Betting odds formats explained: decimal, fractional and American
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Betting odds formats are usually presented as a cosmetic preference: three ways of writing the same number, pick whichever you grew up with. They are not quite that. Each format expresses a different quantity — total return, profit, or stake required — and only one of them converts to a probability without arithmetic. Which format you read a price in genuinely changes what you notice about it, and the two older formats hide precisely the thing worth seeing.
The conversions first, then why the distinction earns its keep.
Decimal: total return per unit staked
Decimal odds state everything you get back, stake included. A winning unit at 2.50 returns 2.50 — your unit plus 1.50 profit.
The reason analysts default to this format is a single division: implied probability is 1 ÷ odds. At 2.50 that is 40%. No format-specific rules, no special cases at even money, and it extends straight into every other calculation you would want to do with a price.
Fractional: profit per unit staked
Fractional odds — 5/2, 4/5, 10/1 — state profit relative to stake, excluding the stake itself. A winning 5/2 bet returns your stake plus two and a half times it.
Conversion in both directions is one step:
decimal = (numerator ÷ denominator) + 1
fractional = decimal − 1, written as a fractionSo 5/2 → 2.5 + 1 = 3.50, and 4/5 → 0.8 + 1 = 1.80. The awkwardness is that “odds-against” (5/2) and “odds-on” (4/5) read as different kinds of object even though they are points on one scale, and that traditional denominators are not standardised — 11/8 and 6/4 sit either side of a price nothing in the notation makes comparable at a glance.
American: two formulas depending on the sign
American odds split at even money and use a different rule on each side.
- Positive (+150): profit on a 100-unit stake.
decimal = (A ÷ 100) + 1, so +150 → 2.50. - Negative (−200): stake required to profit 100.
decimal = (100 ÷ A) + 1, so −200 → 1.50.
Going back the other way: if decimal is 2.00 or above, A = (decimal − 1) × 100; if it is below 2.00, A = −100 ÷ (decimal − 1).
The discontinuity at 2.00 is real, not a rounding artefact — the format has no way to express even money except as +100 or −100 by convention.
The column nobody prints
Every conversion table online stops at the three formats. The useful one has a fourth column:
| Fractional | Decimal | American | Implied probability |
|---|---|---|---|
| 1/5 | 1.20 | −500 | 83.3% |
| 1/2 | 1.50 | −200 | 66.7% |
| 4/5 | 1.80 | −125 | 55.6% |
| 1/1 | 2.00 | +100 | 50.0% |
| 6/4 | 2.50 | +150 | 40.0% |
| 5/2 | 3.50 | +250 | 28.6% |
| 4/1 | 5.00 | +400 | 20.0% |
| 10/1 | 11.00 | +1000 | 9.1% |
That last column is the only one that says anything about whether a price is worth taking. It is a claim about the world — 5/2 asserts this happens about 28.6% of the time — and it is checkable. The other three columns are notation.
Why the format changes what you notice
Run the same question through each format: is this price generous?
In decimal, you divide one by the number and compare the result with your own probability. In fractional you must first add one, and the mental step of turning 11/8 into 2.375 into 42.1% is enough friction that most people skip it and judge the price by feel. In American the sign flip means two different formulas, and the numbers are large enough (+250, −180) to feel like scores rather than rates.
None of this is accidental in its effect, whatever the historical reasons for each convention. A format that makes implied probability one division away invites comparison with your own estimate. A format that takes three steps invites you to compare the price with other prices instead — which is a comparison between things the book controls.
The margin is invisible in all three
One thing no format reveals on its own: a single price never tells you what the book is charging. That requires summing the implied probabilities of every outcome in the market and seeing how far past 100% the total lands — the procedure in converting odds to implied probability, and the reason how bookmakers set their odds is a question about the whole book rather than any line in it.
Do that sum once in each format and the case for decimal makes itself. In decimal it is three divisions and an addition. In fractional or American it is the same arithmetic with a conversion layer on top, performed on numbers designed for a betting slip rather than a spreadsheet.
Our own probabilities are published as probabilities, before kick-off, and graded afterwards on the track record — which sidesteps the format question entirely. That is the honest end state of this topic: formats are a way of writing prices, prices are probabilities with a fee attached, and the fee is the only part of the notation anyone is trying to keep quiet.
Convert any price in any direction with the odds converter — decimal, fractional, American, and the implied probability underneath all three.