Odds, Probability & Bankroll
Odds vs probability formula
The odds vs probability formula converts a probability p into odds using odds = p/(1-p), and odds back into probability using p = odds/(odds+1).
Key points
- Probability is the absolute chance of an event; odds compare the chance of the event to the chance of it not occurring.41
- When probability is 0.5, odds are 1.0 (1 to 1).2
- Betting odds are wagering prices, not the same as the mathematical odds-probability conversion.12
Where this term is used
Not the same as
- Betting odds to probability — a method for converting a bookmaker's odds format into implied probability, whereas the odds vs probability formula is the general mathematical relationship between probability and odds
Related terms
Odds & probability
Odds vs probability
Explains the conceptual difference between odds and probability.
Odds & probability
Decimal odds to probability
Shows how to convert decimal betting odds into implied probability.
Odds & probability
Odds vs probability in statistics
Covers the statistical interpretation of odds and probability.
Odds & probability
Odds
Defines odds as a ratio of event occurrence to non-occurrence.
Odds & probability
Betting odds
Explains how odds are used in wagering to represent payouts.
Odds & probability
American odds to implied probability
Converts American betting odds into implied probability.
Sources
- Odds en.wikipedia.org Provides the odds formula and distinguishes betting odds from mathematical odds.
- 9.2 Binary logistic regression | R for Health Data Science argoshare.is.ed.ac.uk Supplies both conversion formulas and the range of probability and odds.
- [PDF] FEEG6017 lecture: Logistic regression southampton.ac.uk Confirms the odds-to-probability conversion formula.
- 3.10 Odds | Probability, statistics, and the likelihood ratio for non-experts [1st Edition] lrcfs-ap2.dundee.ac.uk Defines odds as a ratio and explains the conceptual difference from probability.
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.