Is the mistaken belief that, if something happens more frequently than normal during some period, it will happen less frequently in the future, or that, if something happens less frequently than normal during some period, it will happen more frequently in the future.
The reason why it is called the gambler's fallacy is that often individuals fall for the this mistake when gambling. For instance many individuals believe that if they are flipping a coin and the previous ten flips all landed on heads, then there is a greater than 50% chance of a tails popping up in the eleventh flip. But of course, this is incorrect because each flip of a coin is independant from the last one so the history of flips has no influence on the next flip. The same logic can be applied to a roulette wheel.