Implied probability
The probability an odds price represents, calculated as one divided by the decimal odds, before the bookmaker's margin is removed.
Implied probability converts odds into the chance they represent. The core formula with decimal odds is p = 1/d. For American odds: p = 100/(A + 100) for positive A, and p = |A|/(|A| + 100) for negative A. For fractional odds n/m: p = m/(n + m).
Example: tennis pair
Illustrative: 1.40 and 2.95.
- 1/1.40 = 71.43%
- 1/2.95 = 33.90%
- Sum: 105.33%, so the market carries a 5.33% overround.
Removing the margin proportionally: 71.43/105.33 = 67.8% and 32.2%. Fair odds: 1.47 and 3.11.
Converting the other way
Fair odds = 1/p. A 36.36% chance corresponds to 2.75; a 20% chance to 5.00.
Why it matters
Expected value per unit staked is p_true × d minus 1. At 2.95, you need a true probability above 1/2.95 = 33.9% for a positive expected value. If you estimate 36%, EV = 0.36 × 2.95 minus 1 = +6.2%.
A note on precision
Implied probability is only as good as the price. Thin markets with low limits can be priced loosely, and closing line value is often a better check of whether a price was accurate.