Odds to probability converter, both directions, with vig removal

How the conversion works

Every notation on this page carries the same information: how likely an outcome is. A prediction-market share at 0.65, an implied probability of 65%, decimal odds of 1.54 — called European odds outside the United States — American odds of −186 and fractional odds of 4/7 are five ways of writing one number. Betting odds and prediction-market prices differ in presentation, not in arithmetic, which is why the same converter handles both.

The formula

probability   p = 1 / decimal
decimal       d = 1 / p
american      a = −100·p / (1 − p)      when p ≥ 0.5
              a =  100·(1 − p) / p      when p < 0.5
fractional    n / m  chosen so that  n / m ≈ d − 1
overround     s = p_yes + p_no
fair (prop.)  p_yes / s
fair (add.)   p_yes − (s − 1) / 2

Decimal odds are the easiest to reason about: they are the total return per unit staked, stake included, so the reciprocal is the implied probability and nothing else needs to be remembered. American odds are the awkward one. Above even money they are negative and read as the stake required to win 100; below even money they are positive and read as the profit on a stake of 100. The convention has no value at exactly ±100 that both branches agree on, so the tool writes even money as −100.

Fractional odds express profit against stake rather than total return, which is why 3/1 and decimal 4.0 are the same price. Converting the other way is less obvious than it looks, because most probabilities do not land on a tidy fraction. Rounding the decimal part to two places would turn 4.33 into 433/100, which no one writes. The converter instead searches for the simplest fraction close to the value, using the continued-fraction expansion, so 4.33 comes back as 10/3.

The second panel handles the part that most converters skip. A two-sided market where both sides can be taken should have prices that sum to exactly 1: buy both and you are guaranteed to receive exactly 1 at resolution. In practice the sum is above 1. On a sportsbook the excess is the stated margin. On a prediction market it is mostly the spread — you cross to the offer on each side, and the two offers do not meet. Either way, the excess is what you pay for the round trip, and it is the reason a price is not a probability.

What the formula assumes

Removing it is called de-vigging, and there is more than one defensible way to do it. The proportional method divides each side by the total, which assumes the margin is charged in proportion to each price. The additive method subtracts half the excess from each side, which assumes it is charged evenly. They agree near even money and diverge at long odds, sometimes by several points on the outsider. The tool shows both rather than picking one and hiding the choice, because the gap between them is itself a measure of how uncertain the fair price is.

What the de-vigged number is for: comparing your own estimate against the market on equal terms. Your estimate has no margin in it, so comparing it to a price that does will make you think you have an edge when you are merely looking at the spread. Comparing it to the de-vigged probability tells you whether you disagree with the market. Whether that disagreement survives the cost of crossing the spread is a separate question, and the price you actually pay is the offer, not the fair value.

None of these conversions include fees. Trading fees, gas costs on on-chain venues, withdrawal costs and the price impact of your own order all sit outside the arithmetic, and on small edges they are frequently larger than the edge itself. Treat the output as the quoted price of a probability, not as the cost of owning it.

Questions

Is a Polymarket price the same thing as a probability?

Almost. A share pays 1 if the outcome happens and 0 if it does not, so its price is the market's probability plus the cost of trading it. The price you pay to enter includes the spread, which is why the two sides of a market usually sum to slightly more than 1. De-vigging removes that part and leaves the market's probability.

Why do decimal and American odds disagree at even money?

They do not disagree, the notation does. At a probability of exactly 0.5 the two American formulas both produce 100, and the sign convention is ambiguous. Market convention writes even money as −100, so the converter does the same. Decimal odds have no such ambiguity: even money is 2.0.

Which de-vigging method should I use?

Proportional removal is the common default and the one shown as the main output. It preserves the ratio between the two sides, which is usually what you want when the market is roughly balanced. The additive method treats the margin as a flat charge and tends to be kinder to the long side. If the two disagree materially for your market, that disagreement is a warning that the fair price is less well determined than a single number suggests.

How do I convert odds to probability by hand?

For decimal odds, divide one by the odds: 2.50 becomes 1 / 2.50 = 0.40, or 40%. For fractional odds, divide the denominator by the sum of both numbers: 3/1 becomes 1 / (3 + 1) = 25%. For American odds, a negative number a gives −a / (−a + 100) and a positive number gives 100 / (a + 100). Converting probability to odds is the same arithmetic run backwards. The calculator does it in both directions so you do not have to pick the right formula.

Background

What this calculation is actually measuring

The calculator does the arithmetic. The guide explains the mechanism underneath it: where the number comes from, what has to be true for it to hold, and the point at which it stops describing the market in front of you. If you are going to act on a figure this page produced, that is the page to read first.