Also known as the Gambler’s Fallacy, the Monte Carlo Fallacy is simple: It’s the belief that the likelihood of a random event is influenced and/or predicted by other independent events.
For example: Someone who flips a fair coin 10 times and gets “heads” on all tries, who then thinks that the likelihood of getting “tails” is now higher than a 50% chance.
It is not.
Each coin flip is independent, and the odds the same (50% for each side) each time, even if a whole sequence of coin tosses can be described as low probability (the odds of getting 11 “heads” in a row are 0.00048828125, or (1/2)^11, but the odds of getting “heads” once you already have 10 “heads” are 0.5).
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”).
* 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”).
A more subtle version of the fallacy is that an “interesting” (non-random looking) outcome is “unlikely” (eg that a sequence of “1,2,3,4,5,6” in a lottery result is less likely than any other individual outcome). Even apart from the debate about what constitutes an “interesting” result, this can be seen as a version of the gambler’s fallacy because it is saying that a random event is less likely to occur if the result, taken in conjunction with recent events, will produce an “interesting” pattern.
I wonder if we’d have less gamblers if this bias was taught to young children in schools. I doubt it would be enough to help people who are already compulsive gamblers, but maybe if they had been exposed to the idea before being hooked, they could have avoided the positive feedback loop of addiction; when someone starts to gamble, what keeps them going at first – before the brain gets hooked on dopamine and adrenaline rushes – is probably often false beliefs about how games based on random outcomes work.
Prevention based on teaching rational thinking probably has a better chance of working than trying to scare people off by showing them images of ruined addicts (most future addicts just won’t believe this could happen to them). Of course, it wouldn’t solve everything, but it might make a bigger dent in the problem than what we’ve been trying so far and have the positive side-effect of making people think more clearly.
A joke told among mathematicians demonstrates the nature of the fallacy. When flying on an airplane, a man decides to always 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!”.
Source: Gambler’s Fallacy at Wikipedia
See also: Rationality Resources