The first time a new bettor opens a British bookmaker and sees “11/4” next to a match, or an American site and sees “-150” beside a moneyline, the reaction is almost always the same: this is a different language, and nobody handed me the dictionary. In reality, all three major odds formats — decimal, fractional and American — describe exactly the same thing, in exactly the same way: the relationship between what you stake and what you can win. The formats are dialects, not different systems, and every one of them can be converted to the others with arithmetic simple enough to do in your head. Yet the confusion they generate is real and expensive: a player who misreads American odds can stake the wrong amount, a player who doesn’t understand fractions can’t compare prices across sites, and a player who never learned the conversions is locked out of the best odds whenever they appear in an unfamiliar format. This guide delivers the dictionary — one table covering every common value in all three formats, the two conversion formulas that connect them, worked examples for each system, and the practical notes on where each format dominates and why.
What odds actually measure
Before the formats, the concept. Betting odds express two things simultaneously: the implied probability of an outcome, and the payout you receive if it happens. These are two views of the same number. Decimal odds of 2.50 mean the outcome has an implied probability of 1 ÷ 2.50 = 40%, and that every € 10 staked returns € 25 total — € 15 of profit plus your € 10 stake back. That’s the whole grammar; everything else is notation.
It’s worth fixing one distinction now, because each format handles it differently. Stake is the money you risk. Profit is what you win on top of the stake. Return is profit plus stake — the total that lands back in your account. Decimal odds express return; fractional and American odds express profit. Half the confusion between formats disappears the moment this distinction is clear, and the conversion formulas exist precisely to bridge it.
The master conversion table
Every common odds value, side by side in all three formats. The fractional column uses the traditional UK notation, and the American column uses positive numbers for underdogs and negative numbers for favorites. All rows are exact equivalents — the same implied probability, the same payout on the same stake.
| Decimal | Fractional | American | Implied probability | € 10 stake returns |
|---|---|---|---|---|
| 1.20 | 1/5 | -500 | 83.3% | € 12.00 |
| 1.33 | 1/3 | -300 | 75.0% | € 13.30 |
| 1.50 | 1/2 | -200 | 66.7% | € 15.00 |
| 1.67 | 2/3 | -150 | 60.0% | € 16.70 |
| 1.91 | 10/11 | -110 | 52.4% | € 19.10 |
| 2.00 | 1/1 (evens) | +100 | 50.0% | € 20.00 |
| 2.20 | 6/5 | +120 | 45.5% | € 22.00 |
| 2.50 | 6/4 | +150 | 40.0% | € 25.00 |
| 3.00 | 2/1 | +200 | 33.3% | € 30.00 |
| 4.00 | 3/1 | +300 | 25.0% | € 40.00 |
| 5.00 | 4/1 | +400 | 20.0% | € 50.00 |
| 6.00 | 5/1 | +500 | 16.7% | € 60.00 |
| 10.00 | 9/1 | +900 | 10.0% | € 100.00 |
| 11.00 | 10/1 | +1000 | 9.1% | € 110.00 |
| 21.00 | 20/1 | +2000 | 4.8% | € 210.00 |
| 51.00 | 50/1 | +5000 | 2.0% | € 510.00 |
A few anchors in the table make the whole system readable at a glance. 2.00, 1/1 and +100 are the same thing — the “evens” point where a winning bet exactly doubles your money, and the center of gravity from which all other values radiate. Below that line, American odds turn negative and grow larger as the favorite gets stronger; above it, they turn positive and grow larger as the underdog gets longer. Once you know that 2.00 is the pivot, you can place any unfamiliar number within seconds.
Decimal odds: the world’s default
Decimal notation is the format used across continental Europe, Australia, Canada and most of the online world, and it dominates for one reason: it’s the easiest to calculate. The decimal number is your total return per unit staked — multiply your stake by the decimal, and the result is what lands in your account if you win, stake included.
The calculation for any decimal odd:
- Total return = stake × decimal odds. € 20 at 3.40 returns € 68.
- Profit = (stake × decimal odds) − stake. The same € 20 wins € 48 of profit.
- Implied probability = 1 ÷ decimal odds. Odds of 3.40 imply a 29.4% chance.
The strength of the format is directness — no fractions to interpret, no signs to track, one multiplication covers everything. Its weakness is cultural, not mathematical: bettors raised on fractional or American notation find decimals less expressive, because the number doesn’t “read” as a probability the way 4/1 does. That’s a habit, not a flaw, and it fades after a few weeks of use.
Fractional odds: the British tradition
Fractional notation is the native format of UK and Irish bookmakers, horse racing and the betting shops that built modern gambling. It reads as profit-to-stake: 11/4 means you win 11 units for every 4 staked. The fraction expresses profit only — the stake comes back separately — which is why the same bet appears as 11/4 in fractional and 3.75 in decimal.
The calculations, using 11/4 as the example:
- Profit = stake × (numerator ÷ denominator). € 10 × (11 ÷ 4) = € 27.50 profit.
