Gambler's fallacy

type: effect · origin: study · evidence: supported · themes: judgements and probabilities

Claim assessed: After a run of identical outcomes in a random process, people expect the opposite outcome to come next.

Published 8 October 2026 · how we work

In short

The gambler’s fallacy means that, after a run of identical outcomes in a random process, we expect the opposite outcome to come next. After five reds at roulette, black seems “due”, although the wheel doesn’t remember what came up. The effect has been found in the lab, in lotteries and in casinos, but also in serious decisions: asylum judges, loan officers and baseball umpires decide slightly differently after a few decisions in the same direction. The effect is small, though, and varies a lot: at roulette about half the players do the opposite and bet on what has come up often, and at baccarat most players bet on the streak continuing.

What it says

The idea. Someone who falls for the gambler’s fallacy treats a random sequence as if it had to “even out” quickly: if one outcome has come up many times, the other should catch up. The classic explanation, from Tversky and Kahneman, is that we expect even a short sequence to look like the whole process, with red and black alternating often and no long runs. There is no meta-analysis of this effect; the evidence comes from separate studies, some of them very large.

Real decisions. Chen, Moskowitz and Shue (2016) analysed three settings in which cases arrive in a nearly random order, so one decision shouldn’t depend on the previous one:

• US asylum judges. Across all cases, after granting a request, judges granted the next one 0.5 percentage points less often. Among judges with grant rates close to half, for cases on the same day and of the same type, the difference rose to 3.3 points. The authors estimate that 1.6% of the decisions in this group would have gone the other way without the order effect.
• Loan officers in India, in a field experiment with files put in random order. Paid the same regardless of accuracy, they approved 8 percentage points less often after an approval. When paid for correct decisions, the effect became small and non-significant.
• Baseball umpires, across about 3.5 million pitches from 2008–2012. For the same pitch location, they called a “strike” less often after a “strike”, and after two in a row the difference was 2.1 percentage points.

The effect was stronger after longer runs, among less experienced decision-makers and for cases close together in time. The authors consider the gambler’s fallacy the best-fitting explanation, but they can’t rule out a contrast effect: a case looks weaker just because it follows a good one.

Lotteries. Jørgensen, Suetens and Tyran (2011) followed 189,531 Danish online lotto players over 28 weeks. Numbers drawn the previous week received on average 2% fewer bets. Most players, however, play the same numbers every week: only 9.2% reacted significantly to the draws. Those who did avoided numbers just drawn, but favoured numbers drawn several weeks in a row, that is, the hot hand. Polin and Benisaac (2023), across hundreds of millions of tickets in Israel, found the same pattern: winning numbers are avoided for a while, then gradually become “hot”.

Casinos. Sundali and Croson (2006) analysed 18 hours of footage from a roulette table in Reno, with 139 players. About half the players bet less often on numbers that had come up frequently, following the gambler’s fallacy, and the other half bet on them more often. Muto et al. (2025) analysed almost 18 million baccarat games by 6,625 customers of a casino and found the opposite: most players bet more and more often on the streak continuing as it grew longer.

What we believe, not just what we pick. Most studies measure a choice (“red” or “black”), not how likely each outcome seems to someone. Xiang, Dorst and Gershman (2025), in preregistered studies with 150 participants each, found the effect when people guessed the colour of the next ball, but not when they estimated its probability. Choi and DeKay (2026) reanalysed the same data and found the effect in the probabilities too, especially after long runs: after four balls of the same colour in a row, the average estimate for one more dropped by about 7 percentage points. Only 25–30% of participants showed a clear individual effect, though. A commentary by Banki and Simonsohn (2026) and a replication by van den Berg et al. (2026) reach the same conclusion, according to Choi and DeKay.

A related version replicated widely. In the retrospective gambler’s fallacy, someone who sees three dice come up 6 believes the player had rolled more times before than someone who sees an ordinary result. The Many Labs 1 project (Klein et al., 2014) repeated the study in 36 samples with about 6,000 participants and found a moderate effect (d ≈ 0.6), significant in most samples.

