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# Gambler’s Fallacy Explained

The gambler’s fallacy is one of the most common beliefs that gamblers, both new and seasoned, can fall trap to. It’s the belief that, based on the results seen, a randomized event is more or less likely to occur next. Many will riposte the gambler’s fallacy with an idea of the law of averages or something similar.

Yet, the randomized element of gambling games and events out of one’s control, like sports games, means that a seemingly logical way of thinking won’t always hold up. The randomized and unknown outcomes provide much of the entertainment value in gambling, but many players ignore this when betting.

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For players, the simplest way to avoid falling into the gambler’s fallacy is to understand that chances don’t mature based on results when determined by elements of randomization. Whenever you don’t have full control of an event, randomness will come into play.

## Gambler’s Fallacy Defined

The definition of the gambler's fallacy refers to the flawed belief that the occurrence of a specific outcome becomes more or less likely based on previous results. In other words, it’s a false assumption that past events influence the probability of future events or independent events. It can take many different forms and even seem like a more minor fallacy in certain circumstances, but the gambler’s fallacy will always indicate erroneous estimations.

### Definition and Explanation

Someone who is thinking along the lines of the gambler’s fallacy will believe that a commonly occurring outcome or an outcome that has seemingly occurred less often per probability will happen next. The easiest example to showcase this is in the game of roulette. Here, someone could think that because red has hit four times in a row – despite there being a near 50-50 chance of red hitting on each spin – black has an increased chance of landing next.

### Historical Cases

Gambler’s fallacy is also known as the “Monte Carlo fallacy”. This is because the faulty line of thinking was observed at Casino Monte-Carlo, one of the top European casinos, in 1913. The example was seen unraveling at the roulette table when gamblers lost millions betting against black, while it went on a 26-round winning streak, and then on red, assuming that a random imbalance was sure to be corrected.

## Cognitive Biases

Cognitive biases represent a systematic pattern of thinking that defies rational judgment. The gambler’s fallacy is a player’s erroneous belief that they can predict the outcome of an event based on previous events where randomization is in play. So it’s very much a cognitive bias in itself. However, other biases also play into this.

### Human Perception of Randomness

The human perception of randomness is inherently flawed by striving to make sense of situations and gain control in some way. Given a set of results, even if randomly generated, humans naturally look for patterns when asked to determine the next result. As such, we attempt to apply probability and mathematics to random events and outcomes, which simply doesn’t align with the nature of what's in play. You cannot apply probability to randomness.

### Influence on Decision-Making

Decision-making ultimately hinges on selecting the option that appears to be the most favourable.

When provided with statistics drawn from previous events, especially those that pertain to that exact game or sports team, people naturally lean on them to make decisions. Still, in wholly randomized games, it’s better to let a dice roll make the decision rather than weigh in previous outcomes.

## Statistical Analysis

A human’s need to make sense of randomness or attempt to control it in some way will usually lead them down the path of statistical analysis. Given a series of locked-in outcomes, it’s natural for you to start running the numbers, looking for discrepancies under the illusion that randomness will even out to given probabilities over time.

### Probability Distribution

You perform probability distribution when you work out all of the potential likelihoods that future event can be produced by a randomized outcome procedure. You’ll look at the likelihood of a single outcome occurring at random, but oftentimes, factor in results that have already occurred into the calculation, which ruins the analysis and is the gambler’s fallacy in play.

### Law of Large Numbers

A theory of probability, the law of large numbers, dictates that a true value will be found if a large enough sample size of independent results is taken. Put into a set of gambling results, the law of large numbers would say that over 37 million spins of the roulette wheel, for example, each number will win 1 million times. However, as every outcome is wholly randomized, it’s unlikely that even a very large sample size will showcase true values.

## Real-Life Examples of Gambler’s Fallacy

It can be difficult to spot the gambler’s fallacy in action. This is primarily because falling into its trap requires what, in any other circumstance, would be considered due consideration.

### Casino Games

In many online roulette games, you’ll see so-called “hot and cold” numbers. These show the series of recent wins recorded at the table. Some will look to this as an indicator of what’s to come if a certain betting zone has been more or less active than the odds suggest.

This is the gambler’s fallacy in practice, because every outcome is entirely random and not at all influenced by what came before. In European roulette, number 23 has a one in 37 chance of winning on every spin, even if the last four spins landed on number 23.

### Sports Betting

In sports betting, the gambler’s fallacy is usually exemplified by consistent bettors, such as those at a horse racing track. After consecutive losses, some will think it more likely that their next bet on a horse has an even better chance of winning.

## Common Misconceptions Based on Gambler’s Fallacy

The most common misconception that derives from the gambler’s fallacy is that a losing streak will end. This could either be when playing at the blackjack table, betting on a team that hasn’t won in several consecutive games or if a betting zone is marked as cold at a roulette table.

In equal measure, the mistaken belief that a winning streak will continue is common. Backing a dominant sports team on a winning streak or a craps shooter who has won several throws in a row, can be examples of the gambler’s fallacy. Another gambler’s fallacy misconception is that, even in a series of wholly randomized individual events, randomness will level out to the estimations of probability.

Even with the most basic bet, a coin flip, just because a coin has landed on tails seven times in a row doesn’t mean that heads is more likely to land on the eighth. Every time, the odds are 50-50. You also see this a lot in slot gaming, where players think that a big win must be coming because their many spins haven’t yet yielded one. It’s the illusion that the slot machine is “loose” and ready to drop.

### Misinterpretation of Patterns

Similarly to the coin flip example above, seeing patterns in a line of wholly randomized outcomes can lead you down the path of the gambler’s fallacy. These patterns are often used for your statistical analysis of potential outcomes. As a result, you put too much or too little weight on set outcomes based on patterns seen before, which will always defy the true likelihood of a randomized game.

### The Illusion of Control

Many players turn to game result histories and sports statistics to inform their bets. While this can help in sports betting, showing the potential strengths and weaknesses of certain teams, these stats do not offer any true reflection of the outcome. What comes next can defy the stats and the odds that they inform. Having this information can give you the illusion of control, a kind of insider information, and result in a belief that the selected outcome will win.

## Gambler’s Fallacy FAQs

### What is an example of the gambler’s fallacy?

An example of the gambler’s fallacy is thinking that heads is more likely to land on a 50-50 coin flip because tails has landed on each of the last seven coin flips before. The outcome on every flip is 50-50 regardless of what’s come before.

### What is a famous gambler’s fallacy?

The next most famous example of gambler’s fallacy is the example seen in Casino Monte Carlo on August 18, 1913. On this occasion, the roulette wheel landed on a black number 26 times in a row. Yielding to the gambler’s fallacy, punters lost millions betting on red assuming that randomness would level out to probability soon. Many also followed by backing a long winning streak for red afterward.

### Is a gambler’s fallacy a cognitive bias?

The gambler’s fallacy is a form of cognitive bias and one that’s proven to be very difficult for people to shake off. Even educating yourself about the pitfalls of applying statistical analysis to a randomized fair game, for example, may not work. This is predominantly because of how our thinking works and how we consider probability even in the face of pure randomness.