Decimal odds of 2.50 imply a 40% chance: 1 / 2.50 = 0.40, and every odds format states that same probability in its own notation. Reading a price back as a percentage is what lets you set the bookmaker's number beside your own estimate, which is the entire point of the conversion.

The formula for each odds format

Decimal odds are the simplest case. Divide 1 by the decimal price and multiply by 100.

Implied probability = 1 / decimal odds × 100%

Decimal 2.50  →  1 / 2.50 = 0.400  →  40.0%
Decimal 1.47  →  1 / 1.47 = 0.6803 →  68.04%
Decimal 2.88  →  1 / 2.88 = 0.3472 →  34.73%

With fractional odds written a/b, the denominator goes over the sum of both parts.

Implied probability = b / (a + b) × 100%

6/4    →  4 / (6 + 4)    = 4/10   = 40.0%
47/100 →  100 / (47+100) = 100/147 ≈ 68.04%
47/25  →  25 / (47+25)   = 25/72  ≈ 34.73%

Two cases cover American odds, split by sign.

Positive odds:  Implied probability = 100 / (odds + 100) × 100%
Negative odds:  Implied probability = |odds| / (|odds| + 100) × 100%

+188  →  100 / (188 + 100) = 100/288 ≈ 34.73%
−213  →  213 / (213 + 100) = 213/313 ≈ 68.04%
−150  →  150 / (150 + 100) = 150/250 = 60.0%

The format is cosmetic. Decimal 2.88, fractional 47/25, and American +188 are the same price and all resolve to 34.73%. The underlying probability is identical across all three.

Knowing this lets you compare odds across bookmakers that display in different formats without losing accuracy in the conversion.

What implied probability tells you

The implied probability is the break-even line for that bet. If the outcome's true chance is higher than the implied probability, the bet has positive expected value. If lower, you lose money on average.

Read it as a threshold. The market arrived at that price through a combination of probabilistic assessment, trading flow, and margin loading, so it is not the bookmaker's honest estimate of what will happen. Your job is to decide whether the real probability sits above or below that threshold.

A price of 2.50 implying 40% does not mean the bookmaker believes this outcome wins 40% of the time. It means they set the price so that a bettor would need to win more than 40% of the time to profit at those odds.

The probability baked into the price is a commercial number, not a research number.

Why the implied probabilities in a market don't add up to 100%

Add the implied probabilities across all outcomes in a market and you get more than 100%. That excess is the overround, the bookmaker's built-in profit on the market.

Margin = (sum of all implied probabilities) − 100%

The 2022 Super Bowl closing prices show this clearly. These were the final market prices at kickoff, taken here as a teaching illustration.

Bengals:  2.88  →  34.73%
Rams:     1.47  →  68.04%
Sum:              102.77%
Margin:             2.77%  (2.77 / 102.77 = 2.69% of total handle)

A three-way football market makes the effect larger. Using a textbook illustrative example with a 120% book:

Home:  implied 60%
Draw:  implied 40%
Away:  implied 20%
Sum:   120%
Overround: 20%

The bookmaker expects to retain roughly $20 of every $120 wagered across the three outcomes. Because the book sums above 100%, the overround inflates each individual implied probability relative to the true probability.

At 34.73%, that price includes the bookmaker's estimate plus a share of the margin. It is not a clean estimate that the outcome has a 34.73% chance.

How to remove the margin

Stripping the margin from implied probabilities is called devigging. The goal is to recover the fair probability behind each price, which reflects the bookmaker's best estimate of the true chance before profit loading distorts it.

The proportional method (also called multiplicative) divides each raw implied probability by the sum of all implied probabilities in the market. Each raw figure gets scaled down in proportion to its share.

The bookmaker inflated every probability by the same relative factor, so dividing by the total restores the correct ratios.

Fair probability = raw implied probability / sum of all implied probabilities

Super Bowl example:
Bengals raw: 34.73%  →  34.73% / 102.77% = 33.79%
Rams raw:    68.04%  →  68.04% / 102.77% = 66.21%
Check:                   33.79% + 66.21% = 100.00%

Once summed, the result is 100%, and the margin is gone. The proportional method works well for two-way and three-way markets and is the most common starting point for devig work. That fair probability is what your model's estimate needs to beat, not the raw implied probability you read off the price.

Two alternative methods handle edge cases differently. The additive method subtracts an equal share of the overround from each implied probability, making it the better choice when you assume the margin is distributed evenly across outcomes.

Shin's method uses a square-root formula to model favorite-longshot bias. It's better suited to large-field markets like horse racing, where longshots carry a disproportionate share of the margin.

From implied probability to spotting value

Once you can convert any price to a probability and remove the margin, value betting becomes a comparison. Your estimated true probability of the outcome goes up against the devigged fair probability embedded in the offered price. When your estimate exceeds the fair probability, the offered price is too generous, and that gap is the edge.

The edge formula uses the offered decimal odds and your probability estimate.

Edge = (your true probability × decimal odds) − 1

A positive result is a value bet. Zero is break-even. Negative means the bet loses money on average, no matter how confident it feels.

Using the Super Bowl example, the devigged fair probability for the Bengals is 33.79%. Suppose your model puts their true win probability at 38% based on your own analysis.

Offered odds:            2.88  →  raw implied probability 34.73%
Devigged fair prob:      33.79%
Your model estimate:     38%   →  0.38

Edge = (0.38 × 2.88) − 1 = 1.0944 − 1 = +0.0944 = +9.44%  ← value bet

Counter-example with 30% estimate:
Edge = (0.30 × 2.88) − 1 = 0.864 − 1 = −0.136 = −13.6%  ← no value

A positive edge is an expected outcome over a large sample of bets, not a guarantee on any single result.

So the price on the board is only the first number in the chain. Turn it into a probability, strip the margin to reach the fair figure, then set that fair figure against your own estimate. That final comparison is where value is settled, and it only holds up when the margin has been taken out first.