Law of truly large numbers

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The law of truly large numbers, attributed to Persi Diaconis and Frederick Mosteller, states that with a sample size large enough, any outrageous thing is likely to happen.[1] Because we never find it notable when likely events occur, we highlight unlikely events and notice them more. The law seeks to debunk one element of supposed supernatural phenomenology.


For a simplified example of the law, assume that a given event happens with a probability of 0.1% in one trial. Then the probability that this unlikely event does not happen in a single trial is 99.9% = 0.999.

In a sample of 1000 independent trials, the probability that the event does not happen in any of them is 0.9991000, or 36.8%. The probability that the event happens at least once in 1000 trials is then 1 − 0.368 = 0.632 or 63.2%. The probability that it happens at least once in 10,000 trials is 1 − 0.99910000 = 0.99995 = 99.995%.

This means that this "unlikely event" has a probability of 63.2% of happening if 1000 independent trials are conducted, or over 99.9% for 10,000 trials. In other words, a highly unlikely event, given enough trials with some fixed number of draws per trial, is even more likely to occur.

In criticism of pseudoscience[edit]

The law comes up in criticism of pseudoscience and is sometimes called the Jeane Dixon effect (see also Postdiction). It holds that the more predictions a psychic makes, the better the odds that one of them will "hit". Thus, if one comes true, the psychic expects us to forget the vast majority that did not happen.[2] Humans can be susceptible to this fallacy.

Another similar (to a small degree, see Psychologism and Anti-psychologism) manifestation of the law can be found in gambling, where gamblers tend to remember their wins and forget their losses,[3] even if the latter far outnumbers the former (though depending on a particular person's environment, behaviors, customs or habits, so the opposite may also be local truth[4]statistical prevalence not featured). Mikal Aasved links it with "selective memory bias", allowing gamblers to mentally distance themselves from the consequences of their gambling[4] by holding an inflated view of their real winnings (or losses in the opposite case).

See also[edit]


  1. ^ Everitt 2002
  2. ^ 1980, Austin Society to Oppose Pseudoscience (ASTOP) distributed by ICSA (former American Family Foundation) "Pseudoscience Fact Sheets, ASTOP: Psychic Detectives"
  3. ^ Daniel Freeman, Jason Freeman, 2009, London, "Know Your Mind: Everyday Emotional and Psychological Problems and How to Overcome Them" p. 41
  4. ^ a b Mikal Aasved, 2002, Illinois, The Psychodynamics and Psychology of Gambling: The Gambler's Mind vol. I, p. 129


External links[edit]