Example

A family has three daughters and thinks the fourth child is “bound” to be a boy. The chance is still about half, as with every birth. The example is an illustration, not a study cited here.

How to apply it

The steps below are a practical way to apply it that we propose, based on the studies cited.

1. Ask whether the process has a memory. Roulette, dice and the lottery don’t remember what came up. A deck of cards you don’t put back does: there, earlier outcomes really change the odds.
2. When deciding in a series, judge each case on its own. If you assess candidates, requests or papers one after another, don’t think “I’ve approved too many in a row”. Chen et al. found the effect smaller among those who spent more time on the current file and among those paid for accuracy.
3. Don’t lean on the opposite error either. Betting on the streak continuing, as at baccarat, is just as wrong in a fair game.

Limits and nuances

• Not everyone does it. At roulette about half the players do the opposite, at baccarat most do, and in lotto the vast majority don’t react to the draws at all. The average effect hides large differences between people and between games.
• The field effects are small. A few percentage points, except for loan officers without incentives. They matter because of the large number of decisions, not their size.
• The alternative explanation. For judges and umpires, Chen et al. can’t rule out a contrast effect, in which the current case is judged by comparison with the previous one.
• It isn’t always a mistake. Choi and DeKay recall the argument that, in short sequences, a run of four alike actually turns up less often than a run that breaks, so the intuition has a basis in what we usually see. And when the process really has a memory, as with cards drawn from a deck, expecting the opposite outcome is correct.
• What we didn’t use. Chen et al. cite a study on admissions interviews co-authored by Francesca Gino, who has had papers retracted for fabricated data. We didn’t use it.
• What we read. Chen et al. (2016), in the February 2016 NBER working paper version (we couldn’t download the QJE article), Choi and DeKay (2026), Sundali and Croson (2006) and Klein et al. (2014), in the published version from the Radboud University repository, we read in full. For Xiang et al. (2025) we read the 2024 preprint in full; the published article is available only behind a paywall and may differ. We read Muto et al. (2025) as a preprint (January 2025) and Jørgensen et al. as a 2011 working paper; we didn’t compare the published versions. For Polin and Benisaac (2023) we read the abstract and the data description. We couldn’t read the commentary by Banki and Simonsohn or the replication by van den Berg et al.; we describe them from Choi and DeKay. There is no meta-analysis of the effect; the review by Oskarsson et al. (2009) and the classic lottery studies (Clotfelter and Cook, 1993; Terrell, 1994) are available only behind a paywall and we haven’t read them. They are unlikely to change the evidence level, because the sources we read are newer and larger.

Sources

• James Sundali, Rachel Croson (2006). Biases in casino betting: The hot hand and the gambler's fallacy
• Claus Bjørn Jørgensen, Sigrid Suetens, Jean-Robert Tyran (2011). Predicting lotto numbers
• Richard A. Klein, Kate A. Ratliff, Michelangelo Vianello et al. (2014). Investigating variation in replicability: A “Many Labs” replication project
• Daniel L. Chen, Tobias J. Moskowitz, Kelly Shue (2016). Decision making under the gambler's fallacy: Evidence from asylum judges, loan officers, and baseball umpires
• Brian A. Polin, Eyal Benisaac (2023). A longitudinal analysis of the hot hand and gambler's fallacy biases
• Yang Xiang, Kevin Dorst, Samuel J. Gershman (2025). On the robustness and provenance of the gambler's fallacy
• Hiroyuki Muto, Ryusuke Nakai, Toshiya Murai, Sakiko Yoshikawa, Nobuhito Abe (2025). Baccarat gamblers follow trends rather than adhere to the gambler's fallacy: Analyses of field data from a casino
• Yeonho Choi, Michael L. DeKay (2026). A gambler's fallacy for probability judgments when event sequences are truly random: A reanalysis of Xiang, Dorst, and Gershman's (2025) data

See also: Hot hand fallacy, Illusion of control, Regression to the mean