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Free toolsimplied-probability

Odds are probabilities
wearing a costume.

American odds, decimal odds, fractional odds, and implied probability are four notations for the same number. −110 means risking $110 to win $100 — which is exactly a 52.38% break-even rate, which is exactly 1.909 in decimal and 10/11 in fractional. Edit any format below and read the other three. Pure conversion — no vig removed, no opinion added.

Edit any format — the other three follow

Negative = favorite (risk that much to win $100); positive = underdog (win that much on $100).

Total return per $1 staked, stake included. Must be greater than 1.

UK notation: profit / stake, so 10/11 wins £10 per £11 risked. “Evens” = 1/1.

The break-even win rate the price implies — vig included when it comes from a book's odds.

Result

American

-110

Decimal

1.909

Fractional

10/11

Implied probability

52.38%

A single price's implied probability includes the book's margin. To see what the market "really" thinks, de-vig BOTH sides with the no-vig calculator. Fractional odds are shown in lowest terms, so −110 comes back as the exact 10/11 rather than a rounded decimal dressed as a fraction.

The conversion formulas

American odds to implied probability (the notation splits on sign):

negative (favorite): p = |odds| / (|odds| + 100)   →  −110 ⇒ 110/210 = 52.38%
positive (underdog): p = 100 / (odds + 100)       →  +150 ⇒ 100/250 = 40.00%

Decimal odds are the total return per $1 staked, so the probability is simply the reciprocal:

p = 1 / decimal   →  1.909 ⇒ 52.38%  ·  decimal = 1 / p

Fractional odds — the UK and Irish convention, and still the default in horse racing — quote profit over stake rather than total return, which is the one difference that trips people up. So the fraction is always the decimal price minus one:

decimal = numerator / denominator + 1   →  5/2 ⇒ 3.5 ⇒ +250 ⇒ 28.57%
10/11 ⇒ 1.909… ⇒ −110 ⇒ 52.38%  ·  1/1 (“evens”) ⇒ 2.0 ⇒ +100 ⇒ 50.00%

Converting the other way needs care: 1.909… is not a tidy fraction of anything, and rounding it to 9/10 quietly changes the price by nearly a point of probability. The converter above walks the continued-fraction convergents instead, which returns the exact 10/11.

One caveat worth internalizing: the implied probability of a single book price includes the book's margin, so both sides of a game sum to more than 100%. To see the market's fair probabilities, de-vig the pair with the no-vig calculator.

More free tools

No-Vig CalculatorStrip the juice from a two-way market: fair probabilities + fair odds from both sides’ prices.EV CalculatorYour probability + the offered price → expected value per $100, and the break-even bar.Kelly CalculatorBankroll-relative stake sizing from the Kelly criterion — full, half, or quarter.Hold CalculatorWhat the market charges: overround + theoretical hold from a two-way price pair.Hedge CalculatorYour open ticket + the current opposite price → the stake that pays the same either way.Parlay CalculatorCombine 2–12 legs: combined odds, payout, and the margin that compounds leg by leg.Half-Point CalculatorHow often games actually land on each number — and what that measured frequency prices a half-point at.

The same math, on live lines.

These calculators run the exact helpers the Blitzen terminal uses on every board. See them applied to real markets — and how we grade everything against the close.