Odds converter: decimal, fractional, American, and the margin inside them
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The whole market
Put in every price of the same market, in the format chosen above. Leave the third empty when the market has only two ways.
Nothing on this page says whether to bet, or that any price is a good one. It converts a price and measures a margin.
The same price in every format
| Decimal | — |
| Fractional | — |
| American | — |
| Implied probability, in percent | — |
| Profit on a stake of 100 | — |
| Stake and profit together | — |
Fractional prices are net and decimal prices are gross, which is one whole stake apart. Eleven to ten is 2.10 and not 1.10; two to one is 3.00 and not 2.00. Reading one as the other misstates what comes back by exactly the amount you put in.
What the market adds up to
| Decimal | Implied, in percent | Without the margin, in percent | Fair decimal price |
|---|
| The implied probabilities added together, in percent | — |
| What is left over, in percent | — |
This is why a converted price is not a probability. The three prices this page starts with imply 47.62, 29.41 and 27.78, which come to 104.81 for three outcomes of which exactly one will happen. The 4.81 that does not fit is the margin, and it is charged whichever way the event goes.
Take the margin out and each price gets longer: 2.10 becomes 2.201, 3.40 becomes 3.563, 3.60 becomes 3.773. That last column is the price a house with no margin would post, which is also the price your own estimate has to beat before a bet is worth making.
The margin is chosen, not left over by rounding, and American prices show it plainly. Plus 150 against minus 150 adds up to exactly one hundred, and no house offers that pair. The pair actually offered on an even contest is minus 110 on both sides, which adds up to 104.76: a coin toss priced as though heads were a 52.38 favourite, and tails as well.
Why do the implied probabilities add up to more than a hundred?
Because the margin of the house is inside every price. Exactly one of the outcomes will happen, so an honest set of chances would come to a hundred; the prices come to more, and the excess is what the house keeps on average whichever way the event goes.
With the three prices this page starts with the sum is 104.81, so the margin is 4.81. It is not a fee charged at the end and it is not a rounding artefact: it is already in the price you were shown.
Is the implied probability the chance of the outcome?
No. It is the price written as a percentage, and it has the margin baked into it. Taking the margin out gives the last column of the table, which is the price with the sum brought back to a hundred.
Even that is not a fact about the world. It is what the market thinks, after the house has protected itself. Your own estimate is what you are comparing it against, and the fair price is the number it has to beat.
Why is two to one not 2.00?
Because a fractional price is net and a decimal price is gross. Two to one means you win two and keep the one you staked, which is three back in total, so the decimal is 3.00.
The two readings are always exactly one stake apart. Mistaking one for the other misstates the return by the whole amount you put in, which is the largest error you can make while still doing the arithmetic correctly.
What win rate do I need just to break even?
One divided by the decimal price. At minus 110, the standard price on an even contest, the decimal is 1.909 and the break-even rate is 52.38 per cent, not 50.
That gap is the whole reason a market with a margin is hard to beat: picking the winning side slightly more than half the time is not enough to come out level.
| Decimal | American | Win rate needed to break even, in percent |
|---|---|---|
| 1.909 | -110 | 52.38% |
| 2.000 | +100 | 50.00% |
| 2.500 | +150 | 40.00% |
| 3.000 | +200 | 33.33% |
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