# What is the implied probability?

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.

- Page: https://www.acalculator.org/game/implied-probability-calculator
- JSON spec: https://www.acalculator.org/game/implied-probability-calculator.json
- Version: 7bc5a713aae3

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| format | Odds format | The format of the odds you type: American, decimal, or fractional. |
| odds | Odds | The odds in the chosen format, for example −110, 1.91, or 10/11. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| probability | Implied probability | The win chance the odds imply: 1 ÷ decimal odds, in percent. |
| against | Chance of losing | The chance the odds imply that the bet loses: 100% − implied probability. |
| oddsFor | Odds in favour | The implied chances of winning to losing as a ratio of whole numbers in lowest terms. |
| oddsAgainst | Odds against | The implied chances of losing to winning as a ratio of whole numbers in lowest terms. |
| oneIn | One win in | The decimal odds: the number of tries per win that the odds imply on average. |

## 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).

## Assumptions

- 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

1. format = american, odds = -110 gives probability = 52.380952%, against = 47.619048%, oddsFor = 11 to 10, oddsAgainst = 10 to 11, oneIn = 1.909091. Source: hand calculation in content.mdx: d = 21/11; 11/21 = 52.380952…%.
2. format = american, odds = +300 gives probability = 25%, against = 75%, oddsFor = 1 to 3, oddsAgainst = 3 to 1, oneIn = 4. Source: hand calculation in content.mdx: d = 4; 1 ÷ 4 = 25%.
3. format = fractional, odds = 6/4 gives probability = 40%, oddsFor = 2 to 3, oddsAgainst = 3 to 2. Source: hand calculation in content.mdx: 6/4 = 3/2, d = 5/2; 2/5 = 40%.
4. format = decimal, odds = 1.25 gives probability = 80%, against = 20%, oddsFor = 4 to 1. Source: hand calculation in content.mdx: 1 ÷ 1.25 = 80%; d − 1 = 1/4.

## FAQ

### 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.

## Sources

- Grinstead and Snell, Introduction to Probability, 2nd ed., American Mathematical Society, section 1.2, odds and probabilities (page 28): https://math.dartmouth.edu/~prob/prob/prob.pdf
- Wikipedia, Fixed-odds betting (fractional, decimal and moneyline odds, overround): https://en.wikipedia.org/wiki/Fixed-odds_betting
- National Council on Problem Gambling, help and treatment (1-800-MY-RESET): https://www.ncpgambling.org/help-treatment/