Why do we think a random event is more or less likely to occur if it happened several times in the past?

 

Gambler's Fallacy

, explained.

What is the Gambler’s fallacy?

The gambler’s fallacy describes our belief that the probability of a random event occurring in the future is influenced by previous instances of that type of event.

“Cognitive

Where this bias occurs

Consider the following hypothetical: Jane loves playing Blackjack, and she’s pretty good at it. But for the last few days, she’s been on a losing streak. Jane has had a few losing streaks in her many years of gambling, and she’s noticed a pattern: they usually end the fifth trip to the casino, when she wins big.

Today is the fifth day of the losing streak she currently finds herself in. She goes into the casino with a grin, knowing that today is her day.

Many hours and many games of Blackjack later, Jane is defeated. She has lost an enormous amount of money. “How could this be?”, Jane asks herself. She always wins on the fifth day!

Jane’s belief that she would find success in the casino that day, and the dismay that followed her unforeseen failure, was a result of gambler’s fallacy. The pattern Jane saw in her gambling history led her to believe that there was a high probability that she would win playing Blackjack. The problem is, the two aren’t causally connected. The length of her past losing streaks has no bearing on how likely she is to end this losing streak.

 

Individual effects

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.

Systemic effects

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.

Why it happens

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.

Why it is important

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.

How to avoid it

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.

How it all started

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

Example 1 - Long odds

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

Example 2 - Financial Analysis

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

Summary

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.

Sources

  1. Stevenson and Mihnea C. Moldoveanu, H. (2014, August 01). The Power of Predictability. Retrieved July 08, 2020, from https://hbr.org/1995/07/the-power-of-predictability
  2. Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science,185(4157), 1124-1131. doi:10.1126/science.185.4157.1124
  3. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  4. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  5. Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science,185(4157), 1124-1131. doi:10.1126/science.185.4157.1124
  6. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  7. Barron, G., & Leider, S. (2010). The role of experience in the Gambler’s Fallacy. Journal of Behavioral Decision Making,23(1), 117-129. doi:10.1002/bdm.676
  8. 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. doi:10.1007/s11166-005-1153-2
  9. Owen, A. M. (2011). The Monte Carlo fallacy. Medical Journal of Australia,195(7), 421-421. doi:10.5694/mja11.10937
  10. Constantinides, G. M. (1985). The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence: Discussion. The Journal of Finance,40(3), 791. doi:10.2307/2327803
  11. 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. doi:10.1007/s11166-005-1153-2