The law of averages is a lay term used to express a belief that outcomes of a random event will "even out" within a small sample.
As invoked in everyday life, the "law" usually reflects bad statistics or wishful thinking rather than any mathematical principle. While there is a real theorem that a random variable will reflect its underlying probability over a very large sample, the law of averages typically assumes that unnatural short-term "balance" must occur. Typical applications of the law also generally assume no bias in the underlying probability distribution, which is frequently at odds with the empirical evidence.
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