Every price a bookmaker shows is also a percentage in disguise. Odds of 2.50, 6/4 and +150 are three ways of writing the same thing: a 40% chance, as the bookmaker prices it. That percentage is called the implied probability, and once you can read it, a lot of things about betting become clearer, starting with why the numbers never quite add up.
This guide shows how to convert decimal, fractional and American odds into implied probability, with a free odds converter to try. Then it uses the same idea to uncover the bookmaker’s margin hidden in every market, and to explain what it means for your own results over time.
In this guide
What implied probability means
Odds tell you how much a bet pays. Implied probability turns that payout back into the chance it corresponds to. If a bet pays 2.50 times your stake, it would break even in the long run if it won exactly 40% of the time: 40 wins out of 100 bets of $1 return $100, the same as the $100 staked.
That is why bettors and analysts talk about odds in percentages. A percentage is easier to compare than three different notations, and it makes one thing obvious that the odds hide: how often a price needs to win just to pay for itself.
From decimal odds: the simplest formula
Decimal odds, used across Europe, Australia and most betting apps, show the total return for each unit staked, stake included. They make implied probability a one-step calculation:
Implied probability = 1 ÷ decimal odds × 100
- Odds of 2.50: 1 ÷ 2.50 = 0.40, so 40%.
- Odds of 1.80: 1 ÷ 1.80 = 0.556, so 55.6%.
- Odds of 5.00: 1 ÷ 5.00 = 0.20, so 20%.
The formula works the other way too. A probability of 25% corresponds to odds of 100 ÷ 25 = 4.00. The shorter the odds, the higher the implied probability, and odds of 2.00 sit exactly in the middle, at 50%.
Fractional and American odds
British and Irish bookmakers often show fractional odds, and American sportsbooks use moneyline (American) odds. Both describe the same prices, so the easiest route is to convert them to decimal first.
Fractional odds
Fractional odds give the profit for a given stake: 6/4 means you win $6 for every $4 staked. Add 1 to get decimal odds, or go straight to the probability with the denominator:
Decimal = numerator ÷ denominator + 1 · Implied probability = denominator ÷ (numerator + denominator)
So 6/4 is 6 ÷ 4 + 1 = 2.50, and 4 ÷ (6 + 4) = 40%. Evens (1/1) is 2.00, or 50%, and 10/11 is 1.91, or 52.4%.
American odds
American odds come with a sign. A plus sign shows the profit on a $100 stake: +150 wins $150. A minus sign shows the stake needed to win $100: −200 means staking $200 to win $100. To convert American odds to decimal:
- Positive odds: decimal = odds ÷ 100 + 1, so +150 becomes 2.50. Implied probability = 100 ÷ (odds + 100), so 100 ÷ 250 = 40%.
- Negative odds: decimal = 100 ÷ odds + 1 (ignoring the sign), so −200 becomes 1.50. Implied probability = odds ÷ (odds + 100), so 200 ÷ 300 = 66.7%.
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.20 | 1/5 | −500 | 83.3% |
| 1.50 | 1/2 | −200 | 66.7% |
| 1.91 | 10/11 | −110 | 52.4% |
| 2.00 | 1/1 (evens) | +100 | 50.0% |
| 2.50 | 6/4 | +150 | 40.0% |
| 3.00 | 2/1 | +200 | 33.3% |
| 5.00 | 4/1 | +400 | 20.0% |
| 10.00 | 9/1 | +900 | 10.0% |
Rather than doing the sums by hand, you can use the odds converter below. Pick the format of your odds, type them in, and it shows the two other formats along with the implied probability.
Odds converter
- Fractional
- 6/4
- American
- +150
- Implied probability
- 40.0%
Odds of 2.50 imply a 40.0% chance: the share of bets at this price you would need to win to break even.
The odds converter also lives on its own page, handy to bookmark.
The bookmaker’s margin: why the total is over 100%
In a match where exactly one outcome must happen, the real probabilities of all outcomes add up to 100%. The implied probabilities never do. Take a football match priced like this on the match result market:
| Outcome | Odds | Implied probability |
|---|---|---|
| Home win | 2.10 | 47.6% |
| Draw | 3.40 | 29.4% |
| Away win | 3.60 | 27.8% |
| Total | 104.8% |
The extra 4.8% is the bookmaker’s margin, also called the overround, the vig or the juice. Each price is a little shorter than it would be in a fair market, so that whichever outcome wins, the bookmaker pays out less than it takes in, provided the money is spread across the outcomes.
Another way to read the same figure is the payout rate: 1 ÷ 1.048 = 95.4%. If stakes come in proportion to the prices, the market hands back about 95.4 cents for every dollar staked. Some sites quote the margin as 100% minus that payout rate, 4.6% here; it describes the same thing from the bookmaker’s side.
Two more examples
The classic American line is −110 on both sides of a point spread: bet $110 to win $100. Each side implies 52.4%, so the total is 104.8%. If $110 is staked on each side, the bookmaker collects $220, pays $210 to the winners and keeps $10, about 4.5% of the money staked.
