What a bet pays at different odds
The table shows a stake of 10 units at five common prices. Shorter prices (lower decimal odds) pay less profit but imply a higher chance. Longer prices pay more profit and imply a lower chance. In every row, total return is the profit plus the 10 units staked, and a losing bet returns nothing.
| Decimal | American | Profit if it wins | Total return | Implied chance |
|---|---|---|---|---|
| 1.50 | -200 | 5.00 | 15.00 | 66.67% |
| 2.00 | +100 | 10.00 | 20.00 | 50.00% |
| 2.50 | +150 | 15.00 | 25.00 | 40.00% |
| 4.00 | +300 | 30.00 | 40.00 | 25.00% |
| 11.00 | +1000 | 100.00 | 110.00 | 9.09% |
To convert odds, change the price to decimal first, then work out the other formats from it. Fractional odds become the top number divided by the bottom, plus 1. Positive American odds become the number divided by 100, plus 1. Negative American odds become 100 divided by the number without its minus sign, plus 1. The odds converter does these steps for you, and the sections below show them by hand.
How do decimal, fractional and American odds relate?
Decimal, fractional and American odds all describe the same thing: what a winning bet pays compared with the stake. Only the way the price is written changes. Decimal odds show the total return for every 1 staked, stake included. Fractional odds show the profit compared with the stake. American odds show the profit on a 100 stake when the number is positive, or the stake needed to win 100 when it is negative.
| Decimal | Fractional | American | Implied probability |
|---|---|---|---|
| 1.20 | 1/5 | -500 | 83.33% |
| 1.50 | 1/2 | -200 | 66.67% |
| 1.91 | 10/11 | -110 | 52.38% |
| 2.00 | 1/1 | +100 | 50.00% |
| 2.50 | 3/2 | +150 | 40.00% |
| 4.00 | 3/1 | +300 | 25.00% |
| 11.00 | 10/1 | +1000 | 9.09% |
How do you convert betting odds by hand?
- Fractional to decimal: divide the top number by the bottom number, then add 1. For 5/2: 5 ÷ 2 = 2.5, plus 1 gives 3.50.
- Positive American to decimal: divide the number by 100, then add 1. For +150: 150 ÷ 100 = 1.5, plus 1 gives 2.50.
- Negative American to decimal: divide 100 by the number without its minus sign, then add 1. For -200: 100 ÷ 200 = 0.5, plus 1 gives 1.50.
- Decimal to implied probability: divide 1 by the decimal odds. For 2.50: 1 ÷ 2.50 = 0.40, or 40%.
Is implied probability the real chance of winning?
An odds price is not a pure statement of probability, because the bookmaker builds a margin into it. Take a two-way market where both sides are priced at -110. Each side implies 52.38%, so the two together add up to 104.76%. The 4.76 points above 100% are the margin, also called the overround or vig. Because the total is above 100%, the implied probabilities taken together overstate the real chances, so the margin has to be removed before a price is treated as a fair probability. Researchers have studied the bias in probabilities derived from betting odds for exactly this reason, and the work that treats bookmaker odds as implicit probability forecasts shows why the raw figures need care.
Example: a bet of 10 at +150 (decimal 2.50) returns 25.00 if it wins, which is 15.00 profit plus the 10 stake. If it loses, the 10 is gone. The price implies a 40% chance, and any margin sits inside that figure.
How to read the result
Profit if the bet wins is what you gain on top of your stake. Total return is that profit plus your stake given back. If the bet loses, you lose the stake and nothing is returned. The three formats are the same price written in different ways, and the chance the odds imply is 1 divided by the decimal odds, before any bookmaker margin is taken out.
How it is calculated
Your odds are first turned into decimal odds. Fractional a/b becomes a divided by b, plus 1. Positive American +A becomes A divided by 100, plus 1. Negative American -A becomes 100 divided by A, plus 1. Then profit is the stake times (decimal minus 1), total return is the stake times decimal, and the implied chance is 1 divided by decimal.
Worked example
Worked example
A stake of 10 at +150 is decimal 2.50. Profit: 10 x (2.50 - 1) = 15.00. Total return: 10 x 2.50 = 25.00. Implied chance: 1 / 2.50 = 40.00%. A stake of 10 at -200 is decimal 1.50, so profit is 5.00, total return is 15.00 and the implied chance is 66.67%.
Limits
The calculator works out what a bet would pay and the chance the odds imply. It does not say whether a price is fair or a bet is worth placing. The implied chance still contains the bookmaker's margin, so it is higher than the real chance. Fractional odds are shown as the closest simple fraction, so 1.91 appears as 91/100 while -110 appears as 10/11. American odds between -100 and +100 are not used in the format. Bookmakers may round prices, and results are estimates, not predictions. A losing bet returns nothing. Fees and tax are not included.