What is the gambler’s fallacy?
The gambler’s fallacy is the mistaken belief that past random outcomes influence future ones in games of chance. It leads players to believe a ‘hot streak’ will continue or that a sequence of losses makes a win more likely soon. Neither is true.
Classic examples
After a roulette wheel lands on red 7 times in a row, many players feel black is ‘due.’ In reality, each spin is independent — the wheel has no memory. The probability of black on the next spin is still 48.6% (on a European wheel), exactly as it was on the first spin. The number of consecutive reds doesn’t change what comes next.
Why it persists
The gambler’s fallacy exploits how humans intuitively expect patterns to self-correct. Over a very long run, we know outcomes should approach their expected frequencies — but that long run is played out through more trials, not through a correction in the next few hands or spins. In the short run, anything can happen. This fallacy is behind chasing losses (the belief a win is coming to balance the recent losses) and is one of the most costly cognitive biases in gambling.