (−) American: implied probability = |odds| / (|odds| + 100)
- −110 → 110 / 210 = 52.38%
- −150 → 150 / 250 = 60%
- −200 → 200 / 300 = 66.67%
- −500 → 500 / 600 = 83.33%
Fractional odds
Implied probability = denominator / (numerator + denominator)
- 3/2 → 2 / 5 = 40% (same as +150)
- 1/1 (evens) → 1 / 2 = 50%
- 10/11 → 11 / 21 = 52.38% (same as −110)
- 5/1 → 1 / 6 = 16.67%
Why implied probability matters
Knowing the implied probability turns "+150" from a weird number into something you can reason about: "the sportsbook thinks this happens 4 times out of 10." That gives you a starting point for two important questions:
1. Do I think the true probability is higher? If you've handicapped the game and estimate the side wins 45% of the time, you have a positive expected-value bet (your 45% > the line's 40%). Run the math through the EV calculator.
2. What's the breakeven win rate I need? The implied probability IS the breakeven rate. Anything above it is profitable long-run; anything below it is a loser long-run.
Implied probability vs true probability — the vig
One catch: implied probability includes the sportsbook's commission. A −110/−110 spread has 52.38% implied probability on both sides. Add those: 104.76%. That extra 4.76% is the book's hold — its long-run profit margin.
To estimate the true (no-vig) probability the book is pricing, divide each side's implied probability by the sum of both:
52.38 / (52.38 + 52.38) = 52.38 / 104.76 = 50.00%
That 50% is the "fair" no-vig probability — what the line would imply if the book took no commission. Walk through the full method on how to remove vig from odds, or use the no-vig calculator to skip the math.