A **statistical impossibility** is a probability that is so low as to not be worthy of mentioning. Sometimes it is quoted as 10^{-50}^{[1]} although the cutoff is inherently arbitrary. Although not truly impossible the probability is low enough so as to not bear mention in a rational, reasonable argument.

In some cases that arise in Gedanken experiments in thermodynamics, the probabilities can be approximately 10^{Avogadro's number}, that is, 10^{1023}, give or take a few billion orders of magnitude.