What this calculator does
Implied probability calculator works out the win probability a set of betting odds represents, in whichever format they were quoted: decimal, fractional or American (moneyline). Odds are just probability dressed up in a payout format, and converting back to a percentage is the fastest way to see what a bookmaker is actually claiming.
The figure this calculator returns is not a claim about the true chance of the outcome, only what the quoted odds imply. Bookmakers build a margin, often called the overround, into their prices, so the implied probabilities of every outcome in a market typically add up to more than 100%, with the excess being the bookmaker's built-in edge rather than a genuine reflection of the odds.
The formula
For decimal odds, implied probability is 1 divided by the decimal odds, expressed as a percentage. For fractional odds a/b, it is b divided by (a + b). For American odds, positive odds use 100 divided by (odds + 100), and negative odds use the absolute value of the odds divided by (absolute odds + 100), each expressed as a percentage.
| Term | Meaning |
|---|---|
| Implied probability | The win chance that a set of odds represents, before any bookmaker margin is stripped out. |
| Decimal odds | The total payout per $1 staked, including the original stake, such as 2.50. |
| Overround | The amount by which the sum of implied probabilities across all outcomes in a market exceeds 100%, representing the bookmaker's built-in margin. |
The inputs explained
| Field | What to enter |
|---|---|
| Odds format | Choose the format the odds were quoted in. |
| Decimal odds | Decimal odds, such as 2.50 meaning a $2.50 total return per $1 staked. Used only when the format above is set to decimal. |
| Fractional odds: numerator | The numerator of fractional odds, such as the 6 in 6/4. Used only when the format above is set to fractional. |
| Fractional odds: denominator | The denominator of fractional odds, such as the 4 in 6/4. Used only when the format above is set to fractional. |
| American odds (positive or negative) | American odds, entered as a positive number for an underdog price (e.g. 150 for +150) or a negative number for a favourite price (e.g. -200). Used only when the format above is set to American. |
When to use it
Comparing odds quoted in different formats
A UK-style fractional price and a US-style moneyline price cannot be compared at a glance; converting both to an implied probability puts them on the same scale.
Spotting the bookmaker's margin
Adding up the implied probability of every outcome in a two-way or three-way market and seeing a total above 100% shows the size of the overround built into that market.
Judging whether a bet looks like value
Comparing a bookmaker's implied probability against your own estimate of the true chance is the standard way to judge whether odds look generous or mean, though it never guarantees the outcome.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How implied probability changes with decimal odds
A range of common decimal odds and the win probability each one implies.
| Decimal odds | Implied win probability | Fair payout for a $100 stake at this probability |
|---|---|---|
| 1.50 | 66.7% | $150.00 |
| 2.00 | 50.0% | $200.00 |
| 2.50 | 40.0% | $250.00 |
| 3.00 | 33.3% | $300.00 |
| 5.00 | 20.0% | $500.00 |
| 10.00 | 10.0% | $1,000.00 |
How implied probability changes with American odds
A range of American odds, from a strong favourite to a long-shot underdog.
| American odds | Implied win probability | Equivalent decimal odds |
|---|---|---|
| -300 | 75.0% | 1.33 |
| -150 | 60.0% | 1.67 |
| -110 | 52.4% | 1.91 |
| +100 | 50.0% | 2.00 |
| +150 | 40.0% | 2.50 |
| +300 | 25.0% | 4.00 |
Questions
Why do implied probabilities across a market add up to more than 100%?
Because bookmakers price in a margin, called the overround, on top of their genuine assessment of each outcome's chance. A perfectly fair, margin-free market would sum to exactly 100%; real bookmaker markets almost always sum a little higher.
Is implied probability the same as the real probability of the outcome?
No. It is only what the quoted odds represent, inflated by the bookmaker's margin. The true underlying probability of the event happening could be higher or lower than the implied figure.
How do I convert fractional odds like 6/4 by hand?
Divide the denominator by the sum of the numerator and denominator: 4 ÷ (6 + 4) = 0.40, or 40%. This calculator does the same division for whatever fraction is entered.
What does negative American odds mean?
Negative American odds show how much needs to be staked to win $100, and always apply to the favourite in a market. Positive American odds show how much a $100 stake would win, and apply to the underdog.
For the probability of a specific poker hand outcome instead of a quoted market price, see the poker odds calculator. For the odds on a specific roulette bet, see the roulette odds calculator.