On a tennis match priced 1.40 and 2.90, the implied probabilities are 71.4% and 34.5%, for a total of 105.9%: a margin of 5.9%. Margins vary by bookmaker, sport and market. They are usually tightest on the main markets of major competitions, and noticeably wider on minor events, player markets and many live markets.
Removing the margin: fair probabilities and fair odds
To estimate what the bookmaker’s prices would look like without the margin, the simplest method is to scale every implied probability down in proportion, so that they add up to 100%:
Fair probability = implied probability ÷ total of implied probabilities
In the football example, the home win becomes 47.6% ÷ 1.048 = 45.4%, the draw 28.1% and the away win 26.5%. Turned back into odds, that gives fair odds of about 2.20, 3.56 and 3.77, against the 2.10, 3.40 and 3.60 on offer.
The proportional method assumes the margin is spread evenly. In practice, bookmakers often load more of it onto long shots, which is why other methods exist (the power method or Shin’s method, for example). They give slightly different figures, but the idea is the same.
Try it with any market: enter the decimal odds of every outcome, and the calculator below works out the margin, the payout rate and the probabilities without the margin.
Bookmaker margin calculator
Enter the decimal odds of every outcome of one market, from one bookmaker.
- Implied
- 47.6%
- Without margin
- 45.4%
- Fair odds
- 2.20
- Implied
- 29.4%
- Without margin
- 28.1%
- Fair odds
- 3.56
- Implied
- 27.8%
- Without margin
- 26.5%
- Fair odds
- 3.77
- Total implied probability
- 104.8%
- Margin (overround)
- 4.8%
- Payout rate
- 95.4%
The calculator also has a page of its own, handy to bookmark.
What the margin means over many bets
A margin of 5% does not mean you lose 5% on every bet: each bet is either won or lost. It means the prices are tilted. Across many bets, the average bettor gets back less than they stake, and the gap is roughly the margin of the markets they bet on. Wins and losses on the way can hide it for a while, but over hundreds of bets it is the force that pulls results down.
The effect compounds in parlays. Each leg carries its own margin, and the payout rates multiply. With legs priced like the −110 example above (a payout rate of 95.5%), a three-leg parlay returns about 87% in theory, and a five-leg parlay about 79%. Our article on parlays versus singles runs through the numbers leg by leg.
This is also why it matters to know how much you stake in total. Our guide to bankroll management explains how to set a betting budget that accounts for it.
Odds are prices, not forecasts
It is tempting to read implied probability as the chance something will happen. It is safer to read it as a price. Bookmakers set their odds from their own estimates, then move them with the money that comes in and the news that comes out: a team sheet, an injury, the weather. The same match can go from 2.10 to 1.95 in a day without anything happening on the pitch.
Short odds are not certainties either. A favourite at 1.50 implies 66.7%, which also means the bookmaker prices it to lose about one time in three. Over a season, a third of those “safe” bets going down is not bad luck; it is exactly what the price said.
Put your own estimate next to the implied probability, and the gap between the two is what staking formulas such as the Kelly criterion work from. Our Kelly calculator turns that gap into a stake size, in full, half or quarter Kelly. It is only as good as your estimate, and with the margin built into every price, the honest gap is usually negative: then Kelly stakes nothing.
Using implied probability to read your own results
The implied probability of a price is also its break-even win rate: the share of bets at those odds you would need to win to end up level. That makes it a handy benchmark once you track your bets.
Say your record shows 180 bets at average odds of around 1.85, with a win rate of 51%. The break-even win rate at 1.85 is 1 ÷ 1.85 = 54.1%. You are three points below it, which with flat stakes puts your ROI at roughly 0.51 × 1.85 − 1 = −6%. Our guide to betting ROI explains that calculation in detail.
It works best by odds range, because a win rate means nothing without the odds next to it. Bets between 1.30 and 1.60 need to win 63% to 77% of the time to break even; bets around 3.00 need only 33%. Group your bets by odds range, in a betting spreadsheet or an app, and compare each group’s win rate with the implied probability of its odds.
BetTrack does this grouping for you: its analysis breaks your results down by odds range, and your stats show your win rate next to your average odds, whatever format the slips were printed in.
Frequently asked questions
How do you calculate implied probability from odds?
Divide 1 by the decimal odds and multiply by 100: odds of 2.50 imply 40%. For fractional odds, divide the denominator by the sum of both numbers (6/4 gives 4 ÷ 10 = 40%). For positive American odds, use 100 ÷ (odds + 100); for negative ones, odds ÷ (odds + 100), ignoring the minus sign.
How do you convert American odds to decimal?
For positive odds, divide by 100 and add 1: +150 becomes 2.50. For negative odds, divide 100 by the odds without the minus sign and add 1: −200 becomes 1.50, and −110 becomes 1.91.
How big is a typical bookmaker margin?
It depends on the bookmaker, the sport and the market. Main markets of major competitions often carry a margin of a few percent; minor events, player markets and many live markets usually carry more. Add up the implied probabilities of every outcome to see it for any market.
Is implied probability the real chance of winning?
No. It is the bookmaker’s price expressed as a percentage, with the margin included, and it moves with the money and the news. Removing the margin gives a fairer estimate, but nobody knows the true probability of a sporting outcome.
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