Odds Calculator

What are odds?

Odds describe how likely an event is by comparing the ways it can happen with the ways it cannot, or, in betting, by stating the price paid if it does. Both ideas are tied to probability, the share of times an outcome is expected to occur.

If an event has probability p, the odds in favour of it are p ÷ (1 − p). A probability of 20% gives odds of 0.2 ÷ 0.8 = 0.25, usually written 1 to 4, or 1:4. Going back, odds of a:b in favour correspond to a probability of a ÷ (a + b), so 3:2 is 3 ÷ 5 = 60%.

Bookmakers publish odds in several styles that carry the same information in different clothes. This calculator translates between them so you can compare prices from different sites or regions.

How to use the odds calculator

1. Pick the odds type you have: American, Decimal, Fractional or Implied.
2. Type the odds in that format, for example -120, 1.91, 10/11 or 55.
3. Optionally enter a bet amount. It is used only to show the profit and the payout, and it can be in any currency.
4. Press Calculate.

The results list the odds in all four formats and the implied probability. If you entered a stake, two more lines appear: To win, the profit if the bet succeeds, and Payout, the profit plus your returned stake.

American odds may be typed with or without a plus sign, and an implied probability may be typed with or without a percent sign. Fractions are reduced to lowest terms, so 20/22 becomes 10/11.

Types of betting odds

The same price can be written four ways. For a bet that returns a 91% profit on the stake, you could see 1.91 (decimal), 91/100 (fractional), −109.89 (American) or 52.36% (implied probability).

Worked examples and conversion table

−120 with a 50 stake. The decimal odds are 1 + 100 ÷ 120 = 1.833, the fraction is 100/120 = 5/6 and the implied probability is 1 ÷ 1.833 = 54.55%. The profit is 50 × 100 ÷ 120 = 41.67 and the payout is 50 + 41.67 = 91.67.

+250. The decimal odds are 1 + 250 ÷ 100 = 3.5, the fraction is 5/2 and the implied probability is 1 ÷ 3.5 = 28.57%.

7/2. The decimal odds are 1 + 7 ÷ 2 = 4.5, which is +350 in American terms, and the implied probability is 1 ÷ 4.5 = 22.22%.

Common prices side by side:

The table rounds the implied probability to two decimals; the calculator shows four. Decimal odds are shown with up to three decimals and the American figure with up to two. When you enter decimal odds with a few decimals, such as 1.833, the fractional form is built from exactly those digits (833/1000), not rounded to a neat fraction like 5/6.

Using implied probability in betting

Comparing the implied probability with your own estimate of the chance is the basic test of a good price. A bet has positive expected value when the true probability is higher than the one implied by the odds.

expected profit per unit staked = true probability × decimal odds − 1

Example: at decimal odds of 2.50 the implied probability is 40%. If you judge the real chance to be 45%, the expected profit per unit is 0.45 × 2.5 − 1 = +0.125. If you think it is only 40%, the expected profit is exactly zero, and below that it is negative.

The bookmaker's margin. Add up the implied probabilities of every outcome in a market and you normally get more than 100%. With −110 on both sides of a two-way market, each side implies 52.38%, a total of 104.76%. The extra 4.76% is the margin, sometimes called the overround or vig. In a three-way market priced at 2.10, 3.40 and 3.50 the implied probabilities (47.62%, 29.41%, 28.57%) sum to 105.6%.

Dividing each implied probability by the total removes the margin and gives a rough "fair" probability. For the two-way example that is 50% each; for the three-way example it is about 45.1%, 27.9% and 27.1%.

Betting involves risk of loss, and odds describe prices, not guarantees. The calculator does not predict outcomes or give betting advice. Only stake money you can afford to lose, and see the disclaimer.

Accepted values and error messages

• American odds cannot lie strictly between −100 and +100; those values do not correspond to any real price.
• Decimal odds cannot be exactly 1, because that would mean a zero profit. Values below 1 are processed, but they do not describe a normal bet.
• Fractional odds need a non-zero denominator, written with a slash, such as 5/2.
• Implied probability must be above 0% and below 100%.
• The bet amount is optional. Leave it empty or at zero and the calculator skips the profit and payout lines.

Odds in statistics and science

Outside betting, odds are a standard way to describe risk. Medical studies often report an odds ratio, the odds of an outcome in one group divided by the odds in another. An odds ratio of 1 means no difference between the groups, and values above 1 mean the outcome is more likely in the first group.

Logistic regression models the log-odds, ln(p ÷ (1 − p)), as a straight-line function of the predictors, which is why odds appear in so many research papers. To compare two groups from a 2×2 table, use the odds ratio calculator. For the probability of a given number of successes in repeated trials, use the binomial probability calculator.