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Free toolsimplied-probability

Odds are probabilities
wearing a costume.

American odds, decimal odds, and implied probability are three 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. Edit any format below and read the other two. Pure conversion — no vig removed, no opinion added.

Edit any format — the other two 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.

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

Result

American

-110

Decimal

1.909

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.

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

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

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.