What each format actually says
An odds price answers one question: if this bet wins, how much comes back? The three formats answer it in three grammars, and confusing the grammars is the single most common conversion mistake.
| Format | What the number means | Even-money example |
|---|---|---|
| Decimal | Total return per 1 unit staked, stake included | 2.00 |
| Fractional | Profit / stake, stake excluded | 1/1 (evens) |
| American | Profit on a 100 stake (+) or stake to win 100 (−) | +100 / −100 |
Decimal is the only format that bakes your stake into the number. A winning 1-unit bet at decimal 2.50 returns 2.50 units in your hand; 1.50 of that is profit and 1.00 is your own stake coming back. Fractional and American both strip the stake out and quote profit alone, which is why they look smaller for the same bet.
Decimal to everything
Decimal is the hub. Learn these two directions and you can route any price through decimal.
# decimal (D) is total return per 1 unit, stake included # decimal to fractional fractional = (D − 1) # expressed as a fraction in lowest terms # D = 2.50 to 1.50/1 = 3/2 = 6/4 # decimal to American if D is 2.00 or higher: American = (D − 1) × 100 # plus price if D is below 2.00: American = −100 / (D − 1) # minus price
Worked: decimal 2.50 is a plus price, so American = (2.50 − 1) × 100 = +150. Decimal 1.50 is a minus price, so American = −100 / (1.50 − 1) = −100 / 0.50 = −200. Round American results to the nearest whole number, because books never display fractional American prices.
Everything to decimal
Going the other way is where implied probability becomes trivial, so this is the direction most models use.
# fractional a/b to decimal D = (a / b) + 1 # 6/4 to 1.5 + 1 = 2.50 # American to decimal if American is positive (+A): D = (A / 100) + 1 # +150 to 1.5 + 1 = 2.50 if American is negative (−A): D = (100 / A) + 1 # −200 to 0.5 + 1 = 1.50
Once a price is decimal, the raw implied probability is a one-step calculation: probability = 1 / decimal. Decimal 2.50 encodes a 40 percent raw probability; decimal 1.50 encodes 66.7 percent. That is the raw figure before removing the book's margin — the implied probability and overround guide covers the fair adjustment.
A quick-lookup table
These are the prices you meet most, aligned across formats. Probabilities shown are raw (pre-margin).
| Decimal | Fractional | American | Raw probability |
|---|---|---|---|
| 1.50 | 1/2 | −200 | 66.7% |
| 1.67 | 4/6 (2/3) | −150 | 60.0% |
| 1.91 | 10/11 | −110 | 52.4% |
| 2.00 | 1/1 (evens) | +100 | 50.0% |
| 2.50 | 6/4 (3/2) | +150 | 40.0% |
| 3.00 | 2/1 | +200 | 33.3% |
| 4.00 | 3/1 | +300 | 25.0% |
Note the −110 row. That standard American price is fractional 10/11 and decimal 1.909…, an ugly number that rounds to 1.91 on most decimal displays. That rounding is deliberate on the book's side and is the origin of most of the cent-level disagreements described below.
The rounding traps
Conversions are exact in algebra and approximate on a screen. Three traps account for nearly every mismatch a bettor notices.
- American is coarse. American prices are whole numbers, so a displayed −115 covers a small band of true decimal prices (roughly 1.865 to 1.875). Converting −115 to decimal gives 1.8696, but the book's underlying number may be a hair away. The coarseness is largest around −100 to −120, where each American step is a bigger probability jump.
- Chaining compounds error. Convert decimal to American, then that American back to fractional, and you have rounded twice. Always convert once, directly, from the most precise format the book gives you.
- Fractional reduction hides precision. Displaying 20/21 as "even-ish" or forcing a price into a familiar fraction like 5/6 can move the true decimal by more than a cent. Treat the fraction as exact only when it is the book's own quoted fraction.
The practical rule: pick one canonical format for your own math — decimal, almost always — convert into it once, and only convert out for display or for comparing against a book that quotes differently.
Why decimal wins for computation
Two properties make decimal the working format for anyone doing the math rather than just reading a slip.
- Probability is one step: raw implied probability = 1 / decimal. No branching on sign as American requires.
- Parlays multiply: the combined decimal price of independent legs is simply the product of the leg prices. A 1.91 and a 1.91 leg combine to 1.91 × 1.91 = 3.648. American parlay math has no such clean form.
Fractional survives mostly in UK racing tradition and American on US screens, but neither is where you want to do arithmetic. Convert, compute, convert back.