samples equal to the size of the human population (in 2021) gives probability of event X: These calculations can be formalized in mathematical language as: "the probability of an unlikely event X happening in N independent trials can become arbitrarily near to 1, no matter how small the probability of the event X in one single trial is, provided that N is truly large." For example, where the probability of unlikely event X is not a small constant but decreased in function of N, see graph. In sexual reproduction, the chances for a microscopic, single spermatozoon to reach the ovum in order to fertilize it is very small. Thus, in every encounter, spermatozoa are released in numbers of millions at once (in mammals), raising the opportunities of fecundation to a nearly-certain event. In high availability systems even very unlikely events have to be taken into consideration (to make system failures less probable redundancy can be used). In criticism of pseudoscience 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 (confirmation bias). Humans can be susceptible to this fallacy. Another similar manifestation of the law can be found in gambling, where gamblers tend to remember their wins and forget their losses, even if the latter far outnumbers the former (though depending on a particular person, the opposite may also be true when they think they need more analysis of their losses to achieve fine tuning of their playing system). Mikal Aasved links it with "selective memory bias", allowing gamblers to mentally distance themselves from the consequences of their gambling by holding an inflated view of their real winnings (or losses in the opposite case – "selective memory bias in either direction"). See also Notes References David J. Hand, (2014), The Improbability Principle: Why Coincidences, Miracles, and Rare Events Happen Every Day External links Math Explains Likely Long Shots, Miracles and Winning the Lottery (Excerpt) in Scientific American by David Hand 2014 skepdic.com on the Law of Truly Large Numbers on the Law of Truly Large Numbers The On-Line Encyclopedia of Integer Sequences – related integer sequence Probability theory Statistical laws