Law of truly large numbers

More concretely, skeptic Penn Jillette has said, "Million-to-one odds happen eight times a day in New York" (population about 8,000,000).

[4] For a simplified example of the law, assume that a given event happens with a probability for its occurrence of 0.1%, within a single trial.

Thus, if one comes true, the psychic expects us to forget the vast majority that did not happen (confirmation bias).

Another similar manifestation of the law can be found in gambling, where gamblers tend to remember their wins and forget their losses,[10] 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[11]).

Mikal Aasved links it with "selective memory bias", allowing gamblers to mentally distance themselves from the consequences of their gambling[11] by holding an inflated view of their real winnings (or losses in the opposite case – "selective memory bias in either direction").

Graphs of probability P of not observing independent events each of probability 1/ n after n Bernoulli trials , and 1 − P vs n . As n increases, the probability of a 1/ n -chance event never appearing after n tries rapidly converges to 1/ e .