Implied Probability Calculator
Convert American, decimal or fractional odds into an implied probability, with every step shown. Switch modes to turn a probability back into odds, strip the margin out of a full market, or compare your own estimate with the break-even rate.
What this implied probability calculator does
Implied probability is the probability that a quoted betting price assumes. A price of -110 implies a 52.38% chance, a price of +200 implies 33.33%, and decimal odds of 2.00 imply 50%. The calculator turns a price into that percentage, and it shows the equivalent odds in the other two formats alongside it.
Short answer: positive American odds give 100 ÷ (odds + 100), negative American odds give |odds| ÷ (|odds| + 100), decimal odds give 1 ÷ odds, and fractional odds n/d give d ÷ (n + d). For a standard win-or-lose bet, the result is also the break-even win rate.
The first mode converts the odds on a single outcome. The second goes the other way, from a probability to odds. The third takes the prices for every outcome in a market, shows how far their implied probabilities exceed 100%, and scales them back to give no-vig probabilities. The fourth compares an estimate of your own with the break-even rate of a price. For the odds as a ratio of chances for and against, use the Odds Calculator.
What to enter, and what not to
Enter the price attached to the bet, as it appears on a moneyline, a spread, a total or a player prop. The number that defines the line is not a price. For a bet on a team to cover -3.5 at -110, the figure to enter is -110. The -3.5 is the spread and has no place in the calculator, and the same goes for a total of 47.5 or a player's stat line of 24.5 points. The calculator converts odds to probability and stops there. It does not work out payouts, suggest stake sizes or compare sportsbooks.
- American odds need their sign. +110 and -110 are different prices, so a bare 110 is rejected rather than guessed. Only 100 can be typed without a sign, because +100 and -100 both mean even money. American odds cannot lie between -100 and +100.
- Decimal odds must be greater than 1. They include the returned stake, so 2.50 pays 2.50 for every 1 staked, a profit of 1.50.
- Fractional odds are profit over stake. 5/2 pays 5 for every 2 staked. Type evens for 1/1. Both parts must be above zero.
- Probabilities can be percentages, decimals or fractions. Type 55%, 0.55 or 11/20, or pick the plain-number setting. A probability of exactly 0% or 100% has no finite odds and is rejected.
- Implied probability, p
- The probability a price assumes, as a fraction from 0 to 1 or as a percentage. It is a property of the price, not a measured chance.
- Odds (A, D, n/d)
- A, D and n/d are the same price written in American, decimal and fractional form. A is the American value, D is the decimal value, and n and d are the profit and stake parts of a fraction.
- Absolute value, |A|
- The size of a number without its sign. The odds -150 have an absolute value of 150, which is the number that goes into the formula.
- Break-even win rate
- The share of bets that must win for a bettor to finish level at that price. For a win-or-lose bet it equals the implied probability.
- Vig, vigorish, juice
- Three names for the margin a sportsbook builds into its prices. It shows up as implied probabilities that total more than 100%.
- Overround and hold
- Overround is the amount by which the implied probabilities exceed 100%. Hold is the share of total money wagered that the sportsbook keeps if bets on all outcomes are balanced. They are related but not the same number.
- No-vig (fair) probability
- An implied probability rescaled so that all outcomes total 100%. It is a market-based estimate, not a verified true probability.
Implied probability formulas
Each odds format has its own conversion, and American odds need two because the sign changes what the number means. Positive odds are the profit on a stake of 100. Negative odds are the stake needed to win 100, so the absolute value of the odds is what enters the formula.
