Law of truly large numbers

The law of truly large numbers (a statistical adage), attributed to Persi Diaconis and Frederick Mosteller, states that with a large enough number of independent samples, any highly implausible (i.e., unlikely in any single sample, but with constant probability strictly greater than 0 in any sample) result is likely to be observed. Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law is often used to refute different pseudo-scientific claims; as such, it is sometimes criticized by fringe scientists.

The law can be rephrased as "large numbers also deceive". More concretely, skeptic Penn Jillette has said, "Million-to-one odds happen eight times a day in New York" (population about 8,000,000). In another illustrative class of cases—which also involve combinatorics—lottery drawing numbers have been duplicated in close or even immediate succession.