Jul 18 2008

## The gambler’s fallacy

Also known as the Monte Carlo fallacy, or the fallacy of the maturity of chances, the gambler’s fallacy 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.

Thus if black has come up many times in succession at a roulette table, a false belief may develop that red is increasingly likely on each subsequent spin of the wheel, to even out the sequence in the long run; or if a mother gives birth to several girls in succession, she may come to believe that the probability of a boy is greater than 50% for her next baby.

For example, consider a series of 20 coin flips that have all landed with the “heads” side up. Under the gambler’s fallacy, a person might predict that the next coin flip is more likely to land with the “tails” side up.

This line of thinking represents an inaccurate understanding of probability because the likelihood of a fair coin turning up heads is always 50%. Each coin flip is an independent event, which means that any and all previous flips have no bearing on future flips.

The gambler’s fallacy gets its name from the fact that, where the random event is the throw of a die or the spin of a roulette wheel, gamblers will risk money on their belief in “a run of luck” or a mistaken understanding of “the law of averages”. It often arises because a similarity between random processes is mistakenly interpreted as a predictive relationship between them. For instance, two fair dice are similar in that they each have the same chances of yielding each number - but they are independent in that they do not actually influence one another.

The gambler’s fallacy often takes one of these forms:

A particular outcome of a random event is more likely to occur because it has happened recently (”run of good luck”);

A particular outcome is more likely to occur because it has not happened recently (”law of averages” or “it’s my turn now”).

Similarly,

A particular outcome is less likely to occur because it has happened recently (”law of averages” or “exhausted its luck”);

A particular outcome is less likely to occur because it has not happened recently (”run of bad luck”).

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