What is the gambler's fallacy in simple terms?

It's the mistaken belief that after a coin lands heads several times in a row, tails is due. The coin has no memory, so the odds are the same every flip.

How is it different from the hot hand fallacy?

The gambler's fallacy is believing a streak is about to end, and the hot hand fallacy is believing a streak will continue. They point in opposite directions, but both come from misperceiving randomness.

Gambler's Fallacy

🧠 Psychology By CampusDown Wiki Editorial Team Last updated October 27, 2026 Views 6

The gambler's fallacy is the cognitive bias of believing that in a random process whose trials are independent, such as coin flips or roulette, an outcome that has come up several times in a row makes the opposite outcome more likely next. Laplace described it as early as 1814, and in 1971 Tversky and Kahneman explained it through the law of small numbers, the belief that even small samples should closely mirror the proportions of the population.

Contents

1. The concept and its psychological roots
2. Perceiving randomness and formal models
3. Evidence from lotteries to the courtroom
4. FAQ
5. References

The concept and its psychological roots

Even if a fair coin lands heads five times in a row, the chance of tails on the sixth flip is still one half. Yet many people feel tails is due. Laplace (1814) recorded fathers who, after several sons in a row, believed the next child was more likely to be a daughter. It is also called the Monte Carlo fallacy, after the story that in 1913 a roulette wheel at the Monte Carlo casino came up black 26 times in a row while gamblers lost fortunes betting on red. Tversky and Kahneman (1971) identified the law of small numbers, the belief that the law of large numbers applies to small samples too, and Kahneman and Tversky (1972) explained the fallacy through the representativeness heuristic, judging that even short sequences should look like a typical random process.

Perceiving randomness and formal models

Bar-Hillel and Wagenaar (1991) reviewed research showing that when people are asked to produce random sequences, they switch outcomes too often and produce too few runs of the same outcome. Synthesizing studies of predicting the next outcome in binary sequences, Oskarsson and colleagues (2009) concluded that whether people commit the gambler's fallacy or its opposite, the hot hand fallacy, depends on whether they see the process as a random device or an intentional agent. Ayton and Fischer (2004) likewise analyzed the two fallacies as two faces of subjective randomness. Rabin (2002) built a model in which people act as if they are drawing balls without replacement from a small urn, and Rabin and Vayanos (2010) used it to show how the gambler's fallacy can lead to belief in a hot hand and how it can explain overreaction in financial markets.

Evidence from lotteries to the courtroom

Clotfelter and Cook (1993) found that in the Maryland lottery, the amount bet on a number fell noticeably for several days after it won. Terrell (1994) found a similar pattern in New Jersey lottery data. Croson and Sundali (2005) showed in actual casino roulette betting records that bets on the opposite color rose after streaks of the same color. Chen, Moskowitz and Shue (2016) showed that the bias affects experts too. US asylum judges, loan officers in India and Major League Baseball umpires were more likely to rule the opposite way the more similar decisions they had made just before. Since each case should be judged independently, this is a bias that affects the quality of real decisions.

FAQ

What is the gambler's fallacy in simple terms?: It's the mistaken belief that after a coin lands heads several times in a row, tails is due. The coin has no memory, so the odds are the same every flip.
How is it different from the hot hand fallacy?: The gambler's fallacy is believing a streak is about to end, and the hot hand fallacy is believing a streak will continue. They point in opposite directions, but both come from misperceiving randomness.

Sources reviewed: 2026-10-26

References

Laplace, P.-S. (1814). Essai philosophique sur les probabilités. Paris: Courcier.
Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105–110.
Kahneman, D., & Tversky, A. (1972). Subjective probability: A judgment of representativeness. Cognitive Psychology, 3(3), 430–454.
Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124–1131.
Bar-Hillel, M., & Wagenaar, W. A. (1991). The perception of randomness. Advances in Applied Mathematics, 12(4), 428–454.
Clotfelter, C. T., & Cook, P. J. (1993). The "gambler's fallacy" in lottery play. Management Science, 39(12), 1521–1525.
Terrell, D. (1994). A test of the gambler's fallacy: Evidence from pari-mutuel games. Journal of Risk and Uncertainty, 8(3), 309–317.
Rabin, M. (2002). Inference by believers in the law of small numbers. Quarterly Journal of Economics, 117(3), 775–816.
Ayton, P., & Fischer, I. (2004). The hot hand fallacy and the gambler's fallacy: Two faces of subjective randomness? Memory & Cognition, 32(8), 1369–1378.
Croson, R., & Sundali, J. (2005). The gambler's fallacy and the hot hand: Empirical data from casinos. Journal of Risk and Uncertainty, 30(3), 195–209.
Oskarsson, A. T., Van Boven, L., McClelland, G. H., & Hastie, R. (2009). What's next? Judging sequences of binary events. Psychological Bulletin, 135(2), 262–285.
Rabin, M., & Vayanos, D. (2010). The gambler's and hot-hand fallacies: Theory and applications. Review of Economic Studies, 77(2), 730–778.
Chen, D. L., Moskowitz, T. J., & Shue, K. (2016). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires. Quarterly Journal of Economics, 131(3), 1181–1242.

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This article was last updated on October 27, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.