## What is the Gambler’s Fallacy?

The gambler’s fallacy is a cognitive bias that occurs when people incorrectly believe that previous outcomes influence the likelihood of a random event happening. The fallacy assumes that random events are “due” to balance out over time. It’s also known as the “Monte Carlo Fallacy,” named after a casino in Monaco where it was famously observed in 1913.

Have you ever flipped a coin and thought it must be “heads” next because it’s been “tails” several times in a row? Or have you been in a casino and believed a particular slot machine is due to pay out because it hasn’t hit the jackpot in a while? If so, you’ve fallen victim to the gambler’s fallacy.

If you flip a coin and get ten heads in a row, the probability of the following coin toss being heads again is still 50/50. Random processes don’t have a “memory” of previous events. For independent, random events, past outcomes do not change the probability of future results.

Learn more about Cognitive Biases.

## Gambler’s Fallacy Examples

The gambler’s fallacy is not limited to gambling scenarios. It can also occur in situations that involve chance events, such as predicting the gender of newborn babies. Consider a family that has three boys and is expecting their fourth child. The parents might fall victim to the gambler’s fallacy by assuming that they are “due” for a girl and that the probability of having a girl has increased since they already have three boys.

However, random processes determine the gender of a baby, and the sex of the previous children does not affect the probability of having a boy or a girl. The chances of having a boy or a girl are 50/50, regardless of the previous outcomes. Therefore, assuming the probability of having a girl has increased is a classic example of this cognitive bias.

The gambler’s fallacy is also evident in the stock market. Investors tend to sell stocks that have been rising, believing that the sequence of gains means that a decline is due.

## Gambler’s Fallacy Problems

The gambler’s fallacy can be dangerous in many situations, but it’s especially problematic in gambling. Some people believe they can beat the odds by using it to their advantage. They might increase their bets or change their strategy based on the false belief that a particular outcome is “due” to happen. Unfortunately, this can lead to significant financial losses and even addiction.

Let’s take an example to illustrate the gambler’s fallacy. Imagine you’re playing roulette, and the ball has landed on “red” for the last five spins. You might think it’s more likely to land on “black” next, but each spin is independent, and the odds of “red” or “black” are always the same. Betting on “black” just because “red” has come up several times in a row is the gambler’s fallacy in action.

## Why It Happens

Researchers started evaluating the gambler’s fallacy during the 1960s when studying how the mind processes probabilities.

In early experiments, researchers asked participants to predict which of two colored lights would illuminate next. When chance caused one color to light up several times in a row, participants were likelier to guess the other color as the next one to light up. They wrongly assumed the lights were somehow “due” to switch to the other color, even though the probability was always 50/50.

This experiment and others helped researchers identify the cognitive biases that underlie the gambler’s fallacy.

The gambler’s fallacy occurs because we look for patterns and meaning in everything we encounter, including the outcomes of random events. When we observe a series of similar events, such as several coin flips resulting in heads, our brains naturally assume that the next event will be tails to “balance it out.”

The incorrect assumption that random chance is fair and balanced rather than just arbitrary drives this cognitive bias. People tend to believe that if an event has occurred too frequently or not frequently enough, it must be due to some external factor or influence. In reality, independent events are entirely random, and no external force governs their outcomes. Past outcomes don’t influence future results.

Gambler’s fallacy can affect anyone assessing the likelihood of a future event by looking at similar past events. This problem occurs in personal and professional contexts, as our brains naturally try to identify patterns and predict the future. However, errors arise when we apply this approach to independent, random events that are inherently unpredictable. Mistakenly assuming these events follow patterns can significantly impact our predictions and subsequent decision-making processes.

## Gambler’s Fallacy and Statistical Concepts

Two crucial statistical concepts play a role in Gambler’s Fallacy—independent events and the law of large numbers. Misunderstanding them can cause you to fall victim to this cognitive bias.

### Independent Events

Independent events are those in which one event doesn’t affect the outcome of the next event. By definition, the gambler’s fallacy applies only to independent events because you can’t use past events to predict future events.

However, there are *dependent* events where one outcome does influence the next. For example, when you draw a card from a standard deck and do not replace it, if the card is NOT an ace, the probability that the next card is an ace is slightly higher.

The gambler’s fallacy occurs when you use a process that works for dependent events for independent events. Be aware of that crucial difference!

When you feel like an event is “due,” determine whether that’s appropriate for the event you’re dealing with!

Learn more about Independent Events and How to Use the Multiplication Rule to Find Probabilities for Independent and Dependent Events.

### Law of Large Numbers

Misunderstanding the law of large numbers or regression to the mean can cause people to fall for the gambler’s fallacy.

The law of large numbers states that as the number of trials increases, sample values tend to converge on the expected result. For example, the more times you flip a coin, the percentage of heads tends to converge on 50%. Learn more about the Law of Large Numbers.

Consequently, if you’ve had only 30% heads, you might think that heads are “due,” and their probability is higher. However, that belief is mistaken.

The Law of Large Numbers applies over a long series of independent events, not just a few events or the next one.

In our coin toss example with 30% heads, the law states you’d expect the percentage to be closer to 50% after flipping the coin *many* more times. However, the next individual coin toss still has a 50% chance of heads.

The gambler’s fallacy is related to the Base Rate Fallacy in that both form of cognitive bias incorrectly apply the underlying probabilities to the situation at hand. Learn more about the Base Rate Fallacy.

In conclusion, the Gambler’s Fallacy is a cognitive bias that can lead people to make irrational decisions based on false beliefs. It occurs because our brains are wired to look for patterns and connections between events, even when none exist.

To minimize this problem, be aware of circumstances where you feel something is “due” or will “balance itself out.” Carefully evaluate the situation and determine whether it is a random process involving independent events. If so, remind yourself that past events do not affect future outcomes!

## References

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.

Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. *Science*, 185(4157), 1124-1131.

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