Odds are a tool for expressing relative chances. If the odds of a tree in a forest being sick versus healthy are 2 : 3, this says that there are 2 sick trees for every 3 healthy trees. (The probability of a tree being sick, in this case, is 25 or 40%.)

Odds are expressed in the form “X to Y”, e.g. “7 to 9 for X versus Y”, more compactly written as \(7:9\).

The representation of chances as odds is often used in gambling and statistics.


  • Odds: Introduction

    What’s the difference between probabilities and odds? Why is a 20% probability of success equivalent to 1 : 4 odds favoring success?

  • Odds: Refresher

    A quick review of the notations and mathematical behaviors for odds (e.g. odds of 1 : 2 for drawing a red ball vs. green ball from a barrel).

  • Odds: Technical explanation

    Formal definitions, alternate representations, and uses of odds and odds ratios (like a 1 : 2 chance of drawing a red ball vs. green ball from a barrel).


  • Probability theory

    The logic of science; coherence relations on quantitative degrees of belief.