Odds Formats Explained: American, Decimal, Fractional
Odds formats explained with 3 conversion formulas and worked examples. Learn how American, Decimal, and Fractional odds hide or reveal the true price.
Three formats, one concept
Odds formats are different ways to express the same thing: the ratio between your potential payout and your stake. American odds dominate US sportsbooks. Decimal odds are the standard across Europe, Australia, and prediction markets like Kalshi and Polymarket. Fractional odds persist in UK horse racing. They all encode the same information. The differences are purely cosmetic.
If you only bet on one platform, you can get by with one format. But if you shop lines across sportsbooks, compare prices on prediction markets, or do any serious math, you need to read all three fluently. Converting odds to probability is the foundational skill behind every concept in sports betting math.
American odds explained
American odds center around $100 and come in two forms:
Positive odds (+150) tell you the profit on a $100 stake. If you bet $100 at +150 and win, you collect $250 total ($150 profit plus your $100 stake returned).
Negative odds (-200) tell you how much you must stake to profit $100. If you bet $200 at -200 and win, you collect $300 total ($100 profit plus your $200 stake returned).
The dividing line is even money: +100 and -100 both represent a 50% implied probability (decimal 2.00). Anything with a plus sign is an underdog. Anything with a minus sign is a favorite.
Converting American odds to implied probability
The formulas differ for positive and negative:
Positive odds: Implied Probability = 100 / (Odds + 100)
Example: +150. Implied probability = 100 / (150 + 100) = 100 / 250 = 40.0%
Negative odds: Implied Probability = |Odds| / (|Odds| + 100)
Example: -200. Implied probability = 200 / (200 + 100) = 200 / 300 = 66.7%
Converting American odds to decimal
Positive odds: Decimal = (Odds / 100) + 1
Example: +150. Decimal = (150 / 100) + 1 = 1.50 + 1 = 2.50
Negative odds: Decimal = (100 / |Odds|) + 1
Example: -200. Decimal = (100 / 200) + 1 = 0.50 + 1 = 1.50
The problem with American odds is that your brain processes positive and negative numbers on different scales. Comparing +135 to -145 requires mental gymnastics. Comparing 2.35 to 1.69 does not. This asymmetry is not accidental.
Decimal odds: the math-friendly format
Decimal odds represent the total return per dollar wagered, including your original stake.
2.50 means you receive $2.50 for every $1.00 bet. Your profit is $1.50 per dollar risked.
1.50 means you receive $1.50 for every $1.00 bet. Your profit is $0.50 per dollar risked.
1.00 is the floor. It means you get your money back and nothing else.
Converting decimal odds to implied probability
Implied Probability = 1 / Decimal Odds
Example: Decimal 2.50. Implied probability = 1 / 2.50 = 40.0%
Example: Decimal 1.50. Implied probability = 1 / 1.50 = 66.7%
This is why decimal is the preferred format for any calculation. Expected value, Kelly Criterion sizing, parlay payouts. All of them become simpler in decimal. Multiplying decimal odds is trivial. Multiplying American odds requires multiple conversion steps.
Prediction markets effectively use decimal odds too. A Polymarket contract priced at $0.40 is equivalent to decimal odds of 1 / 0.40 = 2.50. A Kalshi contract at 55 cents is 1 / 0.55 = 1.818 decimal. If you trade prediction markets, you are already thinking in decimal whether you realize it or not.
Fractional odds and their decline
Fractional odds express profit relative to stake.
3/2 (spoken "three to two") means $3 profit for every $2 wagered. Total return on a $2 bet is $5. This is equivalent to +150 American or 2.50 decimal.
1/4 (spoken "one to four") means $1 profit for every $4 wagered. Total return on a $4 bet is $5. This is equivalent to -400 American or 1.25 decimal.
Converting fractional odds
To decimal: Decimal = (Numerator / Denominator) + 1
Example: 3/2. Decimal = (3 / 2) + 1 = 1.5 + 1 = 2.50
To implied probability: Implied Probability = Denominator / (Numerator + Denominator)
Example: 3/2. Implied probability = 2 / (3 + 2) = 2 / 5 = 40.0%
Fractional odds are declining outside of UK horse racing. They are harder to compare at a glance, awkward for parlay calculations, and confusing when the denominator changes (is 11/8 better or worse than 6/4?). Most European sportsbooks now default to decimal. If you encounter fractional odds, convert them and move on.
