How to Convert Betting Odds to Probability

To convert decimal betting odds to an implied probability, divide 1 by the odds. Multiply by 100 to express the result as a percentage. For example, odds of 2.00 imply 50%, while 1.45 implies about 68.97%. This gives the probability encoded in one quoted price, which can include bookmaker margin.

For a single price in decimal, American or fractional format, the calculator linked below performs the conversion instantly. This guide explains the formulas, the reverse probability-to-odds conversion, and why removing bookmaker margin is a separate complete-market calculation.

Open the Implied Probability Calculator →

With decimal odds, the raw implied probability of an outcome is:

raw implied probability = 1 / decimal odds

raw implied probability (%) = 100 / decimal odds

Odds of 4.00 imply 25%. At odds of 1.45, 100 / 1.45 ≈ 68.97%. Neither conversion tells you how much margin is included in that outcome. For payout conventions and the differences between odds formats, see how betting odds work.

To convert American odds to probability, use a different formula for positive and negative prices:

positive American: probability = 100 / (odds + 100)

negative American: probability = |odds| / (|odds| + 100)

For example, +150 converts to 40.00%, while −200 converts to 66.67%.

For fractional odds a/b, convert odds to probability with b / (a + b). Fractional odds of 3/2 therefore imply 40.00%.

For an instant conversion across decimal, American and fractional formats, use the Implied Probability Calculator.

To convert a probability back to decimal odds, write the percentage as a decimal and take its reciprocal:

decimal odds = 1 / probability

For example, 40% = 0.40, so 1 / 0.40 = 2.50. The same price is equivalent to American odds of +150 and fractional odds of 3/2.

The Implied Probability Calculator performs this conversion in both directions and shows the equivalent decimal, American and fractional formats.

Convert every mutually exclusive outcome in a complete market to a raw probability, then add the results. This total is the booksum. In a standard positive-overround bookmaker market, it exceeds 100%. The excess above 100% is the overround, often called vig. “Margin” is sometimes used loosely for the same concept, but margin expressed as a share of booksum is a different quantity.

Q = sum of raw probabilities expressed as decimals

overround (%) = (Q − 1) × 100

margin as share of booksum (%) = ((Q − 1) / Q) × 100

Use prices from the same bookmaker at the same time, with matching settlement rules. For 1X2, include home, draw and away. For over/under 2.5, include both sides of the line. Prices collected from different bookmakers or promotions can sum to 100% or less.

Overround describes the quoted prices. Margin as a share of booksum equals the bookmaker's theoretical hold on turnover when stakes are balanced across outcomes; actual realized profit still depends on stake distribution and liabilities. The No-Vig Calculator compares the main margin-removal methods.

Proportional devigging, also called normalization or the multiplicative method, divides each raw probability by the booksum:

proportional no-vig probability = raw implied probability / Q

This rescales the probabilities to sum to 100% and preserves their ratios. It assumes the same relative margin adjustment across outcomes: each raw probability is multiplied by the same factor, 1 / Q. It does not subtract the same number of percentage points from every outcome.

The method is the baseline used by ImpliedScore. Other methods allocate the overround differently, so they can produce different no-vig estimates from the same prices. For the next step from normalized odds to a score matrix, see the methodology page.

Open the No-Vig Calculator →

Take a home favourite priced at 1.45 / 4.70 / 8.60 (home / draw / away).

The booksum is Q ≈ 101.87%, so the overround is about 1.87%. Dividing the home raw probability by the booksum gives a proportional no-vig estimate of approximately 67.70%.

Applying the same calculation to draw and away gives 20.89% and 11.41%. These three no-vig estimates add up to 100.00% at the displayed precision.

Calculate with unrounded probabilities and booksum, then round only the displayed results.

For an over/under 2.5 line priced at 2.24 / 1.71, the two outcomes cover all possible total-goal results without a push:

• Raw over probability: 1/2.24 ≈ 44.64%.
• Raw under probability: 1/1.71 ≈ 58.48%.
• Booksum: about 103.12%; overround: about 3.12%.
• Proportional no-vig probabilities: over 43.29%, under 56.71%.

Use the same line and settlement period for both prices. A whole-goal line such as 2.0 can return the stake on exactly two goals; those prices alone do not identify the push probability.

Normalized 1X2 and totals probabilities can then serve as targets for fitting a correct-score probability map.

The quoted odds do not uniquely reveal how the bookmaker distributed its margin. Proportional normalization is one explicit assumption. Shin, power, additive and odds-ratio methods use different assumptions, and the differences can matter more in markets with high overround or long-priced outcomes.

A distribution that sums to 100% is not automatically accurate. A no-vig estimate can still differ from the actual chance of an outcome. Assessing accuracy requires historical forecasts and results, with probabilities recorded before each event.

After converting a complete football market, the football score probability calculator fits home and away goal rates and builds a score matrix. It uses 1X2 odds, with optional over/under 2.5 prices, to estimate scoreline probabilities and derived markets.

Open the score calculator →