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The law of averages is a layman's term for a belief that the statistical distribution of outcomes among members of a small sample must reflect the distribution of outcomes across the population as a whole.As invoked in everyday life, the "law" usually reflects wishful thinking or a poor understanding of statistics 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.