American vs Decimal vs Fractional Odds — How to Convert Between Them

Three odds formats exist in sports betting. They all express the same underlying concept — the relationship between your stake and your potential payout — but they look completely different on screen. American odds dominate North American sportsbooks. Decimal odds are the standard across Europe, Australia, and on prediction market platforms like Polymarket. Fractional odds remain the traditional format in UK and Irish horse racing and high-street betting shops. This guide covers how each format works, the conversion formulas between them, and which format is most useful for analytical betting and model comparison.

American Odds Explained

American odds use a baseline of $100 and split into two categories: negative numbers for favorites and positive numbers for underdogs.

Negative odds tell you how much you must risk to win $100. A line of -150 means you risk $150 to win $100. Your total return if the bet wins is $250 (your $150 stake plus $100 profit). The larger the negative number, the heavier the favorite: -300 means risk $300 to win $100; -110 means risk $110 to win $100 (the standard "juice" line on NFL and NBA sides).

Positive odds tell you how much you win on a $100 stake. A line of +200 means you risk $100 to win $200. Your total return is $300. The larger the positive number, the bigger the underdog: +500 means a $100 bet returns $600 total; +1000 means it returns $1,100.

The even-money line is +100 / -100, meaning you risk $100 to win $100 — a true coin-flip price before vig. In practice, sportsbooks rarely post an actual +100 line because the vig would be invisible.

Converting American Odds to Implied Probability

This is the critical step for evaluating whether a bet has value:

• Negative odds: |odds| ÷ (|odds| + 100)

  • Example: -150 → 150 ÷ 250 = 60.00%
  • Example: -110 → 110 ÷ 210 = 52.38%

• Positive odds: 100 ÷ (odds + 100)

  • Example: +200 → 100 ÷ 300 = 33.33%
  • Example: +150 → 100 ÷ 250 = 40.00%

These implied probabilities include the vig. To get the market's true probability, you need to remove the vig by normalizing both sides back to 100%.

Decimal Odds Explained

Decimal odds represent the total return per unit staked, including your original stake. They are the mathematically cleanest format because the formula never changes regardless of whether the outcome is a favorite or an underdog.

• 1.67: Stake $1, get back $1.67 total (profit of $0.67). This is the decimal equivalent of -150 American.
• 3.00: Stake $1, get back $3.00 total (profit of $2.00). Equivalent to +200 American.
• 1.91: Stake $1, get back $1.91 total. Equivalent to -110 American — the standard vig line in decimal form.
• 2.00: Even money. Stake $1, get back $2.00. Equivalent to +100 American.

Converting Decimal Odds to Implied Probability

The simplest conversion in all of betting:

Implied probability = 1 ÷ decimal odds

• 1.67 → 1 ÷ 1.67 = 59.88%
• 3.00 → 1 ÷ 3.00 = 33.33%
• 1.91 → 1 ÷ 1.91 = 52.36%

Decimal odds are the default in European sportsbooks (Bet365, Unibet, Pinnacle), on betting exchanges (Betfair), and increasingly on US-facing platforms that cater to analytical bettors. Most AI prediction models and probability-based tools — including ensemble networks like Sportstensor — output raw probabilities, which convert to decimal odds with a single division: decimal odds = 1 ÷ probability.

Fractional Odds Explained

Fractional odds show profit relative to the stake, written as a fraction. The numerator (top number) is your profit; the denominator (bottom number) is your stake.

• 2/3: Stake $3, profit $2 (total return $5). Equivalent to -150 American / 1.67 decimal.
• 2/1 (read "two to one"): Stake $1, profit $2 (total return $3). Equivalent to +200 American / 3.00 decimal.
• 10/11: Stake $11, profit $10 (total return $21). Equivalent to -110 American / 1.91 decimal.
• 1/1 (read "evens"): Stake $1, profit $1. Even money.
• 5/1: Stake $1, profit $5. A longshot.

Converting Fractional Odds to Implied Probability

Implied probability = denominator ÷ (numerator + denominator)

• 2/3 → 3 ÷ (2 + 3) = 3 ÷ 5 = 60.00%
• 2/1 → 1 ÷ (2 + 1) = 1 ÷ 3 = 33.33%
• 10/11 → 11 ÷ (10 + 11) = 11 ÷ 21 = 52.38%

Fractional odds remain common in UK horse racing, Premier League betting on British high-street shops, and golf outrights. They are increasingly rare on digital platforms, which have mostly migrated to decimal odds. If you bet on UK racing or follow UK football tipsters, you will still encounter them regularly.

