What is the implied probability?
Enter the odds of a bet to see the win chance they stand for. The results are mathematics, not betting advice.
- Implied probability
- 52.38%
Odds of -110 imply a win chance of 52.38% (11 to 10 in favour).
- Chance of losing
- 47.619%
- Odds in favour
- 11 to 10
- Odds against
- 10 to 11
- One win in
- 1.91
Implied probability: 52.38%. Odds of -110 imply a win chance of 52.38% (11 to 10 in favour).
The results are maths only. They are not betting advice or a promise of a return. Bet only what you can afford to lose. For help with gambling, call 1-800-GAMBLER. Terms of use
How to calculate
Computes the implied probability of American, decimal or fractional betting odds, the chance of losing, and the odds for and against as whole-number ratios.
Example with the default inputs (Odds format American, Odds -110): Odds of -110 imply a win chance of 52.38% (11 to 10 in favour).
Method: Implied probability = 100 ÷ d percent, where d is the decimal odds (American +A: 1 + A ÷ 100; −A: 1 + 100 ÷ A; fractional a/b: 1 + a ÷ b).
- The implied probability includes the bookmaker’s margin, so it is usually higher than the true chance.
- The odds for and against are exact: 1 to (d − 1), written in lowest whole numbers.
- Results are mathematics, not betting advice.
Worked examples
Each example is checked against the calculator on every build.
- Odds format American, Odds -110 gives Implied probability 52.380952%, Chance of losing 47.619048%, Odds in favour 11 to 10, Odds against 10 to 11, One win in 1.909091.Source: hand calculation in content.mdx: d = 21/11; 11/21 = 52.380952…%
- Odds format American, Odds +300 gives Implied probability 25%, Chance of losing 75%, Odds in favour 1 to 3, Odds against 3 to 1, One win in 4.Source: hand calculation in content.mdx: d = 4; 1 ÷ 4 = 25%
- Odds format Fractional, Odds 6/4 gives Implied probability 40%, Odds in favour 2 to 3, Odds against 3 to 2.Source: hand calculation in content.mdx: 6/4 = 3/2, d = 5/2; 2/5 = 40%
- Odds format Decimal, Odds 1.25 gives Implied probability 80%, Chance of losing 20%, Odds in favour 4 to 1.Source: hand calculation in content.mdx: 1 ÷ 1.25 = 80%; d − 1 = 1/4
How it works
First the odds become decimal odds d, the total return for each 1 staked. The calculator keeps d as an exact fraction.
| You type | Decimal odds d |
|---|---|
| American +A (A ≥ 100) | d = 1 + A ÷ 100 |
| American −A (A ≥ 100) | d = 1 + 100 ÷ A |
| Fractional a/b | d = 1 + a ÷ b |
| Decimal d | d |
Then:
- Implied probability = 100 ÷ d percent.
- Chance of losing = 100% − implied probability.
- Odds in favour = 1 to (d − 1). With d − 1 written in lowest terms as n/m, this is m to n.
- Odds against = n to m.
- One win in = d.
What you can type: spaces are ignored and − reads as -. Each format has its own shape, so odds typed in another format are never read as this one: the page says which format they are in and gives the same price in the chosen format. American odds have a + or − sign and a size of at least 100 (+150, -110, +1,000; commas are thousands commas). Decimal odds are a plain number above 1 with no sign (2.5); a single comma with no point is a decimal comma (2,5 is 2.5) unless exactly 3 digits follow it (1,000 is 1000), and any other comma is a thousands comma. Fractional odds are a/b, a:b, a-b or a to b with a and b above 0, or evens, even or evs (any letter case, to too); a bare number is not fractional odds. A number with no sign typed as American odds (100 or more), a whole number typed as fractional odds, or a number below 100 typed as a probability gets a message saying what to add (+150, 4/1, 40%). Decimal odds above 1,000,001 (American +100,000,000) give no answer.
Assumptions
- Implied probability includes the bookmaker’s margin.
- The ratios are exact. Only the shown decimals are rounded.
Worked examples by hand
American −110. d = 1 + 100 ÷ 110 = 21/11. Implied probability = 11/21 = 52.38%; chance of losing 47.62%. d − 1 = 10/11, so the odds in favour are 11 to 10 and against 10 to 11. One win in 1.91.
American +300. d = 1 + 300 ÷ 100 = 4. Implied probability = 1 ÷ 4 = 25%; chance of losing 75%. d − 1 = 3/1: 1 to 3 in favour, 3 to 1 against. One win in 4.
Fractional 6/4. 6/4 = 3/2, so d = 5/2 and the implied probability is 2/5 = 40%. In favour 2 to 3, against 3 to 2.
Decimal 1.25. Implied probability = 1 ÷ 1.25 = 80%, chance of losing 20%. d − 1 = 1/4, so the odds in favour are 4 to 1.
A note on betting
These results are mathematics, not advice. Every bet can lose, and the odds include the bookmaker’s margin. If gambling is causing problems for you or someone you know, the US National Problem Gambling Helpline is 1-800-MY-RESET (call or text).
Other questions people ask
How do I calculate implied probability from American odds?
Turn the odds into decimal odds, then divide 1 by them. For −110, the decimal odds are 1 + 100 ÷ 110 = 1.9091, and 1 ÷ 1.9091 = 52.38%. For +300, the decimal odds are 4, and 1 ÷ 4 = 25%.
How do I calculate implied probability from fractional odds?
For odds a/b, the implied probability is b ÷ (a + b). For 6/4, it is 4 ÷ 10 = 40%. For 1/4 (a heavy favourite), it is 4 ÷ 5 = 80%.
Why do the probabilities of both sides add up to more than 100%?
The bookmaker builds a margin (the vig or overround) into the odds. With −110 on both sides of a game, each side implies 52.38%, which adds up to 104.76%. The 4.76 extra points are the margin. The no-vig calculator removes it.
Is implied probability the real chance of winning?
No. It is the chance the price stands for, including the margin. The true chance is unknown. Removing the margin gives a fairer estimate of what the market expects, but it is still an estimate.
What does "odds against" mean?
It compares the chance of losing with the chance of winning. Fractional odds 3/2 are "3 to 2 against": for every 5 equal chances, 3 lose and 2 win, so the implied probability is 2 ÷ 5 = 40%.
What does the "one win in" number mean?
It is the decimal odds: at 25% the odds imply one win in 4 tries on average. It is an average over many tries, not a promise about any run of bets.