Implied Probability: Turning Odds Into a Percentage
Implied probability turns betting odds into a win percentage. The three conversion formulas for decimal, American, and fractional odds, with worked math.
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Implied probability is the win percentage hidden inside a set of odds — the frequency an outcome must hit for the price to break even. Decimal 2.00 means 50%; American +150 means 40%. Each odds format is just a different notation for that one number, and three short formulas cover all of them.
Decimal odds
Decimal odds state the total return per unit staked, so the conversion is one division:
implied probability = 1 ÷ decimal
2.00→1 ÷ 2.00 = 50%1.50→1 ÷ 1.50 = 66.7%4.00→1 ÷ 4.00 = 25%
Shorter price, higher probability. A heavy favorite pays little because it’s expected to win often.
American odds
Positive and negative American prices each get their own equation. For a positive price (the underdog), the number is your profit on a 100 stake:
implied probability = 100 ÷ (odds + 100) — so +150 gives 100 ÷ 250 = 40%.
For a negative price (the favorite), the number is what you stake to win 100:
implied probability = odds ÷ (odds + 100) — so -200 gives 200 ÷ 300 = 66.7%.
Fractional odds
Fractional odds are written profit-to-stake, so you put the stake over the whole:
implied probability = denominator ÷ (numerator + denominator)
3/1 → 1 ÷ 4 = 25%; 5/2 → 2 ÷ 7 = 28.6%; 1/2 → 2 ÷ 3 = 66.7%.
| Decimal | American | Fractional | Implied |
|---|---|---|---|
| 1.50 | -200 | 1/2 | 66.7% |
| 2.00 | +100 | 1/1 | 50% |
| 2.50 | +150 | 3/2 | 40% |
| 3.00 | +200 | 2/1 | 33.3% |
| 4.00 | +300 | 3/1 | 25% |
Any row reads the same probability four ways; the last column is the only one that drives a decision.
Why a real market sums past 100%
A true 50/50 event has fair odds of +100 a side, and two 50% figures sum to a clean 100%. A book shades that, pricing both sides at -110: 110 ÷ 210 = 52.4% each, totaling 104.8%. Probabilities can’t exceed 100%, so the surplus 4.8% is the vig — the house margin. Divide each side by the total to recover the fair number: 52.4% ÷ 104.8% = 50%. Strip that margin before you trust any single side, or you’ll overstate how likely each outcome really is.
The same test runs the poker table. Your pot odds are an implied probability — a half-pot call needs 25% equity, the implied figure of a 3.00 price. You commit chips when your read beats what the price implies, the identical edge a bettor hunts. (Note this differs from poker implied odds, which count future chips, not a percentage.) More of the same math sits in the poker odds & math hub, ready for the Hold’em felt.