Page "Gambler's fallacy" Paragraph 33

Gambler's fallacy arises out of a belief in the law of small numbers, or the erroneous belief that small samples must be representative of the larger population.

According to the fallacy, " streaks " must eventually even out in order to be representative.

Amos Tversky and Daniel Kahneman first proposed that the gambler's fallacy is a cognitive bias produced by a psychological heuristic called the representativeness heuristic, which states that people evaluate the probability of a certain event by assessing how similar it is to events they have experienced before, and how similar the events surrounding those two processes are.

According to this view, " after observing a long run of red on the roulette wheel, for example, most people erroneously believe that black will result in a more representative sequence than the occurrence of an additional red ", so people expect that a short run of random outcomes should share properties of a longer run, specifically in that deviations from average should balance out.

When people are asked to make up a random-looking sequence of coin tosses, they tend to make sequences where the proportion of heads to tails stays closer to 0. 5 in any short segment than would be predicted by chance ( insensitivity to sample size ); Kahneman and Tversky interpret this to mean that people believe short sequences of random events should be representative of longer ones.

The representativeness heuristic is also cited behind the related phenomenon of the clustering illusion, according to which people see streaks of random events as being non-random when such streaks are actually much more likely to occur in small samples than people expect.