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A simple way to understand this illusion is to imagine casting ten pennies in a one foot square space. Unless all of the pennies fall in an exactly even distribution, which is extremely improbable, some pennies will be closer to each other than others and seem to form a cluster or group solely from the random distribution.
It's sometimes called the "hot hand fallacy" due to the belief common among basketball coaches and players that it was best to use players on a hot streak (i.e., those who had a "hot hand"). A study demonstrated that the hot hand was a matter of coaches picking a short run of baskets out of a larger sequence that was more or less random.
Randomness is not such an intuitive concept for humans. In addition to being poor at recognizing random sequences for what they are, people are also bad at generating random numbers.
 See also
- ↑ Thomas Gilovich, Robert Vallone, and Amos Tversky. The Hot Hand in Basketball: On the Misperception of Random Sequences. Cognitive Psychology vol. 17, pp. 295-314, 1985.
- ↑ Random Number, Wolfram Math