Enter American odds (positive or negative) to convert to implied probability, or enter a probability percentage to reverse-calculate the equivalent American odds.
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Implied Probability Formula
The formula differs by odds format. American odds require two separate equations depending on whether the line is positive or negative. Decimal and fractional odds each use a single equation.
American Odds (Moneyline)
P_{-} = \frac{|O|}{|O|+100}\times 100 P_{+} = \frac{100}{O + 100}\times 100 - Where P- is the implied probability when the odds are negative
- P+ is the implied probability when the odds are positive
- O is the American odds value (use the absolute value for negative odds; e.g., for -250 use 250)
Decimal Odds
P = \frac{1}{D} \times 100- Where D is the decimal odds value (e.g., 1.91 for -110, or 3.00 for +200)
Fractional Odds
P = \frac{b}{a + b} \times 100- Where fractional odds are written as a/b (e.g., for 3/1: a=3, b=1, giving P = 1/4 x 100 = 25%)
Implied Probability Definition
Implied probability is the win percentage embedded in a bookmaker’s odds. It tells you the break-even win rate required to profit at those odds, before accounting for the bookmaker’s margin. Because sportsbooks build a profit margin (the vig or overround) into every market, the sum of implied probabilities across all outcomes in a market exceeds 100%, not exactly 100%. That excess is the bookmaker’s edge on every dollar wagered.
Implied Probability Example
How to calculate implied probability?
- First, determine if the odds are positive or negative.
For this example, we will say the odds are positive (a + sign in front of the number).
- Next, determine the odds value.
For this example we will say they are +500.
- Finally, calculate the implied probability.
Using the formula above we find the % chance of success of the bet to be 100/(500+100)*100 = 16.67%.
Common Odds Reference Table
The table below converts the most common American odds to decimal, fractional, and implied probability. The implied probability column is also the break-even win rate at those odds.
| American Odds | Decimal Odds | Fractional Odds | Implied Probability |
|---|---|---|---|
| -500 | 1.20 | 1/5 | 83.33% |
| -400 | 1.25 | 1/4 | 80.00% |
| -300 | 1.33 | 1/3 | 75.00% |
| -250 | 1.40 | 2/5 | 71.43% |
| -200 | 1.50 | 1/2 | 66.67% |
| -150 | 1.67 | 2/3 | 60.00% |
| -130 | 1.77 | 10/13 | 56.52% |
| -120 | 1.83 | 5/6 | 54.55% |
| -115 | 1.87 | 20/23 | 53.49% |
| -110 | 1.91 | 10/11 | 52.38% |
| +100 | 2.00 | 1/1 | 50.00% |
| +110 | 2.10 | 11/10 | 47.62% |
| +120 | 2.20 | 6/5 | 45.45% |
| +130 | 2.30 | 13/10 | 43.48% |
| +150 | 2.50 | 3/2 | 40.00% |
| +200 | 3.00 | 2/1 | 33.33% |
| +250 | 3.50 | 5/2 | 28.57% |
| +300 | 4.00 | 3/1 | 25.00% |
| +400 | 5.00 | 4/1 | 20.00% |
| +500 | 6.00 | 5/1 | 16.67% |
Vig, Overround, and Fair Odds
Sportsbooks price both sides of a market so that the implied probabilities sum above 100%. The excess is the overround (also called vig or juice), representing the bookmaker’s built-in profit margin regardless of which side wins.
For a standard -110/-110 point spread: each side carries a 52.38% implied probability, so the total is 104.76%. The overround is 4.76%, and the effective vig on each -110 wager is 4.55% of the amount bet.
To find the fair (no-vig) probability for a two-outcome market, divide each side’s implied probability by their combined total:
P_{fair} = \frac{P_{implied}}{P_A + P_B} \times 100For -110/-110: fair probability = 52.38 / 104.76 = 50.00% per side, equivalent to +100 (even money) on both. For a -150/+130 line: P_A = 60.00%, P_B = 43.48%, sum = 103.48%. Fair P_A = 60.00 / 103.48 = 57.98% (fair line approximately -138), fair P_B = 43.48 / 103.48 = 42.02% (fair line approximately +138).
Betting exchanges such as Betfair charge a flat commission (typically 2 to 5%) instead of embedding a margin into the odds, resulting in overrounds far closer to 100% than traditional sportsbooks.
FAQ
Implied probability is the win percentage built into a bookmaker’s odds. It tells you how often an outcome must occur for a bet at those odds to break even. It is called implied because it is derived from the odds, not from any independent analysis of the event.
Odds of -110 mean you must wager $110 to win $100 profit. The implied probability is 52.38%, which is the break-even win rate. On a standard point spread or total, both sides are priced at -110, so the bookmaker collects a 4.76% overround on the market.
The vig (short for vigorish, also called juice) is the commission a bookmaker charges on each bet. It is built into the odds so that the sum of implied probabilities across all outcomes in a market exceeds 100%. On a -110/-110 line the vig is approximately 4.55% of each wager. Removing the vig gives the fair (no-vig) probability.
A value bet occurs when your estimated probability for an outcome is higher than the implied probability in the bookmaker’s odds. For example, if you believe a team has a 55% chance to win but the implied probability from the posted odds is only 50%, you have identified positive expected value. Professional bettors target value bets and are highly selective, often finding value in fewer than 10% of available markets.
For a probability above 50% (favorite): American odds = -(P / (100 – P)) x 100. For a probability below 50% (underdog): American odds = ((100 – P) / P) x 100. For example, a 60% implied probability gives -(60/40) x 100 = -150. A 40% implied probability gives (60/40) x 100 = +150. The calculator above handles this conversion automatically in both directions.
