The Gambler's Fallacy, also known as the Monte Carlo Fallacy, is a cognitive bias where people mistakenly believe that past events can influence the probability of future independent events. In other words, individuals may incorrectly think that the outcome of a random event will "even out" over time or that a certain outcome is "due" to occur after a series of different outcomes.

Here are two simple examples to help you understand the Gambler's Fallacy:

Coin toss: Imagine you're flipping a fair coin and have just observed a streak of six heads in a row. You might be tempted to believe that tails is more likely to come up on the next flip to "balance out" the streak. However, the probability of getting heads or tails remains 50% for each flip, regardless of the previous outcomes, as each flip is an independent event.

Roulette wheel: Suppose you're at a casino watching a roulette wheel that has just landed on red five times in a row. You might think that black is more likely to come up next because it hasn't appeared for a while. However, the probability of landing on red or black remains the same for each spin (ignoring the green zero), regardless of the previous outcomes, as each spin is an independent event.

The Gambler's Fallacy occurs because people often try to find patterns in random events, even when there are none. Being aware of the Gambler's Fallacy can help individuals make more informed decisions when facing situations involving randomness or probability.

The Gambler's Fallacy, also known as the Monte Carlo Fallacy or the negative recency effect, is a cognitive bias and a well-documented phenomenon in probability theory and cognitive psychology. It refers to the erroneous belief that the probability of a random, independent event is influenced by the outcomes of preceding events. This fallacy is grounded in the misconception that probabilities must "even out" or "balance" in the short term, leading individuals to assume that a specific outcome is "due" after a series of different outcomes.

The Gambler's Fallacy has been extensively studied and can be related to various psychological principles, cognitive biases, and scientific fields, including:

1. The law of large numbers: A fundamental principle in probability theory that states that as the number of trials increases, the observed probability of an event converges to its true probability. The Gambler's Fallacy arises from a misinterpretation of this law, as individuals may expect the balancing of probabilities to occur over a smaller number of trials.

2. The representativeness heuristic: A mental shortcut identified by psychologists Amos Tversky and Daniel Kahneman, where people judge the probability of an event based on how similar it is to a perceived "typical" example. The Gambler's Fallacy can be linked to this heuristic, as individuals may expect random sequences to resemble their intuitive notion of randomness, which often includes alternation between outcomes.

The hot-hand fallacy: A cognitive bias where individuals believe that a person who has experienced success in a random event is more likely to experience further success, despite the outcomes being independent. The hot-hand fallacy can be seen as the opposite of the Gambler's Fallacy, as it involves the belief in positive recency rather than negative recency.

The Gambler's Fallacy has significant implications for understanding human decision-making, particularly in situations involving risk and uncertainty, such as gambling, investing, and sports betting. Recognizing the Gambler's Fallacy can help individuals avoid making irrational decisions based on misconceptions about probability and randomness.

References

• Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105-110.
• Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185(4157), 1124-1131.
• Gilovich, T., Vallone, R., & Tversky, A. (1985). The hot hand in basketball: On the misperception of random sequences. Cognitive Psychology, 17(3), 295-314.