Tools

Odds calculator and odds converter

Type odds in any format and see them as decimal, fractional and American odds, as the probability they imply, and with the bookmaker's margin taken out. Plain maths, nothing to sign up for.

Odds converter

One price, three formats and the probability it implies. Auto detect reads 2.50 as decimal, 3/2 as fractional and +150 as American odds.

Decimal·
Fractional·
American·
Implied probability·

Converts one price between the three formats bookmakers use and shows the probability it implies. Fractions are shown the way bookmakers print them, so 1.91 becomes 10/11 rather than 91/100.

decimal = 1 + numerator / denominator · American +X: decimal = 1 + X / 100 · American -X: decimal = 1 + 100 / X · implied probability = 1 / decimal

Worked example

Calculation example

Example: 2.50 is 3/2 in fractional odds and +150 in American odds, an implied probability of 40%.

Implied probability calculator

Enter the odds for every outcome of one market, for example home, draw and away.

Implied·
Implied·
Implied·
Total implied·
Bookmaker margin·

Each price turns into the probability the bookmaker is implying. Because the prices include the bookmaker's margin, the probabilities add up to more than 100%. The amount over 100% is the margin, also called the overround or the vig.

implied probability = 1 / decimal odds · margin = sum of implied probabilities - 100%

Worked example

Calculation example

Example: a match priced 2.10, 3.40 and 3.60 implies 47.62%, 29.41% and 27.78%. Together that is 104.81%, so the bookmaker's margin is 4.81%.

No-vig fair odds

Takes the margin back out of the market in the implied probability calculator above, so the probabilities add up to exactly 100%, and turns them into fair odds. Change the odds.

Fair probabilities and fair odds with the margin removed
OutcomeOddsFair probabilityFair odds
Home2.10··
Draw3.40··
Away3.60··
Total·

Proportional scales every outcome down by the same factor. Additive takes the same number of points off each one. Shin, the method our own model uses, assumes part of the margin protects the bookmaker against better informed bettors, so it takes more off the long shots and less off the favourite.

proportional fair probability = implied probability / sum of implied probabilities · fair odds = 1 / fair probability

Worked example

Calculation example

Example: with proportional de-vigging, 2.10, 3.40 and 3.60 become 45.43%, 28.06% and 26.50%, fair odds of 2.20, 3.56 and 3.77. Shin gives 45.87%, 27.87% and 26.26%.

Fair odds are not an offer from anyone. They are the price with no margin in it, so a real bookmaker will pay less.

Expected value calculator

What a bet returns on average per unit staked, if your probability is right.

Expected value·
Expected profit·
Break-even probability·

Expected value is what the bet would return on average per unit staked if it were repeated many times at your probability. Positive means the price is longer than your probability says it should be. The result is only as good as the probability you type in: a positive number on your own estimate is not proof of value.

expected value per unit staked = your probability × decimal odds - 1 · break-even probability = 1 / decimal odds

Worked example

Calculation example

Example: if you rate an outcome at 50% and it is priced 2.10, expected value is 0.50 × 2.10 - 1 = +0.05, or +5%. On a stake of 10 that is an expected profit of 0.50. The break-even probability at 2.10 is 47.62%.

Kelly criterion calculator

Kelly only makes sense with an edge you can document. The formula trusts your probability completely: if it is too high, Kelly tells you to stake too much. When we tested our own model on matches it had never seen, the bookmakers’ closing price usually won, so we do not claim an edge for our numbers, and nobody should claim one for a number typed into a calculator. Without a proven edge, the honest Kelly stake is zero. See how we trained our model.

Full Kelly·
Your fraction·
Stake·

The Kelly criterion sizes a stake as a share of your bankroll from your probability and the odds. It never stakes on a bet with zero or negative expected value. Full Kelly swings hard even when the probability is right, which is why people who use it usually stake a half or a quarter of it.

Kelly fraction = (probability × decimal odds - 1) / (decimal odds - 1)

Worked example

Calculation example

Example: at 50% and odds of 2.10, full Kelly is (0.50 × 2.10 - 1) / 1.10 = 4.55% of your bankroll. Quarter Kelly is 1.14%, a stake of 1.14 from a bankroll of 100.

How betting odds work

Decimal odds (2.50) show the total return for every 1 staked, stake included. A stake of 10 at 2.50 returns 25, which is 15 profit.

Fractional odds (3/2) show the profit against the stake: win 3 for every 2 staked. Add 1 to the fraction and you have decimal odds, so 3/2 is 1 + 1.5 = 2.50.

American odds work around 100. +150 means a stake of 100 wins 150 profit. -200 means you stake 200 to win 100 profit.

Every price is also a probability. Divide 1 by the decimal odds and you get the chance the price implies: 2.50 is 40%. Add up the implied probabilities of every outcome in a market and you get more than 100%. The extra is the bookmaker’s margin, and it is why fair odds are always a little longer than the prices you are offered.

Common odds in decimal, fractional and American format
DecimalFractionalAmericanImplied probability
1.251/4-40080.0%
1.501/2-20066.7%
1.804/5-12555.6%
1.9110/11-11052.4%
2.001/1+10050.0%
2.503/2+15040.0%
3.002/1+20033.3%
4.003/1+30025.0%
5.004/1+40020.0%
6.005/1+50016.7%
11.0010/1+10009.1%

More free tools

These calculators work on any odds you type in. Our own model’s probabilities for the coming matches are on the predictions page, with every call graded afterwards.

See our AI probabilities for today’s matches

18+. These tools calculate, they do not predict, and nothing on this page is betting advice. Please gamble responsibly: BeGambleAware.