In the summer of 1913, something extraordinary occurred in Monte Carlo that would become a lasting illustration of human psychology. Onlookers crowded around a roulette table, mesmerized as the ball landed on black not once, not twice, but an astonishing twenty times in a row. Faced with such an improbable streak, many players seized the “opportunity,” immediately betting on red, convinced that the next spin must inevitably be red to “balance out” the wheel. But they were wrong. The ball continued to land on black—again and again. Only after twenty-seven spins did the ball finally land on red, and by then, millions of dollars had been wagered on the fallacy of balance. In a matter of minutes, many players found themselves bankrupt.
This incident highlights a pervasive psychological mistake known as the gambler’s fallacy. The belief that independent events—like a roulette spin or a coin toss—are “due” to balance out is deeply ingrained in human thinking. This is why people wrongly assume that a streak of black on the roulette wheel means a red result is imminent. But as the Monte Carlo example shows, the wheel doesn’t have a memory, and past results do not influence future outcomes.
The Gambler’s Fallacy in Action
The gambler’s fallacy, often called the “Monte Carlo fallacy” or “fallacy of the maturity of chances,” stems from the misconception that independent events are connected in some way. People fall victim to this fallacy when they believe that outcomes of random events must somehow “balance out.” This error is deeply rooted in the human desire for order and predictability. In games of chance like roulette, players tend to believe that after a sequence of a particular result, such as a streak of black, the opposite outcome—red, in this case—is due to appear. This belief is what drives them to place increasingly larger bets, hoping for a return to balance.
The Monte Carlo incident from 1913 serves as a perfect demonstration. For 26 consecutive spins, the roulette ball landed on black. The fallacy here was that players began to believe that the streak of black would inevitably be interrupted by red. As more people placed their bets on red, the chances of the ball landing on black remained unchanged. But they couldn’t help but believe that the universe would right itself, making their odds more favorable. By the time the ball did land on red, most players had lost their fortunes. The fallacy here wasn’t just in predicting the outcome; it was assuming that the roulette wheel, a random mechanism, must correct itself after such an unlikely sequence.
This fallacy doesn’t just appear in gambling scenarios. It also occurs in everyday life, such as when people assume that after a few bad events—like bad luck or failures—they are “due” for something good to happen. The false belief that events must be balanced out can lead to poor decisions, especially when individuals do not understand that each event is independent and unaffected by previous outcomes.
The Mathematics of the Gambler’s Fallacy
The mathematics behind the gambler’s fallacy is relatively simple but often misunderstood by those who fall prey to it. Events like coin flips, dice rolls, or roulette spins are governed by probability, which dictates that each individual event is independent of the ones that came before it.
For example, flipping a fair coin has a 50% chance of landing heads and a 50% chance of landing tails every single time. Even if a coin has landed heads five times in a row, the probability of it landing heads or tails on the next flip is still exactly the same: 50/50. The mistaken belief that “tails is due” after a series of heads is a manifestation of the gambler’s fallacy. It falsely assumes that because heads have come up several times, the coin must “correct” itself by landing on tails. This is simply not the case, as the outcome of each flip is independent.
To understand the fallacy mathematically, let’s consider a roulette wheel. In a fair roulette game, the odds of the ball landing on red or black are consistent for each spin, typically 18 out of 38 for both colors in American roulette. The outcome of one spin does not influence the outcome of the next spin. Therefore, the gambler’s assumption that red is “due” after a long streak of black is mathematically unfounded. The odds for red or black remain the same no matter how many times the ball lands on black, and the belief that the odds are “due to balance” is completely erroneous.
This faulty reasoning is also prevalent in more complex scenarios, such as the stock market or lottery. People sometimes believe that if a stock has gone down for several days, it is “due” for a rise, or if a lottery number hasn’t appeared for a while, it is more likely to appear in the next draw. This is simply a misunderstanding of how probability works in independent events, where past results have no bearing on future ones.
The Problem with Regression to the Mean
Regression to the mean is a statistical phenomenon that suggests that extreme events will often be followed by more average or moderate results. It helps explain why a person who performs exceptionally well one day is likely to perform more “normally” the next, or why unusually hot weather is often followed by more typical conditions. The concept is rooted in the idea that extreme values tend to return to a more typical average over time naturally.
However, the gambler’s fallacy often distorts our understanding of regression to the mean. The key mistake is assuming that after a particularly extreme outcome, like a large win or a large loss in gambling, the next result must correct itself in the opposite direction. In the context of gambling, this leads to the belief that after a streak of wins or losses, the next event will be more balanced, as if the universe is seeking equilibrium. The issue here is that extreme events don’t always “correct” themselves; they can persist or even amplify. In games of chance, the results do not automatically follow a predictable, average path. They remain random.
In real life, regression to the mean applies in many areas, but it is not a simple correction mechanism. For example, if someone has a particularly strong performance at work in one quarter, it doesn’t mean they are “due” for a poor performance in the next quarter. Instead, their performance could continue to vary depending on external factors like their work environment, market conditions, or even luck. On the other hand, certain systems, like wealth accumulation, don’t always follow a regression to the mean pattern. The rich, for instance, often continue to get richer, not because of a balancing force, but because of compounding wealth, investments, and external factors that support their continued success.
