Kids are random

We're born with a number of false cognitive intuitions that we shed later in life. Young children (especially those before the age of six) tend to make bizarre cognitive errors in controlled experiments, errors which older children will have learned to avoid. For example, young children tend to believe that pouring liquid from one container to another can change its volume: experiments were done in which kids were presented with a choice of one glass of orange juice out of two, which contained the same amount of juice, but of which one glass was taller than the other, and they almost invariably chose the taller one. What's more, when experimenters showed kids that the volume of liquid in both glasses was the same by pouring juice back and forth from one glass to the other, most kids remained unconvinced and still believed the taller glass had more juice in it.

But there's one specific area that I know of in which kids start off right but then, at about age five, acquire a new intuition, one that is wrong. This area is "mimicking randomness." Adults are notoriously bad at it. For example, when a group of adults is asked to write down a sequence that they think could be a likely result of tossing a fair coin 20 times in a row, they give answers quite different from sequences that are generated by actually tossing a fair coin 20 times in a row. Those differences are systematic, and three of them are repeated by almost everyone: 1) sequences given by participants are much more likely to contain 10 tails than actual random sequences, and much less likely to contain more than 12 or less than 8 tails; 2) they contain much less instances of two or more identical outcomes in a row than true random sequences and 3) the series of same outcomes are noticeably shorter than in actual random sequences; for example, the participants almost never write down sequences containing more than four heads in a row, whereas in true random sequences series of five or even six heads in a row are quite common. In other words, sequences provided by participants resemble the underlying stochastic process much more than sequences that were actually generated by that process. Or, in yet other words, people tend to believe in "the law of small numbers:" that small samples have the same properties as large samples. But what's interesting is that, apparently, people do not start believing in that law until they are older than about five. Most four year olds give sequences which do not exhibit those three systematic mistakes. It's a case of cognitive bias that is learned.