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.