Understanding the Role of Interdependence in Real Life
Life is full of interdependent events—things that are connected and influenced by one another. In contrast to independent events, where past outcomes have no impact on future ones, interdependent events are interconnected, and one occurrence can influence or cause another. Many real-world systems are inherently interdependent, from weather patterns to financial markets and even to personal health.
For instance, the weather doesn’t follow the same independent rules as a coin flip. Extreme cold weather one day can lead to changes in atmospheric conditions that contribute to the next day’s weather. If there’s a large pressure system in place, it could lead to a dramatic shift in temperatures. The weather is not a random, independent event like a dice roll; it’s a highly complex system influenced by a range of factors, including geography, time of year, and ocean currents.
Similarly, the stock market is not a collection of independent events. Stock prices are influenced by economic conditions, interest rates, investor sentiment, and company performance, all of which are interconnected. A successful product launch might lead to a spike in stock price, which could, in turn, increase investor confidence and drive more demand. These events feed into one another, creating a feedback loop that leads to both upward and downward trends. The gambler’s fallacy ignores these interdependencies, mistakenly assuming that the stock market, like a random coin toss, will always correct itself in some way.
Understanding these interdependencies is crucial for navigating the real world. Whether you’re in business, finance, or even health, the outcomes of one event often influence what comes next. Instead of relying on luck or the hope that things will balance out, assessing the factors at play and making decisions based on these interconnected variables is essential. The gambler’s fallacy misleads us by encouraging us to focus on isolated, independent events rather than understanding the complexity of systems.
The Financial Markets: A Case Study in Interdependence
The financial markets offer an excellent case study of how interdependent events operate in real life. Unlike independent events, where each outcome is unaffected by previous occurrences, the financial markets are driven by a web of interconnected factors. Investor sentiment, economic data, and even global events all influence stock prices, bond yields, and other financial instruments. In such a complex environment, it’s easy to fall into the trap of the gambler’s fallacy by expecting a stock that has been declining for a period to “correct” itself in the short term.
However, financial markets don’t behave like a roulette wheel, where past outcomes do not impact future ones. The stock market is affected by various factors, including company performance, government policies, global trade conditions, and even investor emotions. When a company’s stock rises rapidly, it often attracts more investors, driving the price even higher—a feedback loop that defies the idea of “balancing out.” In this case, past performance actually influences future outcomes, creating a self-reinforcing cycle.
On the other hand, market corrections and downturns can be influenced by negative news or events that alter investor perceptions. A sharp decline in the stock market doesn’t necessarily mean that it will automatically recover to “average” levels. It could be the result of systemic issues, such as an economic recession or a financial crisis, which would continue to affect the market for an extended period.
This is why it’s essential to understand the difference between random, independent events and the complex, interdependent events that govern financial systems. Investors who fall victim to the gambler’s fallacy might assume that after a downturn, a recovery is inevitable. However, market dynamics are much more intricate in reality, and future performance is not guaranteed based on past results.
The Illusion of Balance in Human Behavior
The gambler’s fallacy doesn’t just apply to gambling or financial markets; it also influences human behavior and decision-making. Many people mistakenly believe that after a series of bad outcomes, they are “due” for something good to happen, or that after a period of success, they are bound to face a setback. This mindset leads to poor decision-making and unrealistic expectations, both in personal life and in business.
In relationships, for instance, people may feel that after a series of failed attempts or disappointments, they are “due” for a good experience. This might lead them to enter new relationships with misplaced expectations or overly optimistic views, hoping that the next one will somehow “balance out” their past experiences. Similarly, in business or career choices, individuals may assume that their bad luck will eventually give way to success. They may rely on the idea that things will automatically improve after a period of struggle instead of taking proactive steps to influence their future.
The belief in cosmic balance can also lead to a sense of complacency. People who believe things will correct themselves might stop working toward their goals or addressing the challenges that have contributed to their situation. Instead of taking responsibility for their actions, they might wait for “luck” to turn in their favor. This behavior can prevent them from making the necessary changes to improve their circumstances.
Understanding that life doesn’t always “balance out” can be liberating. It shifts the focus from hoping for external forces to correct your situation to actively creating the conditions for your success. Rather than waiting for something to change, individuals can take charge of their decisions, knowing that outcomes are not determined by cosmic justice or a balancing mechanism but by the steps they take to shape their future.
Conclusion: The Gambler’s Fallacy and the Myth of Balance
The gambler’s fallacy leads us to believe that independent events must eventually “balance out,” but this is a false assumption. Past events do not determine future outcomes in the world of roulette, coin flips, and lottery numbers. We can avoid falling victim to irrational thinking by recognizing this fallacy and understanding the true nature of probability and interdependence. While the idea of balance may be comforting, it is not an inherent feature of the universe. Instead, we must learn to understand the systems around us—whether in business, finance or even nature—through the lens of interrelated, often unpredictable forces.
This article is part of The Art of Thinking Clearly Series based on Rolf Dobelli’s book.