BLOG

The most famous gambler's fallacy at the casino

The gambler's fallacy is a thinking error that affects us all and can be extremely detrimental for a player. Knowing and understanding it is essential in the world of gambling. But what exactly is the gambler's fallacy? What is a cognitive bias? Let us explain!

The gambler's fallacy: explanation of cognitive bias

The gambler's fallacy

The "gambler's fallacy," also known as the "fallacy of the maturity of chances," is a judgment error that involves believing that random events occurring in the future are influenced by those that have occurred in the past, meaning that past outcomes influence future outcomes. For example, if we flip a coin one hundred times, we expect it to land heads fifty times and tails fifty times. If it has landed heads sixty times and tails forty times, the human brain expects it to land more on tails in the future to "catch up," while the probability remains ½, regardless of previous flips.

Explanation of cognitive biases

Cognitive bias refers to a mechanism that denotes a logical processing error, a thought process that leads to distorted judgment and, subsequently, flawed decision-making. Cognitive biases are studied in cognitive psychology, analyzed and exploited in various fields, such as gambling, for example.

These cognitive biases arise from:

• our limited memory capacity; our memory can only store a restricted amount of information at any given time;
• our processing and calculation capacity; we are often unable to objectively assess probabilities or complex consequences;
• our spatial and temporal perceptions; our decisions are influenced by the immediate context and perceived time constraints.

Nowadays, many cognitive biases have already been discovered and studied. Among them, some are of particular interest to gamblers.

The outcome bias

The outcome bias is a cognitive bias that denotes a logical processing error, that is, a mathematical mistake. For a serious player or bettor, it is very useful to know and understand this distortion of logical thinking that affects everyone but can have dire consequences for a player. This cognitive bias leads to judging the quality of the decision based solely on the outcome, meaning that the decision, as well as the reasoning and thinking that led to it, is deemed good if the outcome turns out to be the expected one. This cognitive bias is often observed in gamblers, who try to predict a completely random outcome based on independent factors.

The outcome bias feeds into another bias, also present in the gambler's error: the illusion of control bias.

The illusion of control bias

The illusion of control bias concerns situations in which the bettor believes they can control or at least influence the situation, based on random outcomes. For example, an experiment conducted by a psychology professor at Harvard shows that people who chose their own lottery ticket number were more confident about their win than those who were assigned a ticket number randomly.

How to avoid the gambler's fallacy?

The gambler's fallacy can thus lead to erroneous decision-making. To remedy this and be able to make an informed decision regarding a future event, it is important to consider the causal relationship that this event has with past events of the same type. Indeed, we naturally create a link between events that have already occurred in the past and those that will occur in the future. We often see them as causes or indications of how the future will unfold.

This practice can be wise if the two events are indeed linked by a causal relationship; for example, storm clouds in the sky may reasonably suggest that it will rain, leading one to decide to take an umbrella. Conversely, if two events are absolutely not linked by a cause-and-effect relationship, one must be able to recognize the causal independence of the events in question. Reflecting on the actual process by which the event occurred can help understand that certain past events play no role in its unfolding.

Example from the Monte Carlo casino

At the Monte Carlo casino, on August 18, 1913, an extremely rare event occurred: at the roulette table, black came up 26 times in a row. This record has never been equaled. As a result, that day many players lost huge amounts of money. Indeed, from the fifteenth occurrence of black, players seated at the table were betting increasingly larger amounts on red, telling themselves that statistically, black could not come up anymore. The error of these players lay in thinking that previous outcomes influenced subsequent ones, that at each round where black came up, red had even more chances of coming up next. The result: black came up 26 times in a row, the casino recorded the biggest winning streak in its history that day, and many players lost millions. This event gave its name to the gambler's fallacy.

In fact, this error is very widespread among players, but also among most of us, and stems from a misunderstanding of the principles of chance and statistics. They forgot that a roulette wheel is fair, even if it is more complex, just like a coin flip when tossing heads or tails, and with a fair system, one must remember that each spin is independent of the others: the wheel and the ball have no memory.

Taking the example of the French roulette (with 37 numbers, 18 red, 18 black, and one green zero):

• In the first spin, the ball has about a 48% chance of landing on red and the same probability of landing on black;
• In the second spin: the probability will still be about 48% for each color;
• In the third spin: the probability remains the same;
• In the 26th spin: the ball still has about a 48% chance of going to red and the same for black.

There is therefore no reason to believe that the next spin of the roulette will be influenced by the previous ones.