- Positive American odds (+A): p = 100 ÷ (A + 100)
- Negative American odds (−A): p = |−A| ÷ (|−A| + 100), using the absolute value of the odds
- Decimal odds (D): p = 1 ÷ D, with D greater than 1
- Fractional odds (n/d, profit over stake): p = d ÷ (n + d)
- Percentage = p × 100
- Overround = (sum of all implied probabilities) − 1
- No-vig probability of outcome i = pi ÷ (sum of all implied probabilities)
- Theoretical hold = 1 − 1 ÷ (sum of all implied probabilities)
- Probability to American odds: p ≥ 0.5 gives −100 × p ÷ (1 − p); p < 0.5 gives +100 × (1 − p) ÷ p
- Probability to decimal odds = 1 ÷ p; to fractional odds = (1 − p) ÷ p
- Expected profit per unit staked = (estimate × decimal odds) − 1
The formulas return a probability as a fraction between 0 and 1. Multiply by 100 to get the percentage the calculator displays, so 0.5238 and 52.38% are the same number. Mixing the two up is the most common slip when working by hand.
Worked examples and a conversion table
Take odds of -110. The odds are negative, so p = 110 ÷ (110 + 100) = 110 ÷ 210 = 0.5238, or 52.38%. For +200 the odds are positive, so p = 100 ÷ (200 + 100) = 0.3333, or 33.33%. For -150, p = 150 ÷ 250 = 0.60, and for +100, p = 100 ÷ 200 = 0.50. Decimal odds of 2.50 give 1 ÷ 2.50 = 0.40, and fractional odds of 5/2 give 2 ÷ 7 = 0.2857. Choose Fill with an example to load the first one.
| American odds | Decimal odds | Fractional odds | Implied probability |
|---|---|---|---|
| −300 | 1.333 | 1/3 | 75.00% |
| −200 | 1.500 | 1/2 | 66.67% |
| −150 | 1.667 | 2/3 | 60.00% |
| −110 | 1.909 | 10/11 | 52.38% |
| +100 | 2 | 1/1 | 50.00% |
| +150 | 2.500 | 3/2 | 40.00% |
| +200 | 3 | 2/1 | 33.33% |
| +300 | 4 | 3/1 | 25.00% |
Favourites, which have negative American odds, sit above 50%. Underdogs with positive odds sit below it, and even money is exactly 50%. Negative does not mean bad and positive does not mean good: the sign only says which side of even money the price falls on.
Implied probability and the break-even win rate
For a bet that either wins or loses, the implied probability is the win rate at which the bettor neither gains nor loses. At -110 you risk 110 to win 100. Over 100 bets, winning 52.38 of them returns 52.38 × 100 = 5,238 in profit and costs 47.62 × 110 = 5,238 in losses, so you finish level. Win more often than that and you come out ahead, and win less often and you fall behind.
This is a statement about the price, not about the outcome. The implied probability does not say that the event has a 52.38% chance of happening. It says how often you must be right for the price to be fair to you. The two ideas only line up if the price happens to be fair, and no margin is built in. If a bet can also be refunded, as with a push on a spread or a tie on some markets, the stake is returned without a win or a loss and the simple equality no longer holds exactly.
Sportsbook margin and overround
A sportsbook rarely prices a market so that the implied probabilities total exactly 100%. Take a game where both sides are priced at -110. Each side implies 52.38%, so the total is 52.38% + 52.38% = 104.76%. The 4.76% above 100% is the overround, and it is the margin built into the prices. It is also called the vig, vigorish or juice.
The overround is not the same as the hold. Hold is the share of the money wagered that the sportsbook keeps when bets on the different outcomes are balanced, and it is calculated as 1 − 1 ÷ total. With a total of 1.0476 the theoretical hold is 1 − 1 ÷ 1.0476 = 4.55%. The overround (4.76%) is measured against the fair total of 100%, while the hold (4.55%) is measured against the money bet. The hold is also theoretical: it assumes balanced betting, and what a sportsbook actually keeps varies with how bets land.
