gambler’s fallacy also called Monte Carlo fallacy, the fallacy of supposing, of a sequence of independent events, that the probabilities of later outcomes must increase or decrease to ‘compensate’ for earlier outcomes. For example, since (by Bernoulli’s theorem) in a long run of tosses of a fair coin it is very probable that the coin will come up heads roughly half the time, one might think that a coin that has not come up heads recently must be ‘due’ to come up heads – must have a probability greater than one-half of doing so. But this is a misunderstanding of the law of large numbers, which requires no such compensating tendencies of the coin. The probability of heads remains one-half for each toss despite the preponderance, so far, of tails. In the sufficiently long run what ‘compensates’ for the presence of improbably long subsequences in which, say, tails strongly predominate, is simply that such subsequences occur rarely and therefore have only a slight effect on the statistical character of the whole. See also BERNOULLI ‘S THEOREM , PROBABIL – IT. R.Ke.