Market maths
Odds converter
The same price is written five different ways depending on where you are and what you are betting on. Decimal dominates in Europe and on exchanges, fractional persists in British and Irish racing, American moneyline is standard in the United States, and Hong Kong and Malay formats are common across Asian markets.
This converter takes any of them and returns the rest, along with the probability the price implies. Decimal is used as the canonical form internally because it is the only format in which the arithmetic is linear — returns are simply stake multiplied by price, which is why every other calculation on this site works in decimal and converts at the edges.
Inputs
Result
- Decimal
- 3.500
- FractionalNearest tidy fraction — see the note below on why this is approximate
- 5/2
- American / moneyline
- +250
- Hong Kong
- 2.500
- Malay
- -0.400
- Implied probabilityIncludes the bookmaker margin, so it overstates the true chance
- 28.57%
The implied probability of a single price is not an estimate of the real chance — it includes the margin built into that price. To recover what a set of prices implies about actual outcomes, use the overround calculator on the complete market.
How this is calculated
decimal = 1 + net return per unit probability = 1 / decimal American: +a -> a/100 + 1, -a -> 100/a + 1
Every format encodes the same thing — the return per unit staked — and differs only in whether the stake is included and what the unit is. Decimal includes the stake, so 3.50 returns 3.50 for every 1 staked. Fractional and Hong Kong exclude it: 5/2 and 2.50 both mean a net profit of 2.50 per 1 staked, which is decimal 3.50. American expresses the same relationship against a 100 unit, positive when the net return exceeds the stake and negative when it does not, which is why the sign flips at decimal 2.00. Malay is Hong Kong for prices up to even money and its negative reciprocal above, so it also flips at 2.00. Implied probability is simply the reciprocal of the decimal price.
Worked example
Converting a price of 5/2 into every other format.
- 01Fractional 5/2 means a net profit of 5 for every 2 staked, i.e. 2.5 per unit.
- 02Decimal adds the stake back: 5 / 2 + 1 = 3.50.
- 03Hong Kong drops the stake again: 3.50 - 1 = 2.50.
- 04American, for a price above 2.00, is the net return per 100 staked: (3.50 - 1) x 100 = +250.
- 05Malay, for a price above 2.00, is the negative reciprocal of the net return: -1 / 2.50 = -0.40.
- 06Implied probability: 1 / 3.50 = 28.57%.
Questions
Why is the fractional conversion approximate?
Most decimal prices have no tidy fractional equivalent. A price of 3.47 is 247/100 exactly, which no bookmaker would ever display. The converter searches for the closest fraction with a small denominator, which is what a bookmaker does when it prices in fractions — so a fractional price converted to decimal and back will not always return the number you started with.
Why do American and Malay odds change sign at 2.00?
Both express the price relative to an even-money benchmark. At decimal 2.00 the net return equals the stake, so the two directions meet. Above it the selection is an underdog and the formats show the profit on a fixed stake; below it the selection is a favourite and they show the stake needed for a fixed profit.
Is the implied probability the real chance of the outcome?
No. It is what the price implies before removing the bookmaker margin, so it is always higher than the bookmaker's own view of the true chance. Add up the implied probabilities of every outcome in a market and the total exceeds 100% — that excess is the margin, and stripping it out is a separate calculation.
Related calculators
These calculators are information tools. They describe the arithmetic of the prices you enter — they are not advice, and they do not predict outcomes. Betting involves risk. 18+ only. If gambling is causing you harm, support is available from Peluuri.