Odds, Probability & Bankroll
Odds vs probability
Odds compare the chance of an event happening to the chance of it not happening, while probability measures the likelihood of an event as a proportion of all possible outcomes.
Key points
- Odds are the ratio of the probability an event occurs to the probability it does not occur12.
- Probability is the chance of an event out of all possible outcomes, expressed as a number between 0 and 1.
- To convert odds back to probability, use p = odds / (1 + odds)5.
- Odds are used in logistic regression and betting markets, while probability is used for general likelihood statements.
Odds vs probability examples
| Likelihood | Probability (p) | Odds (p/(1-p)) |
|---|---|---|
| Very unlikely | 0.1 | 1 : 9 (9 to 1 against) |
| Even chance | 0.5 | 1 : 1 (even odds) |
| Very likely | 0.75 | 3 : 1 (3 to 1 on) |
Common questions
When to use odds vs probability?
Use probability when you want the share of outcomes — for example, a 25% chance of rain. Use odds when comparing successes to failures, such as in logistic regression or when stating betting odds like 3 to 1.
Where this term is used
Related terms
Odds & probability
Betting odds to probability
How to convert market odds into an implied probability percentage.
Odds & probability
Decimal odds to probability
Converting decimal betting odds into implied probability.
Odds & probability
Odds vs probability formula
The mathematical relationship between odds and probability expressed in formulas.
Odds & probability
Odds vs probability in statistics
How odds and probability differ in statistical contexts like logistic regression.
Odds & probability
Fractional odds to decimal
Converting fractional betting odds to decimal format.
Odds & probability
American odds to implied probability
Converting American moneyline odds into implied probability.
Sources
- 3.10 Odds | Probability, statistics, and the likelihood ratio for non-experts [1st Edition] lrcfs-ap2.dundee.ac.uk Defines odds as the ratio of probability of an event to its complement.
- Making sense of odds and odds ratios pubmed.ncbi.nlm.nih.gov Explains odds and odds ratios in accessible language.
- Understanding logistic regression analysis - PMC pmc.ncbi.nlm.nih.gov Clarifies the range constraints of odds vs probability.
- download?attachment sheffield.ac.uk Describes odds as comparing successes with failures.
- [PDF] FEEG6017 lecture: Logistic regression southampton.ac.uk Provides the core formula and example odds values.
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.