Also known as the Monte Carlo fallacy. Either

1. (i) the mistake of supposing that results on a system such as a roulette table will continue to display some pattern they have recently been showing (e.g. reds are ‘hot’), or

2. (ii) the converse mistake of supposing that an opposite pattern must be becoming due (by ‘the law of averages’).

In fact a fair gambling system is one on which the probability of some outcome remains exactly the same on each occasion: a roulette wheel has no memory. It should be noticed that if a system is not known to be like this there may be no fallacy. If we are betting on the weather, or a horse, it may be quite reasonable to take a sequence of rainy days, or a sequence of wins, as increasing the chance of another.