Master Conversion Table

This table covers the most common odds you will encounter across all three formats:

Implied Probability	American	Decimal	Fractional
90%	-900	1.11	1/9
80%	-400	1.25	1/4
75%	-300	1.33	1/3
66.7%	-200	1.50	1/2
60%	-150	1.67	2/3
57.1%	-133	1.75	4/7
52.4%	-110	1.91	10/11
50%	+100	2.00	1/1 (evens)
47.6%	+110	2.10	11/10
40%	+150	2.50	3/2
33.3%	+200	3.00	2/1
25%	+300	4.00	3/1
20%	+400	5.00	4/1
16.7%	+500	6.00	5/1
10%	+900	10.00	9/1
5%	+1900	20.00	19/1

Bookmark this table. After a few weeks of active use, the conversions become second nature — but having it as a reference accelerates the learning curve.

Cross-Format Conversion Formulas

American → Decimal

• Negative American: (|odds| + 100) ÷ |odds|

  • -150 → 250 ÷ 150 = 1.667
  • -110 → 210 ÷ 110 = 1.909

• Positive American: (odds + 100) ÷ 100

  • +200 → 300 ÷ 100 = 3.000
  • +150 → 250 ÷ 100 = 2.500

Decimal → American

• Decimal less than 2.00 (favorite): -100 ÷ (decimal - 1)

  • 1.67 → -100 ÷ 0.67 = -149.25 (rounded to -150)
  • 1.50 → -100 ÷ 0.50 = -200

• Decimal 2.00 or greater (underdog or even money): (decimal - 1) × 100

  • 3.00 → 2.00 × 100 = +200
  • 2.50 → 1.50 × 100 = +150

Fractional → Decimal

(numerator ÷ denominator) + 1

• 2/1 → (2 ÷ 1) + 1 = 3.00
• 2/3 → (2 ÷ 3) + 1 = 1.667
• 10/11 → (10 ÷ 11) + 1 = 1.909

Decimal → Fractional

This is the trickiest conversion because fractional odds traditionally use whole-number ratios. Subtract 1 from the decimal, then express the result as a simplified fraction:

• 3.00 → 3.00 - 1 = 2.00 → 2/1
• 1.50 → 1.50 - 1 = 0.50 → 1/2
• 2.50 → 2.50 - 1 = 1.50 → 3/2

Some decimal prices do not reduce to clean fractions (1.87 → 0.87/1 is awkward), which is one reason the betting industry is moving toward decimal as the universal format.

Which Format Should You Use?

For analytical work — EV calculations, model comparison, CLV tracking — decimal odds or raw probabilities are the standard. Decimal odds work the same way regardless of the odds range, making formulas cleaner. Raw probabilities are even better because they eliminate the odds-to-probability conversion step entirely.

If you trade on Polymarket, contract prices are already probabilities expressed in cents. A contract at $0.65 is a 65% implied probability — no conversion needed. This is one reason prediction markets appeal to quantitative bettors: the format removes friction from the analytical process.

AI prediction platforms — including ensemble networks like Sportstensor — typically output probabilities directly. A Sportstensor consensus might say a team has a 62.3% probability of winning. To compare that against a sportsbook, convert the book's American or fractional odds to implied probability (remembering to de-vig first), then check whether your model's number is higher or lower. If your model says 62.3% and the de-vigged market says 58%, you may have found edge.

For casual consumption and communication with other bettors, use whatever format your platform displays. But for your spreadsheets, models, and decision-making process — decimal or probability, always.

Frequently Asked Questions

Why do American sportsbooks use the American format instead of decimal? Tradition and familiarity. The American format was designed around the concept of $100 units, which is intuitive for bettors thinking in dollar terms. As the US market matures and more analytical tools enter the space, decimal odds are becoming more common on US platforms.

What does "even money" mean? Even money means your profit equals your stake: bet $100, win $100. In American odds it is +100, in decimal it is 2.00, and in fractional it is 1/1 (evens). It implies a 50% probability before vig.

How do I convert odds to probability in my head? For American favorites, think of -200 as "I need to risk $200 to win $100, so the book thinks it happens about two-thirds of the time." For underdogs, +300 means "the book thinks this happens about one in four times." These mental shortcuts get you within a few percentage points without a calculator.

Which format is used on Polymarket? Polymarket uses neither traditional odds format. Contract prices are denominated in cents from $0.01 to $0.99, which directly represent implied probability as a percentage. A price of $0.72 means a 72% probability. This is the purest format for analytical work.

Key Takeaways

Odds formats are a language barrier, not a conceptual barrier. All three formats express the same information: the implied probability of an outcome and the payout structure of a bet. Learn the conversion formulas, bookmark the table above, and — most importantly — always work in probabilities when doing analytical work. The format your sportsbook displays is a presentation choice. The probability underneath is what determines whether a bet has value.