Implied Probability Calculator

Q: What is implied probability in sports betting?

Implied probability is the likelihood of an outcome suggested by the betting odds. A bookmaker sets odds to reflect their assessment of each outcome's probability, plus a built-in margin (vig) that ensures profit. Converting odds to implied probability lets you see the bookmaker's implied view of the event, and compare it to your own assessment to find value bets.

Q: How do you convert American odds to probability?

For positive American odds (e.g. +150): implied probability = 100 / (odds + 100) x 100. For +150: 100 / 250 = 40%. For negative odds (e.g. -110): implied probability = |odds| / (|odds| + 100) x 100. For -110: 110 / 210 = 52.38%.

Q: How do you convert decimal odds to probability?

Decimal odds represent your total return per unit staked (including stake). Implied probability = (1 / decimal odds) x 100. For decimal odds 2.50: probability = 1/2.50 x 100 = 40%. For 1.91 (common on -110 American): 1/1.91 = 52.36%.

Q: How do you convert fractional odds to probability?

Fractional odds n/d mean you win n units for every d staked. Implied probability = d / (n + d) x 100. For 5/2 odds: probability = 2 / (5+2) x 100 = 28.57%. For 1/1 (evens): 1/(1+1) = 50%.

Q: What is the bookmaker's margin (vigorish or vig)?

Bookmakers set odds so that the sum of all implied probabilities across all outcomes exceeds 100%. The excess above 100% is the margin or vig. For example, if a match has two outcomes with implied probabilities of 55% and 52%, the total is 107% - the vig is 7%. This built-in margin ensures the bookmaker profits regardless of the outcome over the long run.

Q: What do American odds of -110 mean?

American odds of -110 mean you must wager $110 to win $100 profit (plus get your $110 back on a win). The -110 line is the standard on many spread bets and over/under wagers. The implied probability = 110/(110+100) = 52.38%. A bookmaker applying -110 to both sides of a bet profits approximately 4.5% on every bet regardless of outcome.

Q: What do American odds of +200 mean?

American odds of +200 (positive) mean you win $200 profit for every $100 wagered. The + sign indicates an underdog. The implied probability = 100/(200+100) = 33.33%. If you believe the true probability is higher than 33.33%, this represents value since the odds underestimate the outcome's likelihood.

Q: How do I compare betting value using implied probability?

Compare the implied probability from the bookmaker to your own estimated probability for the outcome. If the bookmaker implies 40% but you estimate the true probability is 55%, the odds offer positive expected value (a 'value bet'). Over many such bets, your edge should produce a profit. Value = (your estimated prob / bookmaker implied prob) - 1.

Q: What is the difference between decimal and American odds?

Decimal odds include the stake in the return figure (e.g. 2.50 means you get back $2.50 per $1 staked, profit of $1.50). American odds show only the profit relative to a $100 baseline. They are equivalent representations: American +150 = Decimal 2.50 = Fractional 3/2. Converting between them is straightforward with the formulas this calculator uses.

Q: What are the most common fractional odds in UK horse racing?

Common UK fractional odds include evens (1/1 = 50%), 2/1 (33.3%), 5/2 (28.6%), 3/1 (25%), 4/1 (20%), 5/1 (16.7%), 9/4 (30.8%), 6/4 (40%), and 11/10 (47.6%). UK horse racing traditionally uses fractional odds displayed as how much profit you make for every unit staked.

Convert American, decimal, or fractional betting odds to implied win probability instantly. See all formats at once.

P% What is Implied Probability?

Implied probability is the likelihood of an outcome as implied by the betting odds offered by a bookmaker. When a sportsbook or betting exchange sets odds on an event, those odds embed an implicit probability for each outcome. Converting odds to probability lets you interpret what the bookmaker believes is likely to happen and compare that against your own analysis.

Every odds format — American, decimal, and fractional — encodes the same information in a different way. American odds (also called moneyline) are standard in North American sports betting and show how much profit you make on a $100 bet (positive) or how much you must wager to win $100 (negative). Decimal odds are the standard in Europe, Australia, and New Zealand, and represent the total return per unit staked including the stake itself. Fractional odds are traditional in UK horse racing and show profit per unit staked as a fraction.

Understanding implied probability is fundamental to finding value in sports betting. A value bet exists when the true probability of an outcome is higher than the implied probability reflected in the odds. Over time, consistently finding and wagering on true value bets produces a positive expected return. Without understanding implied probability, comparing odds from different formats is confusing; with it, the comparison becomes straightforward.

Bookmakers build their margin (called the vigorish, vig, or juice) into the odds by setting the sum of all implied probabilities above 100%. For example, on a two-outcome event, they might set odds implying 53% and 51%, totalling 104%. This 4% overround is their expected profit margin regardless of the outcome.

Formulas: Odds to Implied Probability

American Odds to Probability:

Positive odds (e.g. +150): P = 100 / (odds + 100) × 100%

Negative odds (e.g. -110): P = |odds| / (|odds| + 100) × 100%

Decimal Odds to Probability:

P = (1 / decimal odds) × 100%

Fractional Odds to Probability:

P = denominator / (numerator + denominator) × 100%

Example: 5/2 → P = 2 / (5 + 2) × 100 = 28.57%

Converting back from probability to all formats:

Decimal = 100 / P

American (if P ≥ 50): odds = −(P / (100 − P)) × 100

American (if P < 50): odds = +((100 − P) / P) × 100

Fractional = (100 − P) : P (simplified)

How to Use This Calculator

Select your odds format — click the American, Decimal, or Fractional tab to match the odds format you have.
Enter the odds — for American odds, include the sign (e.g. -110 or +200). For decimal odds, enter the multiplier (e.g. 2.50). For fractional odds, enter the numerator and denominator in separate fields (e.g. 5 and 2 for 5/2 odds).
Click Calculate — instantly see the implied probability percentage and the odds expressed in all three formats for easy comparison.
Compare across bookmakers — use the results to compare odds from different sportsbooks that display odds in different formats.

