Originally Posted by
deathworlds
It's the idea that random events have a pattern, the term gambler's fallacy specifically comes from how gamblers tend to switch their bets on stuff like roulette based on what has occured, as opposed to working off of pure probability.
Example: Joe is watching a roulette table, and the ball lands on black five times in a row. Joe decides to bet on red, thinking "it's been a while since red was landed, it must happen soon", when in reality, the odds of the ball landing on red or black are the same as they were the last five times the wheel was spun.