Odds, Probability & Bankroll

Implied probability

Implied probability is the chance of an outcome as expressed by betting odds, representing the bookmaker's or market's estimate encoded in those odds.

Formula (fractional odds a/b): b / (a + b)¹
Formula (decimal odds D): 1 / D¹
Formula (American odds, negative): |odds| / (|odds| + 100)²
Formula (American odds, positive): 100 / (odds + 100)²
Example (6–4 fractional): 4 / (6 + 4) = 0.4 or 40%¹

Key points

Implied probability converts odds into a percentage so you can read the market's estimated chance of an event.¹³
It is the bookmaker's estimate, not the true probability of the outcome.³⁴
For fractional odds a/b, the formula is b/(a+b); for decimal odds D, it is 1/D.¹
For American odds, use |odds|/(|odds|+100) for negative odds and 100/(odds+100) for positive odds.²

Implied probability examples

How common odds formats convert to implied probability.
Odds format	Odds	Implied probability
Fractional	6–4	40%¹
Decimal	2.50	40%
American (negative)	-150	60%²
American (positive)	+200	33.33%²

Common questions

What is implied probability in sports betting?

Implied probability in sports betting is the chance of an outcome as expressed by the odds. It shows the bookmaker's estimate of how likely an event is to happen.¹³

What is the implied probability of odds?

The implied probability of odds is the percentage derived from converting those odds using a formula. For example, fractional odds of 6–4 give an implied probability of 40%.¹

How to calculate implied probability?

To calculate implied probability, use the formula for the odds format. For fractional odds a/b, compute b/(a+b). For decimal odds D, compute 1/D. For American odds, use |odds|/(|odds|+100) for negative odds, or 100/(odds+100) for positive odds.¹²

Where this term is used

Odds and probability

Odds & probability Implied probability vs true probability Explains the difference between the odds-based estimate and the actual chance of an event. Odds & probability Implied probability vs actual probability Compares the bookmaker's implied estimate with the real-world frequency of an outcome. Odds & probability American odds to implied probability Step-by-step guide to converting American odds into an implied probability percentage. Odds & probability Probability vs possibility Clarifies the distinction between mathematical probability and mere possibility. Odds & probability Odds vs probability Explains how odds and probability are different ways of expressing the same likelihood. Odds & probability Likelihood vs probability Distinguishes likelihood, a statistical concept, from probability in betting contexts.

Sources

Mathematics of bookmaking en.wikipedia.org Provides the standard formulas for converting fractional and decimal odds to implied probability.
Player Props: Understanding the Math Behind the Lines wizardofodds.com Supplies the formulas for American odds conversion and example calculations.
Machine Learning for the Prediction of Professional Tennis ... doc.ic.ac.uk Confirms that implied probability is the bookmaker's estimate, not the true probability.
Odds en.wikipedia.org Supports the distinction between implied probability and true probability.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.