Example Calculations

Example 1 — Standard NFL Spread Line

American odds -110 (standard NFL point spread line)

Negative odds: P = |-110| / (|-110| + 100) x 100 = 110/210 = 52.38%

Decimal = 100/52.38 = 1.9091 ≈ 1.91

Two sides at -110 each: total implied = 52.38% + 52.38% = 104.76% → vig ≈ 4.76%

Implied Probability = 52.38% · Decimal = 1.9091 · Fractional ≈ 10/19

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Example 2 — Heavy Underdog

American odds +200 (underdog wins if true probability exceeds 33.3%)

Positive odds: P = 100 / (200 + 100) x 100 = 100/300 = 33.33%

Decimal = 100/33.33 = 3.00

Fractional = 2/1 (you profit $2 for every $1 staked)

Implied Probability = 33.33% · Decimal = 3.0000 · Fractional = 2/1

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Example 3 — European Decimal Odds

Decimal odds 1.91 (common European bookmaker line equivalent to -110)

P = 1/1.91 x 100 = 52.36%

American = -(52.36/(100-52.36)) x 100 = -109.9 ≈ -110

Implied Probability = 52.36% · American = -110 · Fractional ≈ 91/100

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Example 4 — UK Fractional Horse Racing Odds

Fractional odds 5/2 (common UK horse racing price)

P = 2 / (5 + 2) x 100 = 2/7 x 100 = 28.57%

Decimal = 100/28.57 = 3.50

American = +((100-28.57)/28.57) x 100 = +250

Implied Probability = 28.57% · Decimal = 3.5000 · American = +250

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Frequently Asked Questions

What is implied probability in sports betting?+

Implied probability is the likelihood of an outcome suggested by the betting odds. A bookmaker sets odds to reflect their assessment of each outcome's probability, plus a built-in margin (vig). Converting odds to implied probability lets you see the bookmaker's implied view and compare it to your own assessment to find value bets.

How do you convert American odds to probability?+

For positive American odds (e.g. +150): implied probability = 100 / (odds + 100) x 100. For +150: 100/250 = 40%. For negative odds (e.g. -110): implied probability = |odds| / (|odds| + 100) x 100. For -110: 110/210 = 52.38%.

How do you convert decimal odds to probability?+

Decimal odds represent your total return per unit staked including stake. Implied probability = (1 / decimal odds) x 100. For decimal odds 2.50: probability = 1/2.50 x 100 = 40%. For 1.91: 1/1.91 = 52.36%.

How do you convert fractional odds to probability?+

Fractional odds n/d mean you win n units for every d staked. Implied probability = d / (n + d) x 100. For 5/2: probability = 2/(5+2) x 100 = 28.57%. For evens (1/1): 1/(1+1) = 50%.

What is the bookmaker's margin (vigorish)?+

Bookmakers set odds so the sum of all implied probabilities exceeds 100%. The excess is the margin or vig. For example, if a match has two outcomes with implied probabilities of 55% and 52%, the total is 107% - the vig is 7%. This ensures the bookmaker profits over the long run regardless of the outcome.

What do American odds of -110 mean?+

American odds of -110 mean you must wager $110 to win $100 profit (plus get your $110 back on a win). The -110 line is standard on many spread bets. Implied probability = 110/(110+100) = 52.38%. Two sides at -110 mean a bookmaker margin of approximately 4.76%.

What do American odds of +200 mean?+

American odds of +200 mean you win $200 profit for every $100 wagered. The + sign indicates an underdog. Implied probability = 100/(200+100) = 33.33%. If you believe the true probability is higher than 33.33%, this represents value since the odds underestimate the outcome's likelihood.

How do I compare betting value using implied probability?+

Compare the implied probability from the bookmaker to your own estimated probability for the outcome. If the bookmaker implies 40% but you estimate the true probability is 55%, the odds offer positive expected value (a value bet). Value = (your estimated prob / bookmaker implied prob) - 1.

What is the difference between decimal and American odds?+

Decimal odds include the stake in the return figure (e.g. 2.50 means you get back $2.50 per $1 staked, profit of $1.50). American odds show only the profit relative to a $100 baseline. They are equivalent: American +150 = Decimal 2.50 = Fractional 3/2.

What are common fractional odds in UK horse racing?+

Common UK fractional odds include evens (1/1 = 50%), 2/1 (33.3%), 5/2 (28.6%), 3/1 (25%), 4/1 (20%), 5/1 (16.7%), 9/4 (30.8%), 6/4 (40%), and 11/10 (47.6%). UK horse racing traditionally shows how much profit you make for every unit staked.

Implied Probability Calculator

P% What is Implied Probability?

Formulas: Odds to Implied Probability

How to Use This Calculator

Example Calculations

Example 1 — Standard NFL Spread Line

American odds -110 (standard NFL point spread line)

Example 2 — Heavy Underdog

American odds +200 (underdog wins if true probability exceeds 33.3%)

Example 3 — European Decimal Odds

Decimal odds 1.91 (common European bookmaker line equivalent to -110)

Example 4 — UK Fractional Horse Racing Odds

Fractional odds 5/2 (common UK horse racing price)

Frequently Asked Questions

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