British Dictionary definitions for law-of-averages
law of averages
(popularly) the expectation that a possible event is bound to occur regularly with a frequency approximating to its probability, as in the (actually false) example: after five heads in a row the law of averages makes tails the better bet Compare law of large numbers
The idea that probability will influence all occurrences in the long term, that one will neither win nor lose all of the time. For example, If it rains every day this week, by the law of averages we're bound to get a sunny day soon. This colloquial term is a popular interpretation of a statistical principle, Bernoulli's theorem, formulated in the late 1600s.