Gambling terms, explained straight

Odds, Probability & Bankroll

Betting odds to probability

Betting odds to probability is the conversion of a quoted betting price into the implied probability of an outcome, typically by taking the inverse of decimal odds.

Decimal odds
Implied probability = 1 / decimal odds1
Fractional odds (a-b)
Implied probability = b / (a + b)1
American odds
Negative: |odds| / (|odds| + 100); positive: 100 / (odds + 100)2

Key points

  • The conversion gives the implied probability the bookmaker has built into the price.1
  • Raw implied probabilities usually sum to more than 100% due to the bookmaker margin; they can be normalised to remove it.3
  • The same formula works for any fixed-odds market, including sports betting and point spreads.4

Common questions

How to convert betting odds to probability?

For decimal odds, divide 1 by the odds. For fractional odds a-b, divide b by a+b. For American odds, use |odds|/(|odds|+100) for negative odds, or 100/(odds+100) for positive odds.12

Where this term is used

Not the same as

Sources

  1. Mathematics of bookmaking en.wikipedia.org Provides the conversion formulas for decimal, fractional and American odds.
  2. Player Props: Understanding the Math Behind the Lines wizardofodds.com Gives the American odds conversion formula and explains margin removal.
  3. The Betting Odds Rating System: Using soccer forecasts to ... pmc.ncbi.nlm.nih.gov Discusses normalisation of implied probabilities to remove bookmaker margin.
  4. Fixed-odds betting en.wikipedia.org Confirms the conversion applies to fixed-odds betting generally.

Sources are drawn from regulators, universities and published research, and each one is labelled with what it actually is — a preprint is not called a paper. Bookmaker and affiliate pages are never cited here, because a page that sells betting is not a neutral authority on it.