Going with What's Hot

VoxEU on the gambler's fallacy and the hot hand fallacy, via Mark Thoma:

There are two plausible but apparently contradicting intuitions about how people over-infer from observing recent events.

• The “gamblers fallacy” claims that people expect rapid reversion to the mean.

For example, upon observing three outcomes of “red” in roulette, gamblers tend to think that “black” is now due and tend to bet more on “black” (Croson and Sundali 2005).

• The “hot hand fallacy” claims that upon observing an unusual streak of events, people tend to predict that the streak will continue.

The “hot hand” fallacy term originates from basketball where players who scored several times in row are believed to have a “hot hand”, i.e. are more likely to score at their next attempt (e.g. Camerer 1989).
Recent behavioural theory has proposed a foundation to reconcile the apparent contradiction between the two types of over-inference (Rabin and Vayanos 2010). The intuition behind the theory can be explained with reference to the example of roulette play.
A person believing in the “law of small numbers” thinks that small samples should “look like” the parent distribution, i.e. that the sample should be representative of the parent distribution. Thus, the person believes that out of, say, 6 spins 3 should be red and 3 should be black (ignoring green). If observed outcomes in the small sample differ from the 50:50 ratio, immediate reversal is expected. Thus, somebody observing 2 times red in 6 consecutive spins believes that black is “due” on the 3rd spin to restore the 50:50 ratio.
Now suppose such person is uncertain about the fairness of the roulette wheel. Upon observing an improbable event (6 times red in 6 spins, say), the person starts to doubt about the fairness of the roulette wheel because a long streak does not correspond to what he believes a random sequence should look like. The person then revises his model of the data generating process and starts to believe the event on streak is more likely. The upshot of the theory is that the same person may at first (when the streak is short) believe in reversion of the trend (the gambler’s fallacy) and later – when the streak is long – in continuation of the trend (the hot hand fallacy).