Betting Odds Calculator

American, decimal and fractional odds all encode the same number — the price of a payout — in three notations. Converting between them is pure ratio arithmetic.

Decimal odds $d$ state the total return per unit staked:

$\text{return} = S \cdot d, \qquad \text{profit} = S(d - 1)$

Fractional odds $a/b$ state profit per $b$ staked:

$\text{profit} = S \cdot \frac{a}{b}, \qquad d = \frac{a}{b} + 1$

American odds split at 100. A positive price $+A$ is the profit on a 100 stake; a negative price $-A$ is the stake needed to profit 100:

$\text{profit} = S \cdot \frac{A}{100} \;(\text{if } +A), \qquad \text{profit} = S \cdot \frac{100}{A} \;(\text{if } -A)$

Here $S$ is the stake, return is everything handed back (stake included) and profit is return minus stake. Confusing the two is the single most common error in these calculations.

From odds to a percentage

Every price implies a break-even probability — the win rate at which the bet neither gains nor loses on average:

$p = \frac{1}{d} = \frac{b}{a+b} = \frac{100}{A+100} \;(+A) = \frac{A}{A+100} \;(-A)$

Going the other way, $d = 1/p$.

Why the percentages exceed 100%

Add the implied probabilities of every outcome in a market. A fair book sums to exactly $1$; a real one sums to more. The excess is the overround (or vigorish):

$\text{overround} = \sum_j p_j - 1$

Stripping it out gives the fair or true probability and the fair price:

$p_j^{\text{fair}} = \frac{p_j}{\sum_k p_k}, \qquad d_j^{\text{fair}} = \frac{1}{p_j^{\text{fair}}}$

Expected value

With your own probability estimate $q$ for the outcome:

$EV = q \cdot S(d-1) - (1-q) \cdot S$

$EV$ is positive only when $q > 1/d$. The overround is precisely why $\sum p_j > 1$ makes a positive $EV$ hard to find. This page computes the arithmetic of prices you enter; it does not estimate $q$ for you, and no formula here predicts an outcome.

• Reporting return as profit: decimal $3.50$ on a \50$stake returns$$175$but profits$$125$. Fractional and American odds quote profit; decimal quotes total return.
• Inverting a negative American price: $-140$ means stake $140$ to win $100$, so the multiplier is $100/140$, not $140/100$.
• Reading $7/2$ as a probability of $7/2$: fractional odds are a profit ratio. The implied probability is $b/(a+b) = 2/9 \approx 22.2\%$.
• Assuming implied probability is the real probability: it is a break-even threshold that already includes the margin. Fair probability requires normalising by the sum.
• Adding odds across a parlay: legs multiply in decimal form ($d_{\text{total}} = \prod d_j$) and never add.
• Ignoring the overround when comparing books: the market with the smaller $\sum p_j - 1$ is the better price, whatever the headline number looks like.