# The Gambler's Fallacy: Betting on the Past

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• Gambler's Fallacy is a cognitive bias that leads individuals to believe that past random events can influence future random events. This fallacy is particularly common in gambling, where players might think that previous outcomes affect the probabilities of future outcomes. This belief can lead to irrational decision-making and significant financial losses. In this blog post, we will explore the concept of Gambler's Fallacy, provide examples to illustrate the concept, and delve into the psychological mechanisms that cause this fallacy.

## What is the Gambler's Fallacy?

The Gambler's Fallacy, an intuition discussed by the mathematician Pierre-Simon LaplaceOpens in new window, refers to the mistaken belief that after a series of identical outcomes, the probability of a different outcome increases. This fallacy is often observed in gambling scenarios, such as playing the roulette wheel, where after a streak of "reds," individuals wrongly believe that a "black" is due to occur, despite the fact that each spin of the wheel is an independent event with equal probabilities.

This fallacy stems from a misunderstanding of probability. Each independent event, whether it's a coin flip, a dice roll, or a roulette spin, has its own set of probabilities that remain constant, regardless of previous outcomes. The outcome of one event does not influence the outcome of the next. For instance, if a coin is flipped and lands on heads ten times in a row, the probability of it landing on heads on the eleventh flip is still 50%.

The coin has no memory of its past flips. Similarly, a roulette wheel doesn't "remember" the previous colors it landed on. While it might seem intuitive, this fallacy can lead to costly errors in judgment, especially in areas like gambling, investing, and even everyday decision-making, potentially leading to significant financial losses

### Examples of the Gambler's Fallacy

• Gambling: This is where the fallacy gets its name. Gamblers often believe that if a number hasn't come up on a roulette wheel or a slot machine for a while, it's "due" to appear soon. This misconception can lead to significant financial losses.
• Investing: Investors might make poor decisions based on the belief that a stock that has been steadily rising will continue to do so, or that a stock that has fallen sharply is bound to rebound. This can lead to missed opportunities or substantial financial losses.
• Everyday Life: We often apply the gambler's fallacy to everyday situations. For example, someone might avoid flying because there was a recent plane crash, even though the probability of a crash is incredibly low.

### The Representativeness Heuristic

The gambler's fallacy is closely related to the representativeness heuristicOpens in new window, which suggests that people expect a small sample to reflect the characteristics of the larger population. According to Tversky and Kahneman (1974), individuals believe that a series of outcomes, like multiple "reds" in roulette, should be balanced by the occurrence of "black" to resemble a fair distribution. They argue that the occurrence of "black" after many "reds" makes the sequence appear more representative of a truly random process with a 50/50 probability.

### Gambler's Fallacy vs. Hot-Hand Fallacy

The Gambler's Fallacy is often contrasted with the Hot-Hand FallacyOpens in new window. The latter suggests that a person who has experienced success with a random event, like a basketball player making several shots in a row, is more likely to continue having success. Conversely, the Gambler's Fallacy posits that a series of one outcome will be followed by the opposite outcome to balance the sequence.

In gambling, these two fallacies can coexist. For example, while playing dice or roulette, people might believe in hot hands (expecting streaks to continue) even though these games are based on random processes. This paradox shows the complexity of human intuition and belief systems in understanding randomness and probability.

### Psychological Mechanisms Behind the Fallacy

The persistence of the Gambler's Fallacy can be attributed to several psychological factors:

1. Misunderstanding of Probability: Many people lack a deep understanding of statistical independence and randomness, leading them to incorrect assumptions about how random sequences should behave.
2. Expectation of Fairness: There is a natural expectation that random events should be fair and balanced. Deviations from this balance are often expected to be corrected in the short term.
3. Law of Small Numbers: People often believe that small samples should closely reflect the properties of the larger population, expecting short sequences to exhibit perfect balance.

### Conclusion

The Gambler's Fallacy is a common cognitive bias that can lead to irrational decision-making and financial losses, especially in gambling contexts. Understanding that random events are independent and that past outcomes do not influence future ones is crucial in avoiding this trap. Recognizing the psychological mechanisms behind this fallacy can help individuals develop better decision-making strategies.

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• Source:
• Tversky, A., & Kahneman, D. (1971). Belief in the Law of Small Numbers. Psychological Bulletin, 76(2), 105-110.
• 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.
• Kahneman, D. (2011). Thinking, Fast and Slow. Farrar, Straus and Giroux.
• Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185(4157), 1124-1131.
• 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.
• Alter, A. L., & Oppenheimer, D. M. (2006). From a Perceptual to a Rational Basis for Decisions: The Case of the Hot Hand. Journal of Behavioral Decision Making, 19(4), 397-410.