What it is
The gambler's fallacy is the mistaken belief that if an independent random event has occurred more frequently than expected in the recent past, it is less likely to occur in the future — or vice versa. In other words, believing that a sequence of past outcomes affects the probability of future outcomes when the events are, in fact, statistically independent.
A coin does not remember its history. A roulette wheel does not compensate for past results. Each trial is genuinely independent — the probability is reset completely with each spin.
The classic example
In August 1913, at the Monte Carlo Casino, the roulette ball fell on black 26 times in a row. Gamblers lost millions betting on red, convinced that after so many blacks, red was "due." The probability of red on any individual spin was always 48.6% — unchanged by the sequence. Twenty-six consecutive blacks is rare, but it does not make the 27th spin more likely to be red.
The same error appears whenever people play sequences of independent events. Lottery players avoid numbers that "just came up," believing they are overdue for a rest. Slot machine players continue because the machine "is due for a payout." Blackjack players bet heavily after a run of bad cards, convinced the distribution will rebalance.
In trading and markets
Day traders fall for the gambler's fallacy when they expect a stock to reverse after a run in one direction. "It's been down five days — it has to bounce" is not a probabilistic statement, it is the gambler's fallacy. If daily price changes are approximately independent (the evidence suggests they largely are for liquid markets), then past down days carry no information about tomorrow's direction.
Technical chart patterns based on the idea that a stock has been "overbought" or "oversold" are often expressions of the gambler's fallacy. The Relative Strength Index (RSI), for example, signals reversal when prices have moved too far in one direction. Whether this signal works is an empirical question — the point is that it is not justified by the gambler's fallacy reasoning, because price changes would need to be negatively autocorrelated for that logic to hold.
In sports betting, the gambler's fallacy is especially expensive. Teams are not "due" for wins. Players are not "due" for hits. Each game or at-bat is approximately independent, and the historical run tells you almost nothing about the next event.
The right way to think about it: distinguishing fallacy from mechanism
The gambler's fallacy is not the same as mean reversion. Mean reversion describes processes that genuinely have a tendency to revert — not because of fallacy but because of mechanisms.
Interest rates mean-revert because central banks actively push them back toward target levels. Profit margins mean-revert because high margins attract competition. Volatility mean-reverts because calm periods normalize fearful markets.
The question to ask is: is there a mechanism that causes reversion? If yes, you are not observing the gambler's fallacy — you are observing a real statistical property. If no mechanism exists, if the series is genuinely independent, then expecting reversion is the fallacy.
For a roulette wheel, no mechanism exists. For corporate profit margins, competition is the mechanism. The distinction matters enormously for whether you should bet on continuation or reversal.
Where it shows up
In birth ratios: after a run of male births in a hospital ward, nurses and parents expect more females to balance out — but births are approximately independent. In criminal sentencing: research by Kahneman and colleagues found that asylum judges were more likely to reject an application after granting several in a row, as if trying to "balance out" their approvals. In sports: fans and commentators expecting a shooter to "heat up" or "cool down" based on recent shots, when most sports show limited hot hand effects.
One thing most people get wrong
People confuse the law of large numbers with the gambler's fallacy. The law of large numbers says that over many, many trials, the observed frequency will converge to the true probability. After one million coin flips, the ratio of heads to tails will be close to 50/50.
But this convergence happens through addition of new observations, not through compensation of old ones. The past flips are not "corrected" — they are simply swamped by the volume of new flips. In a sample of 10 flips, the individual flips matter a lot. In a sample of a million, they matter almost nothing. The law says nothing about what comes next — it describes what happens across very large aggregates. Applying it to small sequences is the gambler's fallacy dressed in statistical language.