Gambling terms, explained straight

Odds, Probability & Bankroll

Odds vs likelihood

Odds express the ratio of an event's probability to its complement, while likelihood describes how well a statistical model fits observed data.

Odds formula
P(event) / P(no event) or p/(1-p)12
Odds range
0 to infinity2
Example
Fair coin odds of heads: 1:14

Key points

  • Odds compare an outcome to its alternative; likelihood measures data support for a model or hypothesis.15
  • The terms are often confused but are not interchangeable in statistics or Bayesian inference.23
  • Likelihood appears in Bayesian updating as the evidence term that multiplies prior odds.56

Where this term is used

Odds & probability Odds Explains the ratio of event to non-event probability. Odds & probability Betting odds Covers how bookmakers express implied probability. Odds & probability Fractional odds to decimal Shows conversion between two common odds formats. Odds & probability Odds vs probability Distinguishes odds from probability as measures of chance. Odds & probability Likelihood vs probability Clarifies the difference between likelihood and probability. Odds & probability American odds Explains the moneyline odds format used in the US.

Sources

  1. Common pitfalls in statistical analysis: Odds versus risk - PMC pmc.ncbi.nlm.nih.gov Defines odds as P(event)/P(no event) and contrasts with likelihood.
  2. Understanding logistic regression analysis - PMC - NIH pmc.ncbi.nlm.nih.gov States odds range from 0 to infinity and notes confusion with likelihood.
  3. Relative vs absolute risk and odds: Understanding the difference pmc.ncbi.nlm.nih.gov Reinforces that odds and likelihood are not interchangeable.
  4. What's the Risk: Differentiating Risk Ratios, Odds Ratios, and ... pmc.ncbi.nlm.nih.gov Provides the fair coin odds example (1:1).
  5. Likelihood function en.wikipedia.org Defines likelihood as support for a model given data.
  6. Likelihood Ratios - Oxford Centre for Evidence-Based Medicine cebm.ox.ac.uk Explains likelihood ratios in Bayesian updating.

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.

Written and maintained by Ellis Warrender, writer and maintainer.

Last updated 28 July 2026. Spotted an error? Tell me and it gets fixed and logged on the corrections page.