Raw implied probability and no-vig probability
The probability worked out directly from a price is the raw implied probability, and it includes the margin. To estimate what the market would say without the margin, convert every outcome's odds to a probability and divide each one by the total. This proportional normalisation scales the total back to 100%.
| Outcome and odds | Raw implied probability | No-vig probability |
|---|---|---|
| Team A, −130 | 56.52% | 54.27% |
| Team B, +110 | 47.62% | 45.73% |
| Total | 104.14% | 100.00% |
The raw probabilities, 56.52% and 47.62%, total 104.14%. Dividing each by that total gives 54.27% and 45.73%. The same steps work for three outcomes, such as a home win, a draw and an away win, as long as every outcome is included. Leaving one out gives a total that is too small and no-vig figures that are too high.
Handle the result with care. The no-vig probability is a market-based estimate. It assumes the margin is spread in proportion across the outcomes, which is a modelling choice, and other methods for allocating the margin exist. It also inherits any error in the prices themselves. It is a better guide to the market’s view than the raw figure, but it is not a verified true probability. If the total comes out below 100%, check that the odds are entered correctly and belong to the same event.
Converting a probability into odds
The second mode runs the conversion in reverse. A probability of 60% is -100 × 0.60 ÷ 0.40 = -150 in American odds, 1 ÷ 0.60 = 1.667 in decimal odds and 0.40 ÷ 0.60 = 2/3 in fractional odds. A probability of 40% gives +150, 2.50 and 3/2, and exactly 50% gives +100, 2.00 and 1/1. Some probabilities give a fraction with no simple form, and the calculator then marks the fraction as approximate.
These are the fair odds for that probability, with no margin. They show what the probability means in betting terms. They are not odds that a sportsbook is offering, and a real price would usually be worse for the bettor because of the margin.
Comparing an estimate with the implied probability
Implied probability is useful for judging a price against a view of your own. Suppose your analysis puts a team’s chance of winning at 55%, and the price is -110. The break-even rate is 52.38%, so your estimate is 2.62 percentage points higher. On a bet of 100 the win pays about 90.91, so the expected profit is 0.55 × 90.91 − 0.45 × 100 = 5.00. An estimate of 50% against the same price would give an expected loss of about 4.55 per 100. You can see the same bet worked through in the Expected Value Calculator.
A high implied probability does not mean a bet is worth making. A heavy favourite at -500 implies 83.33%, and if the true chance is 80% the bet still loses money on average. What matters is the gap between your own estimate and the break-even rate, and that gap is only as reliable as the estimate. The calculator does not know the true chance of any event, and a positive expected value does not guarantee a profit on any single bet or over a short run. Gambling carries a real risk of loss. This is arithmetic for checking numbers, not betting or financial advice.
Input checks and edge cases
The calculator stops and explains the problem, rather than showing a misleading number, when:
- American odds lack a sign, other than 100, or fall between -100 and +100;
- decimal odds are not above 1, or fractional odds have a zero or negative part;
- a probability is below 0%, above 100%, or exactly 0% or 100%;
- a market has fewer than two outcomes with odds, or an outcome has a name but no odds in the first two rows;
- an entry is not a number in the chosen format.
A market takes up to six outcomes. If the implied probabilities total exactly 100% the calculator reports that there is no margin to remove, and if they total less than 100% it says so and suggests checking the entries.
Assumptions and limitations
- The calculator treats a bet as a standard win-or-lose wager at a fixed price, with the stake returned on a win. Pushes, ties that refund the stake, boosted odds, bonus bets, parlays, each-way terms and exchange commission are not modelled.
- The odds you enter must belong to the same event and be quoted at the same time, from the same source, if you want a meaningful market total.
- Implied and no-vig probabilities describe prices. They are not forecasts, and neither is a statement about the real chance of an outcome.
- Payout, stake-sizing and staking-strategy tools are outside the scope of this page. For expected value, use the Expected Value Calculator, and for the general rules of chance, the Probability Calculator.
- This calculator provides a mathematical result from the values you enter. It is an informational and educational tool, not professional, financial or betting advice.
