How to Convert Odds to Probability: Step-by-Step Guide
Convert an offered price into its break-even probability, then decide what that number can and cannot tell you. The examples distinguish raw implied probabilities, normalized market estimates, and expected net profit. All examples are hypothetical and exclude fees, taxes, pushes, and voids unless stated otherwise.
Convert the Offered Price
| Format | Formula for raw implied probability q | Worked examples |
|---|---|---|
| Negative American A | abs(A) / (abs(A) + 100) | -110: 52.38%; -150: 60.00%; -300: 75.00% |
| Positive American A | 100 / (A + 100) | +110: 47.62%; +200: 33.33%; +350: 22.22% |
| Decimal D | 1 / D | 1.50: 66.67%; 2.00: 50.00%; 3.50: 28.57% |
| Fractional a/b | b / (a + b) | 5/2: 28.57%; 1/2: 66.67%; 7/4: 36.36% |
The implied break-even probability is the win rate needed to offset losses at that fixed price. The unknown true probability need not equal it. Keep full precision through a calculation and round only displayed results.
If the formats are unfamiliar, start with American Odds Explained.
Add the Raw Probabilities Before Normalizing
Use all mutually exclusive, exhaustive outcomes from the same operator, market, rules, and timestamp. A three-way market requires the draw price too. Do not combine unrelated quotes into a supposed complete market.
At -110/-110: qA = qB = 110/210 = 52.38%. The raw probability sum S = qA + qB = 104.76%. Overround means the excess S - 100%: 4.76 percentage points in this example. It is not realized bookmaker profit.
Proportional Normalization Is an Estimate
Normalized estimate rA = qA / S, where S is the sum, not the excess above one. Using decimal probabilities, 0.5238095 / 1.047619 = 0.50. Both sides normalize to 50%.
This method assumes margin is allocated proportionally. Other methods can allocate it differently. Normalized probabilities sum to one, but that arithmetic constraint does not validate the estimates or reveal the unknown true probabilities.
| Hypothetical outcome | Offered price | Raw probability | Normalized estimate |
|---|---|---|---|
| A | -175 | 63.64% | 61.87% |
| B | +155 | 39.22% | 38.13% |
Using unrounded inputs: S = 175/275 + 100/255 ≈ 1.0285205. For A, (175/275)/S ≈ 61.87%; for B, (100/255)/S ≈ 38.13%. The sum is 102.85% before normalization, an overround of 2.85 percentage points.
Compare Your Assumption with the Offered Break-Even Threshold
Beating a normalized estimate is insufficient. In the -175 example, an analyst assuming 62% exceeds the normalized 61.87%, but remains below the offered 63.64% break-even threshold.
With stake s, decimal price D, and assumed win probability p: expected net profit = p × s(D - 1) - (1 - p) × s = s(pD - 1). Total return on a win is sD, including stake; net profit on a loss is -s.
For a $100 stake at -175, D = 1 + 100/175. If p = 0.62, EV = 0.62 × $57.142857 - 0.38 × $100 ≈ -$2.57. A probability-point difference is not itself a dollar amount.
At +150, D = 2.50 and the break-even threshold is 40%. An assumed 45% creates a 5-percentage-point gap but EV = 0.45 × $150 - 0.55 × $100 = +$12.50 on a $100 stake. This is a model result, not evidence that the 45% assumption is correct.
The definition follows OpenStax’s expected-value rule: weight each net outcome by its probability and add. The numerical examples here are derived, not observed market results.
From Calculation to Review
Record the quoted price, settlement rules, timestamp, and your probability assumption. Keep expected profit separate from realized profit: the +150 selection returns $250 on a win or $0 on a loss, not its expected value every time.
For pushes and uncertainty in these estimates, continue to the mathematical interpretation guide.
Frequently Asked Questions
How do you convert American odds?
For positive odds, divide 100 by odds + 100. For negative odds, divide the absolute odds by absolute odds + 100. Thus +150 implies 40% and -200 implies 66.67%.
How do decimal and fractional odds convert?
For decimal odds D, use 1 / D. For fractional odds a/b, use b / (a + b). Decimal 3.50 and fractional 5/2 both imply 28.57%.
What does proportional normalization estimate?
Divide each raw implied probability by the sum for every mutually exclusive, exhaustive outcome in the same market. This produces normalized market probability estimates that sum to 100%; it does not reveal true probabilities or prove value at the offered prices.
What is the difference between probability advantage and EV?
A probability-point difference is not monetary expected value. With stake s, decimal return D, assumed win probability p, and win/loss outcomes only, expected net profit is s × (p × D - 1). The estimate is positive only when p exceeds 1 / D.