Gambler’s Fallacy

What it is

The gambler’s fallacy (also called the Monte Carlo fallacy) is the mistaken belief that past independent random events influence future ones. People assume that a run of similar outcomes makes the opposite outcome more likely next, even when each event has the same probabilities and is independent.

Key takeaways

• The fallacy treats independent events as if they were dependent.
• Past outcomes do not change the probability of future independent events.
• It appears in gambling, investing, and everyday judgments about chance.
• Historical and modern decisions—such as heavy betting after perceived streaks—illustrate its consequences.
• Avoiding it requires relying on objective methods and independent analysis, not perceived short-term patterns.

How it distorts probability perception

When events are independent (coin flips, roulette spins, many market moves), the probability of each outcome remains constant. The gambler’s fallacy leads people to expect a balancing effect after a streak—e.g., thinking tails is “due” after several heads—despite unchanged odds.

Coin-flip example

If a fair coin lands heads ten times in a row, the probability the next flip is heads is still 50%. Believing an 11th flip is less likely to be heads because of the previous ten is the gambler’s fallacy. By the same logic, refusing a bet that 11 consecutive heads will occur before seeing any flips is rational; accepting that bet after seeing ten heads is not—because the next flip’s odds remain unchanged.

Historical example

In 1913 at the Casino de Monte-Carlo, a long run of one color on roulette led many gamblers to bet heavily on the other color, expecting it to be “due.” Those expectations ignored the independence of spins and resulted in large losses when the run continued.

Why it happens

The fallacy stems from a cognitive bias called the “law of small numbers”: people expect small samples to reflect long-run probabilities. They perceive short-term patterns as meaningful and infer corrective forces where none exist.

How to avoid the fallacy

• Recognize independence: identify when events are truly independent and treat each outcome on its own merits.
• Use objective systems: in trading or gambling, follow predefined rules or models with explicit risk management rather than intuition about streaks.
• Base decisions on evidence: use independent research, up-to-date information, and statistical reasoning.
• Track and review behavior: record outcomes and decisions to reveal patterns in your own thinking and remove bias.
• Get feedback: consult peers or advisers to challenge intuitive judgments about probability.

Bottom line

The gambler’s fallacy leads people to see non-existent corrective patterns in random sequences, causing poor decisions. Understanding independence and applying systematic, evidence-based approaches helps prevent this common error in gambling, investing, and everyday probabilistic reasoning.