Gambling terms, explained straight

Odds, Probability & Bankroll

Risk vs odds

Risk is the probability of an event occurring, while odds compare the probability of the event occurring to the probability of it not occurring.

Risk formula
events / total population, or p
Odds formula
p / (1 − p), or events / non-events
Example
If risk is 10%, odds are 0.11 or 1/93

Key points

  • Risk is a proportion between 0 and 1; odds range from 0 to infinity.2
  • Odds increase faster than risk as an event becomes more common.12
  • In gambling, odds are often used to express payout, but statistically they are a ratio of occurrence to non-occurrence.1

Where this term is used

Odds & probability Odds Explains the statistical definition of odds as a ratio of events to non-events. Odds & probability Betting odds Covers how odds are used in gambling to represent implied probability and payout. Odds & probability Fractional odds to decimal Shows how to convert between fractional and decimal odds formats. Odds & probability Odds vs probability Distinguishes the statistical concept of odds from the broader concept of probability. Odds & probability American odds Explains the moneyline odds format used primarily in the United States. Odds & probability Risk of ruin Describes the probability of losing an entire bankroll given a betting strategy.

Sources

  1. Risks, Rates and Odds: What's the Difference and Why Does It ... pmc.ncbi.nlm.nih.gov Provides the definition of odds and risk, and explains how odds increase faster than risk.
  2. Relative vs absolute risk and odds: Understanding the difference pmc.ncbi.nlm.nih.gov States the range of risk (0 to 1) and odds (0 to infinity), and the relationship between them.
  3. Risk Comparisons ncbi.nlm.nih.gov Gives the example of converting a 10% risk to odds of 0.11 or 1/9.

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.