The Gambler's Fallacy can lead to suboptimal decision-making. Part of making an informed decision surrounding a future event is considering the causal relationship it has with past events. In other words, we connect events that have happened in the past to events that will happen in the future. They are seen as causes or indications of how the future will unravel.

This is a good practice when the two events are indeed causally related. For instance, when we notice storm clouds in the sky, it is reasonable to assume that it will rain, and then decide to pack an umbrella. Past experience dictates that storm clouds are good indicators of rain because they are causally related.

But this can be problematic when two events are not causally related but we think they are. This is because we are basing our decisions surrounding a future event on false information. What follows is a probabilistic outlook that is off the mark, and an ignorance to the true causes of the event. Think of an investor that takes her successful track record as an indicator for the likelihood of her future investment being a success. The two aren’t necessarily causally related. As a result of mistakenly thinking that the future will imitate the past, she might overestimate the probability of success and not fully scrutinize her assets for true indicators of their future worth.

Looking at the Gambler's fallacy in the aggregate can have undesirable implications for institutions and professions that rely on accurate projections and causal analysis. When an institution fails to recognize the statistical independence of random events, unrelated events or populations can be identified as causes in search for an explanation. Consider the scenario in which a government blames an unexplainable market crash on a new immigration program and therefore decides to close its borders. Or a physicist who cannot recognize the random movement of particles and therefore conjures a pattern out of several past movements to create a scientific law that is quickly disproven.

The gambler’s fallacy can even cause professionals to autocorrect patterns in their own decision-making, influencing outcomes in various high-stakes areas such as approving loans or granting asylum to refugees. Research by Daniel Chen, Tobias Moskowitz, and Kelly Shue revealed that a significant portion of decisions are erroneous (up to 5% in some cases) because people autocorrect streaks of decisions in one direction by suddenly making the reverse decision.¹² For example, a judge or loan officer might reject an application after approving a number of applications just because they mistakenly believe that having a number of affirmative or negative decisions in a row is unlikely to happen by chance. This happens despite cases being presented in a completely random sequence—a string of strong applicants does not increase the likelihood that the next one will be a poor-quality candidate and vice versa.

The Gambler’s fallacy stems from our tendency to assume that if a random event has occurred many times in the past, that it will occur more or less often in the future. We do this for several reasons. One of them is that we don’t like randomness. So, we try to rationalize random events to create an explanation and make them seem predictable.

We try to make sense of random events

A random event is the product of chance. This makes it unpredictable. Some people find this exhilarating, but most of us find it unsettling. We like predictability, order, and explainability in most aspects of our lives.¹ So, when a random event occurs or is set to happen, we try to rationalize it by finding patterns or indications in the history of events similar to it-- even when they aren’t actually related. This is a natural way for our mind to make sense of a chaotic world.

We think the few represents the many

In what’s known as the “law of small numbers,” we often take small samples of information to represent, or speak for, the larger population from which they are drawn. Renowned psychologists Amos Tversky and Daniel Kahneman describe this phenomenon as an “insensitivity to sample size.”²

Tverski and Kahneman believe our insensitivity to sample size can largely be attributed to the “representativeness heuristic.” Heuristics are mental shortcuts our brains use to help us make decisions quickly. According to this heuristic, we often determine the likelihood of something happening by assessing how similar it is to past experiences.³

We often choose past experiences that we want future events to be similar to, or that we think should be representative of an ideal outcome. A gambler may take a few successful turns at the slot machine to represent a longer winning streak that will continue (as it has sometimes done in the past), or conversely, to assume there will be a loss which will even out their wins and therefore represent what a night at the casino should look like.⁴

Tverski and Kahneman go on to note that we also do this because of our misconceptions surrounding chance, which we think of as a fair process rather than a random one.

We put too much faith in chance

Many of us think of chance as a “self-correcting process.” This is to say, we think that chance aims at a fair and balanced equilibrium. Deviations away from this equilibrium are restored by an opposing outcome as a chance process unfolds.⁵ Consider our example of the slot machine gambler. Maybe they think a turn at the machine is filled with both wins and losses, so when they have a streak of wins, they start to expect a loss. Or a student who thinks they have circled too many “A” options in a row on their multiple choice exam, and so they select a “C” to break the suspicious pattern.

Gambler's fallacy doesn’t just affect those of us who go to casinos — that much should be clear by now. It can affect any of us when we are assessing the probability of a future event by looking at past events that are similar. We do this all the time in both our personal and professional lives. It is easy to make the mistake of doing this with events that are causally independent, which can mess up our predictions surrounding probability and the decisions that follow from them. We don’t want to misidentify characteristics of past relationships as indicators that our current relationships will necessarily follow that path. Nor do we want to look at a string of job rejections as a sign that we won’t find a job in the future.

To counter the effect of this cognitive bias, we need to recognize the causal independence of the events in question. This isn’t always easy, especially when we have a vested interest in their relationship. Thinking through the actual process by which an event occurs may help us realize that certain past events which resemble it don’t really play a role in it unfolding.⁶ It might also be helpful to think about why you think a past event has some bearing on a future one, and evaluating the reason in a way that doesn’t give too much credence to chance or superstition.

