Law of truly large numbers

Not to be confused with Law of large numbers.

The law of truly large numbers is the observation in statistics that any highly unlikely result (i.e., an event with constantly low but non-zero probability across samples) is likely to occur, given a large enough number of independent samples. It is not a mathematical law, but a colloquialism. The law has been used to rebut pseudo-scientific claims.

The observation is attributed to statisticians Persi Diaconis and Frederick Mosteller. Skeptic and magician Penn Jillette similarly said that "million-to-one odds happen eight times a day" among the roughly 8 million inhabitants of New York City. In another illustrative class of cases—which also involve combinatorics—lottery drawing numbers have been duplicated in close or even immediate succession.

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