The gambler's fallacy is well-known but still far too common.

People generally know what outliers are and why you shouldn't attach much significance to them. Most people probably don't use a definition that involves precisely three standard deviations from the mean of a distribution, but our basic heuristics are useful enough that we know seeing one tall person doesn't imply there will be many more tall people in the next few we see.

However, our heuristics frequently fail to understand why the Central Limit Theorem works. Outliers don't have much of an effect on the mean of a distribution because, as the population of a distribution increases, each outlier is a smaller and smaller percentage of the distribution--and thus has a smaller and smaller effect on the mean. But for some reason, humans tend to naturally think that outliers on one end of a distribution don't have much effect because they're canceled out by outliers on the other end. This is wrong. Very unlucky days are not canceled by very lucky days, they are drowned out by average days. You cannot rely on seeing more coins come up tails just because you saw heads five times in a row.

You can observe people making this mistake yourself. Find a local bar that does a "flip night," where the bartender flips coins to decide the price of drinks. Wait for a big group to have ordered several drinks, so there are several flips in a row, and write down their predictions. If there are a lot of heads, people will frequently start calling tails, and vice versa. There is, in fact, an optimal coin-flip prediction strategy, but people rarely follow it. (If the coin is being spun on a surface instead of flipped, always call tails; if it's being flipped, always call whichever side is primarily face down for a very small advantage.)

Why are we so good at discounting outliers but so bad at predicting future events following outliers? I suspect it's because of confirmation bias. In most distributions there will be outliers on both ends; those times when an outlier on one end is shortly followed by an outlier on another, it confirms our suspicions. When it is not (which is most of the time), we ignore the evidence. Just because there wasn't an outlier this time doesn't mean there won't be in the future, so seeing many average results in a row doesn't disconfirm the hypothesis in the salient way we need to snap us out of our delusion. If this hypothesis is correct, the gambler's fallacy is built atop another bias. One way to control these compound biases is to write your predictions down in advance and record observations as they come. Having them written will make them less easy to ignore or forget. In other words, do science to yourself.

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