Boost your statistical literacy

Improving your ability to understand statistical information can be a powerful way to mitigate the gambler’s fallacy. Truly grasping the nature of randomness can counteract the belief that previous events influence future outcomes. For example, a sequence of heads in a coin toss does not increase the coin’s chance of landing on tails. The same goes for sequences of events we encounter every day: a streak of sunny days does not make rain more probable the next day, and multiple boys being born into a family does not make the next child more likely to be a girl.

Understanding probability can help us recognize that each event is independent. Why is this important? Because it helps us better navigate a world where we often make choices based on the probability of random events occurring. There are plenty of great books on this topic written for those without a technical background in statistics. If you’re looking for somewhere to start, consider Naked Statistics by Charles Wheelan, The Art of Statistics by David Spiegelhalter, and Understanding Uncertainty by Dennis Lindley.

Is the gambler’s fallacy always irrational?

Like other cognitive biases, the gambler’s fallacy often results in incorrect reasoning, but this doesn’t always imply that our resulting behavior is irrational. The gambler’s fallacy might not be a mistaken belief so much as a reasonable way of thinking based on our previous experiences. Consider this: people are generally good at spotting patterns in a sea of randomness, and how we experienced random events in the past seems to shape how we think about randomness overall. This was illustrated in a 2017 study: showing participants a sequence of coin tosses (100 at a time) changed their perception of randomness and improved their ability to generate their own random sequences, reducing the gambler’s fallacy.¹³ However, participants who viewed the same sequence in chunks of five did not show significant improvements in their perception of randomness. The researchers suggest this is because seeing five coin flips in a row is familiar and aligns with the participants’ previous experiences—larger sequences reveal that randomness doesn’t always balance out.

Our everyday encounters with randomness often occur in short sequences like the five-series coin flip, which causes us to expect balance. As such, it might be reasonable for us to make these assumptions, given that we rarely encounter random events in large enough sequences to update our mental models of randomness for a given sequence. Think of it like this: looking at the short-term forecast, it might be reasonable to assume that a few sunny days in a row tends to result in rain, but when you look at the historical weather patterns over a month, it’s easier to understand that weather can be more random and unpredictable.

What is the difference between the gambler’s fallacy and the hot hand fallacy?

Both the gambler’s fallacy and the hot hand fallacy involve making incorrect assumptions about a random process. While the gambler’s fallacy is the belief that there’s a lower chance of something happening again if it has already occurred, the hot-hand fallacy is the belief that a successful streak will lead to more success. For example, someone who continuously calls the correct flip of a fair coin may assume their streak of good luck is bound to continue. This term is often used in basketball, as someone on a scoring streak is often said to have a “hot hand,” suggesting that subsequent shots are more likely to make it in the basket—research shows that this assumption is not correct.¹⁴

Despite what you might think, the gambler’s fallacy and hot hand fallacy are not opposites and can occur at the same time. Someone can believe that after three coin flips resulting in heads, tails is due (gambler’s fallacy) but also believe that after correctly guessing three coin flips in a row, they are more likely to correctly guess the next outcome as well (hot hand fallacy). The gambler’s fallacy has to do with the probability of a given outcome occurring, while the hot hand fallacy is about the success of an individual person. The co-occurrence of these two fallacies was demonstrated in an interesting roulette study. In the study, participants placed more bets against a streak than with it but also put more money on numbers after winning than losing, showing that both these biases can occur simultaneously.¹⁴

An account of the gambler's fallacy was first published by French polymath Marquis de Laplace in 1820. In A Philosophical Essay on Probabilities, Laplace noticed that men who wanted sons thought that each birth of a boy would increase the likelihood of their next child being a girl.⁷

Beliefs that resembled gambler’s fallacy were first seen in experimental settings during the 1960s, when researchers were exploring how the mind makes decisions using probabilities. In these experiments, subjects were asked to guess which of two colored lights would light up next. After seeing a succession of one colour being illuminated, researchers noticed that subjects were much more likely to guess the other.⁸

While the gambler’s fallacy is often associated with financial decisions, it can also have a significant influence on product development and consumer behavior. At the business level, the bias can make companies overly cautious after a series of successes. A product that has been doing well for a while is bound to tank soon, right? Objectively, no, a run of success has nothing to do with a product’s future success. But the gambler’s fallacy says otherwise. As a result, companies might delay a product launch or unnecessarily make changes to something that’s already working—and selling—well. Ironically, these decisions can make customers unhappy and cause sales to slump anyway.

The gambler’s fallacy can also influence consumer behavior, especially when companies run promotional contests or sweepstakes. Think of Tim Hortons Roll Up To Win or McDonald’s Monopoly. Unlike the random outcomes of gambling, these contests have predetermined odds of winning, but they can still trigger the gambler’s fallacy. For example, McDonald’s advertises that the odds of winning an instant prize (like a food item) are one in five, but this doesn’t mean each unsuccessful attempt increases your chances of winning next time.¹⁵ Collecting five tickets does not mean one of them will always be an instant win. Rather, every time you peel back the sticker on your coffee, you have a 20% chance of winning, and these odds don't change no matter how many times you play.

