# Gambler's fallacy

## "When I go to the casino, I choose machines that haven't won in a long time since they are due to win."

#### Definition

Certain trends have been identified regarding the choices people make when participating in games of chance. One is to avoid the number of the lottery ticket that was drawn recently [1] for fear that it will be less likely to be drawn twice in a row. This phenomenon is the gambler’s fallacy. We can speak of the gambler's fallacy when a person believes that a random event is less likely to occur because of previous results [2]. In reality, if an outcome is random and each draw or toss is independent, the probability of a specific outcome is equivalent to all others and is not influenced by the results of other draws. The gambler's fallacy has been demonstrated in the laboratory using experiments, as well as by observation of behavior in natural environments like casinos. Research suggests that this bias is present in the general population, but individuals with gambling addiction problems are even more susceptible to it [2]

#### Example

If you flip a coin (with a non-rigged coin), you are dealing with chance. A common thought in the world of chance is that when an event occurs multiple times, for example, three tails tosses in a row, there is less chance that the 4th toss will also be tails. However, since each toss is independent, the probability of tossing heads or tails is equivalent in each draw regardless of the results obtained in previous tosses.

#### Explanation

The gambler’s fallacy is said to originate, at least partially, from a misinterpretation of the patterns of chance. This misinterpretation would be associated with the erroneous belief that chance should be self-correcting. The principle of self-correction means that chance should approximate its overall probability rather than following some specific sequence. In other words, a small sample should be representative of the overall probability that individual events will occur [2]. For example, imagine a coin toss of four tosses. The overall probability of heads or tails is 50% and so, in theory, there should be as many heads as there are tails. Let us imagine that three consecutive tosses are tails; individuals who believe in the principle of self-correction will predict that the 4th toss will be “heads,” thus converging towards the overall probability of 50%. Put differently, chance would thus be “balanced”. This vision is erroneous, because the probability that the 4th toss will be “heads” remains at 50% since each toss is independent of the previous ones.

The gambler's fallacy could also arise due to individuals' misunderstanding of the concept of chance. Indeed, it is common to think that chance leads, for example, to a sequence of unrelated numbers, and therefore should not include a long series of identical numbers. With this understanding of chance, individuals would tend to consider the results of previous draws when trying to predict the outcome of a future draw [3]. However, each draw is an independent event in itself, and therefore has no influence on the results of other draws.

#### Consequences

The misinterpretation of random sequences has mainly been linked to consequences in games of chance. Its effects have been documented particularly in casinos and lottery games, as manifested by the tendency not to choose a number that has already been a winner. This type of interpretation has also been observed in the context of financial decisions [1]. Indeed, this bias is part of the tendency to overinterpret random events. That is to say, to believe that there is an underlying logic or pattern to chance. This belief leads some individuals to invest more against the trends, believing that losing investments have a greater probability of becoming winners [1]. Finally, although economic decisions are difficult to study, the gambler's fallacy has also been associated with a greater probability of having a negative bank balance [4].

#### Thoughts on how to act in light of this bias

Remember that random events linked to luck are independent and not linked by any logic.

Be vigilant regarding betting strategies that involve predicting chance.

#### How is this bias measured?

This bias was notably measured using tasks aimed at producing, orally, a simulation of a series of 150 tosses of heads or tails that a participant considers representative of random chance [5]. The objective is to see if the participants create sequences including repetitions. For example, if, in the simulation of 150 heads or tails, a participant does not include any sequence of 3 or more “heads” in a row, then he or she probably exhibits this bias. In reality, if you make 150 tosses, it is highly likely to have sequences of 3 or more "heads" in a row due to the large number of tosses.

This bias is discussed in the scientific literature:

This bias has social or individual repercussions:

This bias is empirically demonstrated:

#### References

[1] Stöckl, Thomas, Jürgen Huber, Michael Kirchler, Florian Lindner (2015). Hot hand and gambler’s fallacy in teams: Evidence from investment experiments. *Journal of Economic Behavior & Organization *117: 327-339. https://doi.org/10.1016/j.jebo.2015.07.004

[2] Farmer, George D., Paul A. Warren, Ulrike Hahn (2017). Who believes in the gambler’s fallacy and why? *Journal of Experimental Psychology *146(1): 63-76. https://doi.org/10.1037/xge0000245

[3] Boynton, David M. (2003). Superstitious responding and frequency matching in the positive bias and gambler’s fallacy effects. *Organizational Behavior and Human Decision Processes *91(2): 119-127. https://doi.org/10.1016/S0749-5978(03)00064-5

[4] Dohmen, Thomas, Armin Falk, David Huffman, Felix Marklein, Uwe Sunde (2009). Biased probability judgment: Evidence of incidence and relationship to economic outcomes from a representative sample. *Journal of Economic Behavior and Organization *72(3): 903-915. https://doi-org.proxy.bibliotheques.uqam.ca/10.1016/j.jebo.2009.07.014

[5] Rabin, Matthew (2002). Inference by believers in the law of small numbers. *Quarterly Journal of Economics *117(3): 775-816. https://doi.org/10.1162/003355302760193896

#### Tags

Need for cognitive closure, Availability heuristic, Individual level

#### Related biases

Law of small numbers

Hot hand fallacy

#### Author

Olivier Vivier is a doctoral student in psychology at the University of Quebec in Montreal. He is affiliated with the Laboratoire des processus de raisonnement.

#### How to cite this entry

Vivier, O. (2024). Gambler’s fallacy. In G. Béghin, E. Gagnon-St-Pierre, C. Gratton, & E. Muszynski (Eds). Shortcuts: A handy guide to cognitive biases Vol. 5. Online: www.shortcogs.com.

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