Gambler's fallacy
The gambler's fallacy is the mistaken belief that a random result is more or less likely to happen because of what happened in earlier rounds.
Also called Monte Carlo fallacy, gamblers fallacy, fallacy of the maturity of chances
In games where each round is independent, the past has no effect on the next result. A roulette wheel, a dice roll and a slot spin have no memory. The gambler's fallacy is the feeling that they do: that red is "due" after a run of black, or that a slot is "ready to pay".
Example. At European roulette, black has come up eight times in a row. The chance of red on the next spin is still 18 in 37, about 48.6%, the same as before the run started. The best-known case is from the Monte Carlo Casino on 18 August 1913. Black is reported to have come up 26 times in a row, and players lost heavily betting on red.
What people get wrong. People mix this up with the idea that results even out. Over a huge number of spins the share of reds does move towards 18 in 37. But the wheel does not correct itself. Early streaks are swamped by the many spins that follow.
The same goes for a casino RNG. Betting more because a win feels due, as in the martingale, does not change the expected result.
Related terms
- Martingale
The martingale is a betting system where you double your stake after every loss, hoping the next win recovers all your losses plus one base bet.
- Random number generator (RNG)
A random number generator (RNG) is the software that produces the unpredictable numbers a casino game turns into spins, cards and dice rolls.
- Variance
Variance is a measure of how far results are spread around their average, worked out as the average squared distance from the expected value.
- Expected value (EV)
Expected value (EV) is the average result of a bet if you could repeat it a huge number of times, found by weighting each possible outcome by its chance.