Gamblers fallacy
The Gambler's Fallacy is a cognitive bias that leads individuals to believe that future probabilities are altered by past events, despite the events being independent. It is the mistaken belief that if something happens more frequently than normal during a given period, it will happen less frequently in the future, or vice versa.
How it works
This fallacy arises from the incorrect assumption that random processes are self-correcting. People confuse the law of large numbers, which states that as a sample size grows, the sample mean will get closer to the population mean, with the belief that deviations from average outcomes in a short sequence of random events means future deviations will balance out immediately.
Examples
- A classic example is flipping a fair coin. After getting heads five times in a row, an individual might believe that the next flip is more likely to result in tails, despite each flip being a separate event with a 50% chance for heads or tails.
- Another instance is in lottery draws. If certain numbers haven't been drawn in a while, some people believe those numbers are 'due' to appear, affecting their choice when selecting lottery numbers.
Consequences
Believing in the Gambler's Fallacy can lead to poor decision-making in gambling, investments, and even personal life. It can cause individuals to place unwarranted bets based on supposed 'patterns' and 'hot streaks', often resulting in financial loss, increased risk-taking, and decision paralysis.
Counteracting
To counteract the fallacy, it's important to understand the nature of randomness and independence in events. Education about probability and statistical independence can help. Cognitive-behavioral strategies can also be used to challenge erroneous beliefs and encourage a more analytical approach to risk and probability.
Critiques
Some critics argue that what is often classified as the Gambler's Fallacy may be rational in contexts where individuals lack information, such as uncertain complex systems, where perceived patterns might sometimes result from underlying factors not yet understood. Nonetheless, in strictly independent random processes, the fallacy holds no ground.
Fields of Impact
Also known as
Relevant Research
What's next? Judging sequences of binary events
Oskarsson, A. T., Van Boven, L., McClelland, G. H., & Hastie, R. (2009)
Psychological Bulletin, 135(2), 262-285
The 'Gambler's Fallacy' in Lottery Play
Clotfelter, C. T., & Cook, P. J. (1993)
Management Science, 39(12), 1521-1525
Case Studies
Real-world examples showing how Gamblers fallacy manifests in practice
Context
A mid-sized long-short equity fund with $200M assets under management (AUM) tracked a large-cap technology stock that had experienced a steady three-week decline after broad-market weakness. The fund's investment team had historically taken concentrated tactical positions when they perceived outsized value opportunities.
Situation
Elena, a senior portfolio manager, noticed the stock had fallen 12% over three weeks and felt it was "over-sold" and therefore likely to rebound. Against the team's typical position-sizing limits, she increased the fund's exposure to the name from 2% of AUM to 8% over two trading days to take advantage of the perceived imminent reversal.
The Bias in Action
Elena's decision was driven by the belief that the recent string of down days made a rebound more likely — a classic Gambler's Fallacy: past independent price movements were treated as influencing future direction. She overweighted the pattern of recent declines and underweighted fresh fundamental or event-driven analysis (e.g., upcoming earnings risk). The team accepted her narrative without demanding new quantitative stress tests because the "streak" story felt intuitively compelling. Risk controls that flagged size breaches were overridden by an ad hoc justification that the position was "due to bounce."
Outcome
One week after the increased allocation, the company reported weaker-than-expected guidance and the share price dropped a further 18%. The fund's concentrated position magnified the impact, turning what might have been a routine drawdown into a material hit. The fund underperformed its benchmark that month and triggered internal stop-loss and client-investor questions.