The Gambler’s fallacy is a term used to describe a cognitive bias in which an individual assumes that a departure from what normally occurs will be corrected in the short term. For example, since a coin has two sides, the probability of it landing on either heads or tails when dropped is 0.5. If the coin is dropped and it happens to land on “heads” 3 times in a row, a person would commit the Gamblers fallacy if he/she believed that, since the coin has already landed on heads 3 times in a row, it is more likely to land on tails. The reality is that the probability of the coin showing the tails side is still 50%, regardless of whether or not it landed on heads the previous coin toss.
The Gambler’s fallacy comes from an erroneous belief that smaller samples must necessarily be representative of a larger population. Amos Tversky and Daniel Kahneman proposed that the Gambler’s Fallacy was a type of cognitive bias in which people erroneously evaluate the probability of an event occurring in the near future based on how often the events have happened in the past.
Tversky, A., Kahneman, D. (1974). “Judgement under uncertainty: Heuristics and biases”. Science 185 (4157): 1124–1131 (Link to PDF file).