Page "Gambler's fallacy" Paragraph 32

When the probability of repeated events are not known, outcomes may not be equally probable.

In the case of coin tossing, as a run of heads gets longer and longer, the likelihood that the coin is biased towards heads increases.

If one flips a coin 21 times in a row and obtains 21 heads, one might rationally conclude a high probability of bias towards heads, and hence conclude that future flips of this coin are also highly likely to be heads.

In fact, Bayesian inference can be used to show that when the long-run proportion of different outcomes are unknown but exchangeable ( meaning that the random process from which they are generated may be biased but is equally likely to be biased in any direction ) previous observations demonstrate the likely direction of the bias, such that the outcome which has occurred the most in the observed data is the most likely to occur again.