Data Source and Methodology

This calculator is based on the fundamental principles of probability theory. It converts any given format into its core **implied probability** (the statistical likelihood of the outcome) and then uses that value to derive all other equivalent formats.

All calculations are strictly based on the standard mathematical formulas for probability conversion, ensuring unbiased and accurate results.

The Formulas Explained

All calculations are normalized by first finding the implied probability, $P$, as a decimal (e.g., 25% = 0.25). The following formulas are then used to convert $P$ into each odds format.

1. From Probability to Other Formats

2. American Odds Formulas

American odds have two different formulas depending on whether the probability is greater or less than 50%.

Glossary of Variables

Implied Probability (%)

The most direct measure of likelihood. A 25% implied probability means the event is expected to happen 1 out of every 4 times.

Probability (1 in X)

A common way to express probability. "1 in 5" means a 1-in-5 chance of winning, which is the same as a 20% implied probability.

Fractional Odds (A/B)

Popular in the UK. Odds of '4/1' (four-to-one) mean you profit 4 units for every 1 unit staked. This represents a 1-in-5 chance of winning (1 win + 4 losses).

Decimal Odds

Popular in Europe and Canada. Decimal odds represent the total payout (stake + profit). Odds of 5.00 mean a 1-unit bet returns 5 units (4 profit + 1 stake).

American Odds (+/-)

The US standard. Positive (+) odds (e.g., +400) show the profit on a $100 bet. Negative (-) odds (e.g., -150) show the amount you must bet to profit $100.

How it Works: A Step-by-Step Example

Let's convert **4/1 Fractional Odds** into all other formats.

1. Find Implied Probability (P): The formula for fractional odds (A/B) is $P = \frac{B}{A + B}$.
2. With 4/1 odds, A=4 and B=1.
3. $P = \frac{1}{4 + 1} = \frac{1}{5} = 0.20$
4. Convert P (0.20) to other formats:
   • Percentage: $0.20 \times 100 = 20\%$
   • Probability (1 in X): $X = \frac{1}{0.20} = 5$. The odds are **1 in 5**.
   • Decimal Odds: $\frac{1}{0.20} = 5.00$
   • American Odds: Since P (0.20) is less than 0.5, we use the positive odds formula: $(\frac{100}{0.20}) - 100 = 500 - 100 = +400$

Result: 4/1 odds are equivalent to +400, 5.00, a 1-in-5 chance, and a 20% implied probability.

Frequently Asked Questions

American \ Odds = \left( \frac{100}{P} \right) - 100

American \ Odds = - \left( \frac{P \times 100}{1 - P} \right)

Implied Probability ($P$) = The core decimal value (e.g., 0.25) Percentage = $P \times 100\%$ Probability (1 in X) = $X = \frac{1}{P}$ Fractional Odds (A/B) = $\frac{A}{B} = \frac{1 - P}{P}$ (simplified to lowest terms) Decimal Odds = $\frac{1}{P}$

If $P < 0.5$ (Underdog/Positive Odds): $American \ Odds = \left( \frac{100}{P} \right) - 100$ Example: $P = 0.25 \rightarrow (\frac{100}{0.25}) - 100 = 400 - 100 = +300$ If $P \ge 0.5$ (Favorite/Negative Odds): $American \ Odds = - \left( \frac{P \times 100}{1 - P} \right)$ Example: $P = 0.60 \rightarrow -(\frac{0.60 \times 100}{1 - 0.60}) = -(\frac{60}{0.40}) = -150$