AI-powered tools could help us mitigate gambler’s fallacy and make better decisions. For instance, Dr. Lance B. Eliot explores the idea of using AI to help judges avoid the gambler’s fallacy—an issue we discussed earlier where judges are more likely to grant asylum to refugees after denying the previous applicant and vice versa.¹⁶ Dr. Eliot suggests that AI could be used to uncover and flag concerning patterns in judicial decisions and help humans avoid fallacies that get in the way of fair, objective decision-making. But this opens up another can of worms. AI systems are trained on data from historical legal databases, meaning they often inherit the biases reflected in previous court cases. It would be wrong to assume that AI could help solve the failings of our human reasoning, but this emerging technology can certainly be used as a tool to help us make better decisions in the face of ever-present biases like the gambler’s fallacy.

The most famous example of gambler’s fallacy took place at the roulette tables of a Monte Carlo casino in 1913. For the last 10 spins of the roulette wheel, the ball had landed on black.

Because the gamblers thought a red was long overdue, they started betting against black. But the ball kept on landing on black. As the trend continued, the gamblers became more and more convinced that the next turn would land on red. The crowds and wagers increased-- and so did their losses.

It was only after 26 consecutive blacks that the ball finally landed on red and the streak came to an end. By this time, the losses were staggering. The casino had made a fortune. This became known as the “Monte Carlo fallacy,” which is synonymous with gambler’s fallacy.⁹

Gambler’s fallacy has been shown to affect financial analysis. According to economists Hersh Shefrin and Meir Statman, investors tend to hold onto stocks that have depreciated and sell stocks that have appreciated. They call this a “general disposition to sell winners too early and hold losers too long.”¹⁰

Investors may see the continual rise of a stock’s value as an indication that it will soon crash, therefore deciding to sell. Likewise, if a stock has lost value, this can be taken as an indication that it is due to appreciate, and so they decide to hold onto those stocks. Gambler’s fallacy may be at work here, as investors are making decisions based on the probability of a fairly random event (the stock’s price) based on the history of similar past events (the trend in its previous price points). The two are not necessarily related. A stock that has been appreciating may well continue to appreciate, just as it could crash. Its past price trajectory in itself does not determine its future trajectory.¹¹

What it is

Gambler’s fallacy refers to our belief that the probability of a random event occurring in the future is influenced by the past history of that type of event occurring.

Why it happens

First, we don’t like randomness. As a result, we try to rationalize it by finding patterns or indications in the history of events similar to it-- even when they aren’t actually related. Second, is that we often take small samples of information to represent, or speak for, the larger population from which they are drawn. This “insensitivity to sample size” can largely be attributed to the “representativeness heuristic,” through which we determine the likelihood of something happening by assessing how similar it is to past experiences. We often choose past experiences that we want future events to be similar to, or that we think should be representative of an ideal outcome. Lastly, many of us think of chance as a “self-correcting process.” We think that chance aims at a fair and balanced equilibrium. Deviations away from this equilibrium are restored by an opposing outcome as a chance process unfolds.⁴

Example 1 - Long odds

One night at the roulette tables of a Monte Carlo casino in 1913, the roulette wheel had been repeatedly landing on black. Because the gamblers thought a red was long overdue, they started betting against black. But the ball kept on landing on black. As the trend continued, the gamblers became more convinced the next turn would be red, and increased their wagers. It was only after 26 consecutive blacks that the ball finally landed on red and the streak came to an end. This became known as the “Monte Carlo fallacy,” which is synonymous with gambler’s fallacy.

Example 2 - Financial analysis

Gambler’s fallacy has been shown to affect financial analysis. Investors tend to hold onto stocks that have depreciated and sell stocks that have appreciated. For instance, they may see the continual rise of a stock’s value as an indication that it will soon crash, therefore deciding to sell. Gambler’s fallacy may be at work here, as investors are making decisions based on the probability of a fairly random event (the stock’s price) based on the history of similar past events (the trend in its previous price points). The two are not necessarily related. Its past price trajectory in itself does not determine its future trajectory.

How to avoid it

To counter the effect of this cognitive bias, we need to recognize the causal independence of the events in question. Thinking through the actual process by which an event occurs may help us realize that certain past events which resemble it don’t really play a role in it unfolding. It might also be helpful to think about why you think a past event has some bearing on a future one, and evaluating the reason in a way that doesn’t give too much credence to chance or superstition.

Decision Biases Among Lawyers: Conjunction Fallacy

The conjunction fallacy describes another interesting way we perceive probability, occurring when we think that the probability of two events happening together is more likely than one event alone. Like the gambler’s fallacy, this effect can influence the decision-making of lawyers and judges. Check out this article for some fascinating examples of conjunction fallacy and how it can sway judicial decisions.

Why We See Gambles As Certainties

Gambler’s fallacy isn’t the only bias at play when people follow erroneous beliefs into financially damaging gambling strategies. This article explores gambling through the lens of overconfidence bias, in which sports betters assume they are more skilled and informed than they objectively are. Check out the full article to learn how commercial sportsbooks take advantage of this and how research-based regulatory policies could help.