What is implied probability?

Explained, with an example

Example: decimal odds of 2.50 imply 1 / 2.50 = 40%; American +150 implies 100 / 250 = 40%; American −200 implies 200 / 300 ≈ 66.7% ^{[1] [2]}. Across all outcomes of a bookmaker market the figures add up to more than 100%; the excess is the Overround. Comparing implied probabilities across venues is the basis of value and Arbitrage analysis.

Formula

decimal: p = 1 / odds
American +A: p = 100 / (A + 100)
American −A: p = A / (A + 100)
fractional a/b: p = b / (a + b)

Related terms

• Decimal, American and fractional odds — Decimal, American and fractional odds are three ways of writing the same price: decimal shows the total return per 1 staked, American shows profit on 100 (or stake needed to win 100), and fractional shows profit relative to stake.
• Overround (vig, juice, margin) — The overround is the amount by which a bookmaker market's implied probabilities exceed 100%; it is the bookmaker's built-in margin, also called the vig or juice.
• Expected value (+EV) — Expected value is the average result per unit staked if the same bet could be repeated many times; a positive-EV (+EV) price is one above your fair-odds estimate.
• Arbitrage (arb) — Arbitrage is a price gap across venues where the best available odds for every outcome imply a combined probability below 100%, so covering all outcomes locks in the same return whatever happens (at the quoted prices).

Try it: tools and tutorials

• Odds converter
• Implied probability & no-vig calculator
• Arbitrage and +EV finder with Odds-API.io
• Prediction-market prices vs bookmaker odds

Frequently asked questions