Overview
The gambler’s fallacy is the belief that random outcomes of the past affect the probability of future outcomes. For example, if you’re flipping a coin and it lands on 5 heads in a row, the fallacy would be in assuming that a tail is due imminently because a 50-50 chance of tails should balance out in the long-run. In reality, the coin always has a 50-50 chance of landing on heads or tails, so there’s no reason to expect a tails is more likely than a heads the next time you flip the coin. The coin does not contain any memory of past flips.
That doesn’t mean betting on 5 heads in a row before a single coin has been flipped has a 50-50 chance though, since that would be a bet placed on 5 events with a 50% chance each all happening is 3.135% (1 in 32).
For many with a process addiction to gambling, the gambler’s fallacy can be a tempting rationalization to keep gambling, especially with an appeal to some kind of superstitious counter that runs differently.