Truth Trader

Wikipedia

The gambler’s fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the false belief that the probability of an event in a random sequence is dependent on preceding events, its probability increasing with each successive occasion on which it fails to occur. If a fair coin is tossed repeatedly and tails comes up many times in a row, a gambler may believe, incorrectly, that heads is more likely on the following toss. Such an event may be referred to as “due”. This is an informal fallacy.

The inverse gambler’s fallacy deals with the belief that a particular outcome is less likely to occur because it has happened recently (”law of averages” or “exhausted its luck”), or because it has not happened recently (”run of bad luck”).

A joke told among mathematicians demonstrates the nature of the fallacy. When flying on an airplane, a man decides always to bring a bomb with him. “The chances of an airplane having a bomb on it are very small,” he reasons, “and certainly the chances of having two are almost none!”.

Also see Non-examples of the fallacy