- Total return = profit + stake. € 27.50 plus the € 10 stake = € 37.50 — matching decimal 3.75.
- Implied probability = denominator ÷ (numerator + denominator). For 11/4: 4 ÷ 15 = 26.7%.
The format’s charm is linguistic: “four-to-one on” or “ten-to-one against” communicates a bet’s shape in a sentence, and racing culture speaks it natively. Its practical weakness appears in prices like 29/10 or 13/8, which require arithmetic to compare, and in the simple fact that the rest of the world doesn’t use it. Modern British operators display fractional and decimal side by side for exactly this reason.
American odds: profit on a ±100 pivot
American (moneyline) notation is the native format of US sportsbooks, built around a pivot at 100. Negative numbers describe favorites: they tell you how much you must stake to win $ 100. Positive numbers describe underdogs: they tell you how much profit you make on a $ 100 stake.
The two halves of the system, worked separately:
- Negative odds (favorites): profit = stake ÷ |odds| × 100. At -150, a $ 30 stake wins $ 20 of profit (30 ÷ 150 × 100). A -200 favorite needs $ 200 staked to win $ 100 — equivalent to decimal 1.50.
- Positive odds (underdogs): profit = stake × odds ÷ 100. At +240, a $ 50 stake wins $ 120 (50 × 240 ÷ 100). Equivalent to decimal 3.40.
- Implied probability: for negatives, |odds| ÷ (|odds| + 100); for positives, 100 ÷ (odds + 100). At -150 that’s 150 ÷ 250 = 60%; at +240 it’s 100 ÷ 340 = 29.4%.
The format looks alien to outsiders and is second nature inside the American market, where moneyline prices also encode a cultural shorthand: -110 is the standard “juice” on even-sided markets, and anything at +100 or better is, by convention, a good price on a near coin-flip. The negative-positive split does have one genuine advantage: it marks favorites and underdogs at a glance, without any calculation.
The two conversion formulas that connect everything
All three formats reduce to two conversions, and knowing them turns any odds display into any other. They’re short enough to memorize and worth memorizing, because comparing prices across international bookmakers is where real value is found.
- Fractional or American to decimal: add the profit-per-unit to 1. For fractions, decimal = (numerator ÷ denominator) + 1 — so 7/2 becomes 4.50. For American odds, decimal = (odds ÷ 100) + 1 for positives (+150 becomes 2.50) and (100 ÷ |odds|) + 1 for negatives (-200 becomes 1.50).
- Decimal to implied probability: divide 1 by the decimal and read it as a percentage. 4.00 implies 25%, 1.25 implies 80%.
The second formula carries more practical weight than the first, because implied probability is the unit in which all odds become comparable. When one site prices a team at 2.10 and another at 2.20, the difference sounds trivial — but in probability terms it’s 47.6% versus 45.5%, a two-point gap that over a season of bets is the entire difference between profit and loss. Bookmakers display in whichever format their market prefers; serious bettors think in implied probability, and convert everything else on arrival.
Which format to use, and how to set it
Every licensed bookmaker lets you switch display formats in account or display settings, usually with one click — and there’s no penalty for doing so, since the underlying price is identical. The sensible defaults follow your reading habits: decimal if you’re in Europe, Canada or Australia; fractional if you bet racing in Britain or Ireland; American if you follow US sports or use American platforms.
Three practical habits make the formats interchangeable in daily use:
- Convert once, compare always. When price-shopping across bookmakers in different formats, convert everything to decimal and implied probability first. A price difference invisible in fractions (13/8 vs 8/5) is obvious in decimals (2.63 vs 2.60).
- Know your anchors. 2.00 / 1/1 / +100 (evens), 1.50 / 1/2 / -200 (two-to-one on), 3.00 / 2/1 / +200 (two-to-one against) — with three anchors memorized, any new price can be bracketed mentally before you reach for a calculator.
- Watch for rounding in American odds. Bookmakers sometimes display -105 or +115 rather than clean numbers; the conversions still work exactly the same, but the implied probabilities of near-pivot prices cluster tightly, and small differences there matter more than they look.
One final note belongs to every odds conversation: the formats differ, but the margin doesn’t. All three notations embed the bookmaker’s overround the same way, and converting between them changes nothing about the house edge. The format question is about reading, not about value — value comes from finding the best number across books, in whichever notation each of them displays it.
Conclusion
Decimal, fractional and American odds are three spellings of one word, and the table above is the complete translation key. Decimal multiplies; fractional divides; American pivots around 100 with signs for favorites and underdogs. Two formulas — add-one conversion and one-over-implied-probability — connect any format to any other and to the probability underneath them all.
The practical takeaway outranks the arithmetic: think in implied probability, display in whichever format your market uses, and convert ruthlessly when comparing prices across bookmakers. A bettor who reads all three formats fluently sees the entire global market as a single menu — and the best price on any outcome, wherever in the world it’s quoted, is never more than one formula away. That fluency costs an afternoon to acquire and pays for itself the first time the best odds on your bet turn out to be written in a language you’d have scrolled past.
