The Gambler's Fallacy

A fallacy in which an inference is drawn on the assumption that a series of chance events will determine the outcome of a subsequent event. Also called the Monte Carlo fallacy, the negative recency effect, or the fallacy of the maturity of chances.

In an article in the Journal of Risk and Uncertainty (1994), Dek Terrell defines the gambler's fallacy as "the belief that the probability of an event is decreased when the event has occurred recently." In practice, the results of a random event (such as the toss of a coin) have no effect on future random events. 

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Slippery Slope Fallacy - Definition and Examples

By Richard Nordquist

Examples and Observations

Jonathan Baron: If you are playing roulette and the last four spins of the wheel have led to the ball's landing on black, you may think that the next ball is more likely than otherwise to land on red. This cannot be. The roulette wheel has no memory. The chance of black is just what it always is. The reason people may tend to think otherwise may be that they expect the sequence of events to be representative of random sequences, and the typical random sequence at roulette does not have five blacks in a row.

Michael Lewis: Above the roulette tables, screens listed the results of the most recent twenty spins of the wheel. Gamblers would see that it had come up black the past eight spins, marvel at the improbability, and feel in their bones that the tiny silver ball was now more likely to land on red. That was the reason the casino bothered to list the wheel’s most recent spins: to help gamblers to delude themselves. To give people the false confidence they needed to lay their chips on a roulette table. The entire food chain of intermediaries in the subprime mortgage market was duping itself with the same trick, using the foreshortened, statistically meaningless past to predict the future.

Mike Stadler: In baseball, we often hear that a player is 'due' because it has been awhile since he has had a hit, or had a hit in a particular situation.
"The flip side of this is the notion of the 'hot hand,' the idea that a string of successful outcomes is more likely than usual to be followed by a successful outcome... People who fall prey to the gambler's fallacy think that a streak should end, but people who believe in the hot hand think it should continue.

T. Edward Damer: Consider the parents who already have three sons and are quite satisfied with the size of their family. However, they both would really like to have a daughter. They commit the gambler's fallacy when they infer that their chances of having a girl are better, because they have already had three boys. They are wrong. The sex of the fourth child is causally unrelated to any preceding chance events or series of such events. Their chances of having a daughter are no better than 1 in 2--that is, 50-50.