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.
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
- Sports betting odds explained — a general topic about how odds are quoted and read, not the specific mathematical conversion to probability
Related terms
Odds & probability
Betting odds
Explains how odds are quoted in different formats.
Odds & probability
Odds vs probability
Distinguishes the two concepts and their relationship.
Odds & probability
Decimal odds to probability
Focused on the conversion for decimal odds only.
Odds & probability
Futures betting odds
Covers odds for long-term bets and their probability conversion.
Odds & probability
Odds vs probability formula
The mathematical formulas linking odds and probability.
Odds & probability
Odds vs probability in statistics
The statistical distinction between odds and probability.
Sources
- Mathematics of bookmaking en.wikipedia.org Provides the conversion formulas for decimal, fractional and American odds.
- Player Props: Understanding the Math Behind the Lines wizardofodds.com Gives the American odds conversion formula and explains margin removal.
- The Betting Odds Rating System: Using soccer forecasts to ... pmc.ncbi.nlm.nih.gov Discusses normalisation of implied probabilities to remove bookmaker margin.
- 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.