Odds vs Probability

The terms Odds and Probability are related but distinct concepts used to describe the likelihood of events.

Concept	Definition	Formula	Range
Probability	Likelihood of event	$P=\frac{a}{a+b}$	$[0,1]$
Odds	Ratio of success to failure	$\text{Odds}=\frac{a}{b}$	$[0,\infty )$

Odds are commonly used in gambling and logistic regression, while probabilities are more general across statistics and decision theory. From probability to odds:

$$\text{Odds}=\frac{P}{1-P}$$