Three formats describe every sports bet on Earth: American (+200 / −110), decimal (3.00 / 1.91), and fractional (2/1 / 10/11). They're identical bets in different clothes. This guide explains what each format means, how to convert between them with simple math, and — most importantly — why implied probability is the only number you actually need to make decisions.
If you're staring at a sportsbook screen wondering why the same game shows −150 in one place and 1.67 in another, you're not missing anything — they're the same price. The reason multiple formats exist is historical (Americans use one convention, Europeans another, the UK a third), not mathematical. The math is identical. Once you understand the conversions and what implied probability means, every odds format becomes the same thing: a price you can either take or pass on.
American odds use $100 as the reference unit. The number tells you either what you'd win on a $100 bet (positive odds) or what you'd have to risk to win $100 (negative odds).
The flip between positive and negative at the +100 line is what makes American odds awkward for math. There's no continuous number axis — just two formulas depending on which side of even the price is on. That's why every other format exists.
Decimal odds are the European standard and the easiest format for math. The number is what a winning $1 bet pays back in total, including your stake. Multiply your stake by the decimal odds to get total return on a win.
Decimal odds have one mathematical superpower: implied probability is just 1 / decimal odds. No formula switching, no positive/negative cases. 1.91 implies 1/1.91 = 52.4%. 3.00 implies 1/3 = 33.3%. That's why anyone doing serious betting math converts to decimal first.
Fractional odds are the UK standard, common in horse racing and traditional British bookmakers. The fraction expresses the ratio of profit to stake.
Fractional odds are the least useful for math because they don't reduce cleanly to common formulas. To convert to decimal: decimal = (numerator / denominator) + 1. So 2/1 = 3.00, 10/11 = 1.91. Then proceed from decimal as above.
Format doesn't matter for decisions; implied probability does. Implied probability is what the odds say the market thinks the outcome's chance of happening is. It's the breakeven win rate — the rate at which the bet exactly cancels itself out over time, before vig.
From decimal odds: implied prob = 1 / decimal
From American positive: implied prob = 100 / (American + 100)
From American negative: implied prob = |American| / (|American| + 100)
From fractional: implied prob = denominator / (numerator + denominator)
The reason implied probability is the only number that matters: it's the benchmark your own probability estimate gets compared against. If you think a team should win 55% of the time and the market's implied probability says 47.6% (−110), you have ~7.4 percentage points of edge. The dollar value of that edge falls out of the EV formula. Run the math through the EV Calculator.
One important nuance: the implied probability you compute from the posted price includes the sportsbook's vig. The two sides of any two-way market always sum to more than 100% — the excess is the book's margin. To get the market's true probability estimate, you have to strip out the vig. The de-vigged implied probability is the consensus number sharp bettors compare their estimates against, not the raw posted implied probability.
Every common price across the three formats plus implied probability:
| American | Decimal | Fractional | Implied Prob |
|---|---|---|---|
| +500 | 6.00 | 5/1 | 16.7% |
| +300 | 4.00 | 3/1 | 25.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +150 | 2.50 | 3/2 | 40.0% |
| +120 | 2.20 | 6/5 | 45.5% |
| +100 | 2.00 | 1/1 | 50.0% |
| −110 | 1.91 | 10/11 | 52.4% |
| −120 | 1.83 | 5/6 | 54.5% |
| −150 | 1.67 | 2/3 | 60.0% |
| −200 | 1.50 | 1/2 | 66.7% |
| −300 | 1.33 | 1/3 | 75.0% |
| −500 | 1.20 | 1/5 | 83.3% |
Or skip the table entirely and use the Odds Converter — type any odds in any format, get all four representations instantly.
Walk into a professional bettor's spreadsheet and you'll find decimal odds and implied probability everywhere, with American odds shown only where the screen they're reading from forces them to. The reason is that every downstream calculation — EV, Kelly, no-vig, CLV — works in decimal or probability. American odds are read-only for sharps: they're the display format, not the working format.
For anyone working through this guide because they want to do their own math: convert posted American prices to decimal as your first step, then to implied probability for the decision, then back to American only when you need to communicate the bet to someone (or compare it to a screen). It's three steps but each step is short, and it eliminates the formula-switching errors that plague math done directly in American odds.
+200 American odds means you win $200 profit on every $100 you risk if the bet hits. Equivalently, it implies the outcome has about a 33.3% chance of happening (100 / (200 + 100) = 33.3%). Positive American odds always indicate the underdog.
−110 American odds means you have to risk $110 to win $100 profit. The implied probability is about 52.4% (110 / (110 + 100) = 52.4%). −110 is the standard price on most NFL and NBA point spreads — the extra $10 you risk vs $100 is the sportsbook's vig.
For positive American odds: decimal = (American / 100) + 1. So +200 = 3.00. For negative American odds: decimal = (100 / |American|) + 1. So −150 = 1.67. Decimal odds tell you the total return per dollar staked, including your stake back on a win.
They're three formats describing the same bet. American (+200 / −150) is the U.S. standard and uses $100 as a reference unit. Decimal (3.00) is the European standard and is the easiest for math — it's profit-per-dollar-staked plus 1. Fractional (2/1) is the UK standard and expresses profit-to-stake ratio. Every line can be converted to every other format.
Implied probability is what the odds say the market thinks the outcome's chance of happening is. It's calculated as 1 / decimal odds (or 100 / (American + 100) for positive American odds). On a −110 line, implied probability is 52.4% — the win rate at which the bet breaks even over the long run.
For doing math on the bet (computing EV, devigging, calculating CLV), decimal odds are the easiest format. For comparing to true probability, convert to implied probability. American odds are the U.S. retail standard and what you'll see on screens — but they're worse for math because the formula flips between positive and negative numbers.