Quick conversion reference
| American | Decimal | Fractional | Implied Prob |
|---|---|---|---|
| +300 | 4.00 | 3/1 | 25.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +150 | 2.50 | 3/2 | 40.0% |
| +100 | 2.00 | 1/1 | 50.0% |
| -110 | 1.909 | 10/11 | 52.4% |
| -150 | 1.667 | 2/3 | 60.0% |
| -200 | 1.50 | 1/2 | 66.7% |
| -300 | 1.333 | 1/3 | 75.0% |
The odds converter handles all three formats instantly. Plug in any number and it shows the equivalent in every format plus the implied probability.
How odds formats hide the vig
This is where formats stop being trivia and start costing you money.
A standard NFL spread is priced at -110 on both sides. In American format, it looks balanced. The number is the same. Your brain processes it as fair.
Convert to implied probability: each side implies 52.4%. The total is 104.8%. That 4.8% above 100% is the overround, and it represents the sportsbook's margin. You are paying a 4.6% hold on every dollar wagered in that market.
Now consider a market priced at -115 / +105. In American format, one side is slightly more expensive than the other. It still looks reasonable. But convert: -115 implies 53.5% and +105 implies 48.8%. Total: 102.3%. That is actually less vig than the -110/-110 market, even though the American format makes it look skewed. Your intuition about the raw numbers is wrong because positive and negative American odds operate on different scales.
Decimal makes the vig visible. The -110/-110 market in decimal is 1.909 / 1.909. The overround: (1/1.909) + (1/1.909) = 52.4% + 52.4% = 104.8%. You can calculate that in two seconds.
The -115/+105 market in decimal is 1.870 / 2.05. The overround: (1/1.870) + (1/2.05) = 53.5% + 48.8% = 102.3%. Instantly visible.
This is not a conspiracy. Sportsbooks use the format that makes their margin hardest to detect. American odds accomplish that because your brain does not naturally intuit the asymmetry between positive and negative numbers. Understanding what vig is and how to strip it is the first step toward finding real value. The de-vig calculator removes the margin using 7 different methods and shows the true probability underneath.
Why decimal is the only format that matters for math
For reading a US sportsbook, American odds are fine. For comparing lines, calculating EV, running Kelly Criterion sizing, pricing parlays, or doing anything quantitative, convert to decimal first.
Here is the conversion pipeline for cross-platform price comparison:
A Kalshi contract at $0.55, a Pinnacle line at -122, and a Bet365 line at 1.82 are all approximately the same price (54.5% to 55%). You cannot see that until they are in the same format.
If you trade across sportsbooks and prediction markets, the prediction market converter translates between contract prices and traditional odds formats in both directions.
The format you see on screen is a design choice. The math underneath is universal. Learn the conversions, use decimal for calculations, and never let the display format trick you into misjudging a price.
Frequently asked questions
- How do you convert American odds to decimal?
- For positive odds: divide by 100 and add 1. So +150 becomes 2.50. For negative odds: divide 100 by the absolute value and add 1. So -200 becomes 1.50.
- How do you convert betting odds to probability?
- For decimal odds, divide 1 by the odds. Decimal 2.50 implies 40% probability. For American positive, use 100 / (odds + 100). For American negative, use |odds| / (|odds| + 100). These give implied probability before removing the vig.
- Why do sportsbooks use American odds instead of decimal?
- American odds make the vig harder to see. The split between positive and negative numbers creates an asymmetry that obscures the true overround. Decimal odds make the margin visible in seconds, which is why sharp bettors and prediction markets prefer them.
- What is the difference between implied probability and true probability?
- Implied probability is derived directly from the odds and includes the sportsbook's vig. True probability is the implied probability after removing that margin. Use a de-vig calculator to convert from implied to true probability.
- Which odds format should I use for parlay calculations?
- Decimal. Always decimal. To calculate a parlay payout, multiply the decimal odds of each leg together. In American format, you would need to convert each leg first, making the calculation unnecessarily complicated.