Recognize that random sequences don’t "owe" balance

Random processes have no memory — a run of heads doesn’t make tails more likely.

Why it works

The gambler’s fallacy is a direct product of representativeness: a long run of heads doesn’t look like a "random" sequence, so the mind expects a correction. But the coin has no memory. The representativeness of the whole sequence is irrelevant to the probability of the next flip. The fallacy appears everywhere from roulette tables to hiring decisions (avoiding a third female hire because "we’ve already taken two"), and the mechanism is always the same: the expected sequence looks more representative, so it feels more probable.

How to do it

1. Identify when you’re making a prediction about a sequence of independent events.
2. Ask: "Does the past sequence change the underlying probability of the next event, or does it just change what a balanced sequence would look like?"
3. If the events are genuinely independent, treat each outcome as starting fresh.
4. Reserve sequential updating for cases where outcomes are actually dependent (e.g., drawing without replacement).

Evidence

The gambler’s fallacy is one of the most replicated biases in probability research; it appears in laboratory studies, casino data, financial trading, and field judgments like bail decisions and asylum rulings. (observational)

The hot-hand fallacy (the opposite error — expecting streaks to continue) can also occur in certain skill contexts; which fallacy applies depends on whether the underlying process is random or skill-based.

Sources

• Tversky & Kahneman (1974), Judgment under uncertainty: Heuristics and biases, Science
• Chen, Moskowitz & Shue (2016), Decision making under the gambler’s fallacy, Quarterly Journal of Economics

Common mistake

Applying gambler’s fallacy correction to genuine momentum situations (e.g., a skilled player’s performance), where sequential dependence is real.