The gambler's fallacy is the mistaken belief that if a random event has occurred more frequently than expected in the past, it is less likely to happen in the future — or vice versa.

The Classic Example

A fair coin lands heads 10 times in a row. The gambler's fallacy says tails is now "due." In reality, the coin has no memory. The probability of tails on the next flip is still exactly 50%.

Why the Brain Does This

The brain is a pattern-detection machine. It interprets streaks as meaningful signals — a survival advantage in a world where patterns usually do mean something. In truly random systems, it misfires.

Where It Causes Harm

• Casinos: Players bet more after losing streaks, believing a win is "due"
• Investing: "The market has been up 5 years in a row — a crash is overdue"
• Hiring: After rejecting several candidates, interviewers become more likely to accept the next one

Key Distinction

The gambler's fallacy applies to independent random events. For dependent events, past outcomes do matter.

Reference:

Wikipedia: Gambler's Fallacy

https://en.wikipedia.org/wiki/Gambler%27s_fallacy