Gambler's fallacy

The gambler’s fallacy is a type of fallacy that occurs when people mistakenly believe that the outcomes of independent events are linked to the outcomes of other events. For example, each flip of a coin is an independent event having a 50 percent chance that it will land on one side. Each flip of the coin has an equal chance of landing on heads or tails. However, a person who falls for the gambler’s fallacy will believe that, if the coin has landed on heads ten times in a row, it is more likely to land on tails on the eleventh toss. When people mistakenly fall into the gambler’s fallacy, they assign a probability to a random event based on history or other events. The gambler’s fallacy received its name from a group of people betting in a casino in the early 1900s. The fallacy helps explain people’s beliefs and behaviors, including those of people with gambling problems.

Background

The gambler’s fallacy is also called the Monte Carlo fallacy because the phenomenon is named after the behavior of gamblers observed in a Monte Carlo casino. One night in 1913, gamblers in this casino were playing roulette. Roulette players can make various wagers, but one of the most common is to bet on either black or red. The roulette ball has a roughly 50 percent chance of landing on either black or red. (Roulette also has one green space on which both red and black lose, so it is not exactly a 50 percent chance.) Each spin of the roulette wheel has the same potential to land on either red or black, but on this night, the ball kept landing on black. Black won over and over again, and people began betting aggressively on red. They believed that, since the ball had landed on a black space so many times, it would soon land on a red space. More and more people began betting as they believed the ball landing on red was imminent. The ball landed on black twenty-six consecutive times before landing on red. During that time, the gamblers betting against black had lost roughly one million dollars, even though the probability of each spin landing on black was the same as the probability of the first spin landing on black. This example shows that people sometimes think that independent events can influence each other. This type of thinking is incorrect because past independent events do not change the probability of future independent events.

Overview

People believe in the gambler’s fallacy because they see patterns in the world around them. For example, the gamblers at the Monte Carlo casino saw an erroneous pattern—the ball landed on black so many times that they were certain it would soon land on red. Humans have evolved to find patterns and notice structures in the world around them. Understanding patterns has helped people survive, as they can use patterns to predict events and take action. However, this tendency also makes people more likely to see patterns that do not actually exist.

People tend to erroneously identify patterns, in part because the human brain focuses more on the frequency of an event than on its probability. The human brain does not determine the probability of an event happening as much as it notes when the event happened. For example, suppose someone lives in an area that experiences an extremely strong storm that, on average, happens only once every one hundred years. That person might mistakenly believe that the area will never experience that type of storm again because it occurs only once in one hundred years. Although the storm’s average occurrence is once in one hundred years, it is still a random event. A terrible storm one year does not decrease the likelihood of a terrible storm occurring the next year. The storms themselves are independent events. The overall probability makes the chances of the storm occurring low; however, it can still occur again.

Because the brain is more likely to notice frequency than probability, humans are not good at understanding long odds. People play the lottery in part because they know that someone has to win the prize in the end. While someone will win, the odds of any single individual winning a large lottery are extremely small. It is difficult for the human brain to fully comprehend long odds, such as having a one in one million chance of winning. This belief that a past event must be highly probable because it occurred once is called the lottery fallacy and occurs for the same reasons as the gambler’s fallacy.

The gambler’s fallacy and the lottery fallacy help explain some human behaviors. Slot machine gambling is an example of this behavior; gamblers may continue spending money because they believe that they have been playing long enough to be “due” for another win. Nevertheless, slot machines are random, and playing one for a certain amount of time does not ensure a win.

People who want to overcome the gambler’s fallacy have to be able to identify individual, or random, events. If an event is random, it will not be influenced by similar events that happened before. Therefore, if an event has a 50 percent probability of occurring, it will have a 50 percent probability of occurring every time. A coin is not more or less likely to land on heads during one flip just because it landed on tails during the previous flip. To overcome the gambler’s fallacy, people should focus on the overall probability of an event happening and try to avoid thinking about the frequency of the event.

Bibliography

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