Formula sources
The conversion formulas, the margin and the proportional no-vig method were checked against these independent references:
- Action Network, How to Remove Juice/Vig from Sports Betting Odds (American odds to probability, summing and removing the vig)
- Calculator Academy, Implied Probability Calculator (separate formulas for positive and negative odds, and probability back to American odds)
- MiniWebtool, Betting Odds Converter (conversions between American, decimal and fractional odds, and scaling the sides back to 100%)
- Odds-API.io, Implied probability glossary entry (decimal and American formulas and the bookmaker margin)
Frequently asked questions
What is implied probability in sports betting?
Implied probability is the chance of winning that a betting price assumes. It is worked out from the odds, so a price of -110 implies 52.38% and a price of +200 implies 33.33%. It is not an independent forecast: it reflects how the sportsbook set the price, including its margin.
How do I convert American odds into implied probability?
For positive odds, divide 100 by the odds plus 100. +150 gives 100 / 250 = 40%. For negative odds, drop the minus sign and divide that number by itself plus 100. -150 gives 150 / 250 = 60%. Type the odds with their sign in the calculator and it picks the right formula.
Why do positive and negative American odds use different formulas?
The two signs describe different things. Positive odds show the profit on a 100 stake, while negative odds show the stake needed to win 100. The reference amount of 100 therefore sits in a different place in each case, so each sign needs its own expression. That is also why negative odds are entered as an absolute value.
How do I convert decimal odds into a probability percentage?
Divide 1 by the decimal odds and multiply by 100. Odds of 2.50 give 1 / 2.50 = 0.40, which is 40%. Decimal odds include the returned stake, so they must be greater than 1.
How do I convert fractional odds into implied probability?
For odds of n/d, where n is the profit and d is the stake, the implied probability is d / (n + d). Odds of 5/2 give 2 / 7 = 28.57%. Evens, written 1/1, give 50%.
What is the implied probability of -110 odds?
110 / (110 + 100) = 110 / 210 = 52.38%. The equivalent decimal odds are about 1.909 and the fractional odds are 10/11. If both sides of a market are priced at -110, each side carries 52.38% and the two together total 104.76%.
Is implied probability the same as the win rate needed to break even?
For a standard bet that either wins or loses, yes. At -110 you risk 110 to win 100, so winning 52.38% of such bets leaves you level. The match breaks down when a bet can also be refunded, as with a push or a tie, because the stake comes back without a win or a loss.
Why do the implied probabilities of both sides add up to more than 100%?
Because the prices contain the sportsbook's margin. If two outcomes were priced fairly, their implied probabilities would total exactly 100%. With -110 on both sides, each is 52.38% and the total is about 104.76%. The excess over 100% is the overround, also called the vig or juice.
How do I remove the vig to calculate no-vig probabilities?
Convert every outcome's odds to an implied probability, add them, and divide each probability by that total. With -130 and +110 the raw figures are 56.52% and 47.62%, which total 104.14%. Dividing gives 54.27% and 45.73%. You need the odds for every possible outcome, so a market with a draw needs all three prices.
Is no-vig probability the same as an outcome's true chance of winning?
No. The no-vig figure is the market's implied view with the margin scaled out, using the assumption that the margin is spread in proportion to each probability. Other methods exist, the sportsbook's prices can be wrong, and the real chance is never observed directly. Read it as a market-based estimate.
How do I convert a probability percentage back into American odds?
If the probability is 50% or higher, American odds are -100 x p / (1 - p). 60% gives -150. If it is below 50%, they are +100 x (1 - p) / p. 40% gives +150, and exactly 50% gives +100. These are the fair odds with no margin. A sportsbook would not necessarily offer them.
How can I compare my estimated win probability with implied probability to assess betting value?
Work out the implied probability of the price, then compare it with your own estimate. If your estimate is higher, the bet has a positive expected value on your numbers, and if it is lower the expected value is negative. At -110 the break-even rate is 52.38%, so an estimate of 55% implies an expected profit of about 5 per 100 staked. The result is only as good as the estimate, and a high implied probability on its own says nothing about value.