Odds converter (fractional, decimal, American, probability)

How to convert odds to implied probability

Divide 1 by the decimal odds: p = 1/d. Fractional 5/2 is decimal 1 + 5/2 = 3.5, so it implies 1/3.5 = 2/7 = 28.57%, the win rate at which the bet breaks even. American +250 is the same price, and −110, common on US point spreads, implies 110 ÷ (110 + 100) = 52.38%.

The shortcut for each format:

• Decimal d: p = 1/d
• Fractional a/b: p = b ÷ (a + b), so 5/2 gives 2/7
• American +M: p = 100 ÷ (M + 100), so +250 gives 100/350 = 28.57%
• American −M: p = M ÷ (M + 100), so −110 gives 110/210 = 52.38%

How to convert between fractional, decimal and American odds

• Fractional to decimal: d = 1 + a/b. 5/2 becomes 3.5, 1/2 becomes 1.5 and evens, 1/1, becomes 2.0.
• Decimal to American: +100(d − 1) when d is 2 or more, and −100 ÷ (d − 1) below 2. 3.5 becomes +250 and 1.5 becomes −200.
• American to decimal: 1 + M/100 for +M, and 1 + 100/M for −M. −110 becomes 1 + 100/110 = 21/11 = 1.909091.
• Probability to decimal: d = 1/p. A 25% chance is decimal 4.0, fractional 3/1 and American +300.

Profit vs total return

Decimal odds quote the total return per unit staked, stake included. Fractional odds quote profit only, which is why d = 1 + a/b (UK Gambling Commission).

A winning 10-unit bet at 5/2 or 3.5 pays back 35 in both cases: the 10 staked plus 25 profit. Counting the 35 as profit counts the returned stake twice.

How American (moneyline) odds work

A plus number is the profit on a 100 stake, and a minus number is the stake needed to win 100. At +250, 100 staked wins 250 profit. At −150, 150 staked wins 100, which is decimal 1.667 and an implied 60%.

+100 and −100 both mean evens, decimal 2.0. No American odds exist between −100 and +100. The minus sign marks how the price is quoted, not a negative payout or probability.

Why implied probability is the break-even rate

Stake 1 at decimal odds d. A win earns d − 1 and a loss costs 1, so with a true win probability p the expected result is p(d − 1) − (1 − p) = pd − 1. That is zero when p = 1/d.

So at −110 a bettor must win 52.38% of the time just to break even. Implied probability describes the price, not the true chance of the event.

Odds-on and odds against

Odds-on means the price implies more than 50%: fractional odds below 1/1, decimal odds below 2.0 and negative American odds. At 1/2 (decimal 1.5, American −200) you stake 2 to win 1, an implied 66.67%.

Odds against is the reverse. 5/2 (3.5, or +250) pays more than the stake and implies less than 50%.

Payout odds are not the "odds in favor" of probability textbooks. A 25% chance is odds of 1 to 3 in favor, or 3 to 1 against, which matches a fair fractional price of 3/1 (Grinstead and Snell).

Overround: the bookmaker's margin

The implied probabilities of every outcome in a market add up to more than 100%, and the excess is the overround. With both sides of a bet at −110, the total is 52.38% + 52.38% = 104.76%, an overround of 4.76%.

The bookmaker's margin on stakes, the vig, is 1 − 1/1.0476 = 4.55%. Dividing each implied probability by the total, 52.38 ÷ 104.76, removes the margin and gives 50% each. That adjusted figure is still an estimate built from prices, not a measured chance.

Odds conversion examples

"Default" is fractional 5/2. The other rows start from decimal 1.5, American −110, a 25% probability and decimal 2.0.

Inputs worth checking

• Fractional terms must both be positive; 10/4 reduces to 5/2.
• American odds must be +100 or more, or −100 or less.
• Probability is a percentage strictly between 0 and 100: 25 means 25%. Entering 0.25 means 0.25%, which converts to decimal 400.

The conversions assume a simple win-or-lose bet. Commissions, taxes and partial settlements change the real break-even rate.

To weigh a bet's payouts against your own probability estimates, use the expected value calculator. For chances of dice totals, coin runs and card draws, use the dice, coin and card probability calculator.