How odds conversion works
Decimal odds describe the total return per unit staked, including the stake. Decimal odds of 2.50 represent a return of 2.50 on a stake of 1 if the outcome wins.
For positive American odds A, decimal odds are 1 + A / 100. For negative American odds, decimal odds are 1 + 100 / |A|. Fractional odds a/b convert to 1 + a/b. Implied probability is 1 / decimal odds.
Worked example
+150 American, 3/2 fractional, and 2.50 decimal describe the same return. Their implied probability is 40%. An implied probability includes any margin embedded in the price. To estimate margin-removed probabilities, use a complete market in the no-vig calculator.
Questions
Do decimal returns include my stake?
Yes. At 2.50, a winning 10-unit stake returns 25 units, including the original 10.
Why are fractional results approximate?
The converter rounds the fractional profit multiplier to four decimal places before reducing the fraction.
Read the odds format guide and API data conventions before processing prices in an application.