Fallacies are reasoning errors within arguments that explain or prove events with wrong or misleading premises. There is a vast variety of fallacies that are prominent in debates or everyday dialogue. One of them is the Gambler’s fallacy. The name of this fallacy originates from the sector it most commonly occurs: Gambling. Everything you need to know about the Gambler’s fallacy will be explained in this article.
Definition: Gambler’s fallacy
The classic Gambler’s fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, describes an erroneous belief and perception of the event of streaks of randomness. It’s the misconception that a random permutation of events will always even out over time, regardless of the nonexisting correlation between the current and the history of events.
In other words, this fallacy is the mistaken belief that random outcomes are more or less likely to occur based on the outcome of previous events. This assumption is false, since all subsequent events and their respective future outcomes in this scenario are independent of each other and not influenced by previous events.
The Gambler’s fallacy is a common event in games of chance, like rolling a die or flipping a fair coin. The name Monte Carlo fallacy originates from a game of roulette in the Monte Carlo Casino in 1913, where with a degree of randomness, the ball landed on black 26 times consecutively. Based on this nature of randomness, the favourable outcome for many gamblers during the game was that there was a higher probability that it would land on red after such a long streak of black. The ideal outcome of their belief turned out to be false, which resulted in a loss of large sums of money.
If the ideal outcome for you is that there is a higher or lower degree of randomness, then you just experienced the Gambler’s fallacy.
The correct answer is that the chance of rolling a 6 again has the same likelihood as the previous three rolls. The probability of rolling a 6 is 1 in 6 on every roll, and the previous rolls do not influence the next one.
Rolling a die is a random event, meaning that an event of streaks does not impact the future outcome of the subsequent events and determine what number it will show. The nature of randomness stays the same, meaning the current roll will also not impact the chance process of rolling a certain number in the future.
The erroneous belief that a current outcome was the result of a previous event or will influence the next one is false as long as it regards independent events.
Note: To understand the Gambler’s fallacy, you need to know the meaning of independent and random events in relation to this fallacy:

Independent event
An event that is not influenced by any former or future events. All outcomes of an independent event are unrelated. 
Random event
A random outcome lacks any predictable pattern or order, meaning every outcome has an equal probability of happening.
Psychology behind the Gambler’s Fallacy
The false assumption which originates in our cognitive thinking can be subdivided into three main aspects, which make us believe in the Gambler’s Fallacy.
Search for Order and Meaning
The psychological reason behind the Gambler’s fallacy lies in the human tendency to perceive patterns and, as a result, expect randomness to align with a pattern over time. Our minds naturally seek order and meaning in random events, leading us to assume that if a certain outcome has not occurred for a while, it becomes more likely to happen in the near future.
Law of Small Numbers
The Gambler’s fallacy can be attributed to a cognitive bias called the “law of small numbers.” This bias causes individuals to assume that small samples will reflect the same distribution as a larger population. In gambling, this manifests as a mistaken belief that a short streak of losses or wins will somehow correct itself and align with the expected probabilities.
Illusory Correlation
The Gambler’s fallacy can be influenced by the concept of “illusory correlation.” This refers to the tendency to perceive a relationship between random events that are actually unrelated. When experiencing a history of events of loss, gamblers may mistakenly associate certain external factors or personal behaviours with their losses, leading them to believe that changing those factors will increase their chances of winning.
Examples
The following examples will outline common events with the Gambler’s fallacy in motion, providing further explanations in the context of reallife situations.
Psychology of coin toss
Psychology of Roulette
Psychology of Lottery Gambling
Wrong use of the Gambler’s fallacy
You always need to keep in mind that the Gambler’s fallacy can only be applied to random, independent events. If the result isn’t random or independent, the Gambler’s fallacy can’t occur. There are basically two possibilities that deny the Gambler’s fallacy:

The event isn’t independent.
This case occurs when the result of the current event is influenced by a previous or future event. 
The event isn’t random.
This case occurs when the result is predictable and the probability of different outcomes varies.
Types of Gambler’s fallacy
The classic Gambler’s fallacy is the most widely recognized and strongest Gambler’s fallacy form, which can be subcategorized into various nuances and related misconceptions in terms of probability. The following will elaborate on the various types of Gambler’s fallacy.
Inverse Gambler’s fallacy
The inverse Gambler’s fallacy refers to the law of small numbers in a psychological aspect. It describes the irrational belief that a rare event must have had many prior attempts for it to happen without evident or supportive observation. In other words, if someone attributes a larger sample size to the occurrence of a rare event, the inverse gambler’s fallacy occurs.
Retrospective Gambler’s fallacy
This fallacy refers to a misunderstanding of the nature of randomness, where someone reflects on past permutations of events and, based on this, concludes that they have produced a favorable outcome in the present. In other words, the mistaken belief that a current outcome is a product of previous events.
Reverse Gambler’s fallacy
In contrast to the inverse Gambler’s fallacy, the reverse Gambler’s fallacy refers to the law of large numbers. It is the fallacious belief that when a sequence of trials carries repetitive outcomes of past events, it is more probable for a sequence of similar nature to happen in the future.
How to avoid the Gambler’s fallacy
There is no real way of avoiding the Gambler’s fallacy, as there are no instructions about randomness. The most effective strategy is to be aware of the actual process. If you have a closer look at the gambling conditions, you can change your role of experience and learn to identify whether an event is random or predictable.
The key is to analyze every situation on its own to avoid the Gambler’s fallacy. However, overcoming the psychological aspect behind this fallacy can be a difficult task, as you have to actively manipulate and train your instincts and mind.
FAQs
The Gambler’s Fallacy is a misunderstanding of dependence and the randomness of a streak of events in gambling. After a row of the same result, people think it’s more likely for another result to appear next, but this is a wrong belief.
It’s a psychological reason because the human mind seeks for patterns and expects randomness to even out. Together with the belief that a small number will be representative for a whole, it is the psychological foundation for the fallacy.
An example of the appearance of the Gambler’s Fallacy is roulette. Every round is independent and random and if the result is black for 5 rounds in a row, it’s still as likely as before that the sixth result is black.
The key to avoiding the Gambler’s fallacy is to be fully aware of it. However, there are tools such as seeking independent research, keeping a diary, or asking for external feedback.
The Hothands fallacy or hothand belief refers to a type of experience of success. It is a type of reverse gambler’s fallacy and involves the mistaken belief that a successful streak is likely to continue. For example, if a hockey player has made two consecutive goals, he has a higher probability of making a third goal.