The Gambler’s Fallacy is the misleading belief that the probability of a specific occurrence in a random sequence is dependent on preceding events—that its probability will increase with each successive occasion on which it fails to occur.

• Roulette Strategy Gambler's Fallacy
• Roulette Gambler Fallacy Definition
• Roulette Gambler Fallacy Example

Suppose that you roll a fair die 14 times and don’t get a six even once. According to the Gambler’s Fallacy, a six is “long overdue.” Thus, it must be a good wager for the 15th roll of the dice. This conjecture is irrational; the probability of a six is the same as for every other roll of the dice: that is, 1/6.

Chance Events Don’t Have Memories

In practical terms, the Gambler’s Fallacy is the hunch that if you play long enough, you will eventually win. For example, if you toss a fair coin and flip heads five times in a row, the Gambler’s Fallacy suggests that the next toss may well flip a tail because it is “due.” In actuality, the results of previous coin flips have no bearing on future coin flips. Therefore, it is poor reasoning to assume that the probability of flipping tails on the next coin-toss is better than one-half.

The gambler’s fallacy is sometimes referred to as “The Monte Carlo Fallacy”. This nickname was borne out of a particularly crazy night at a Monte Carlo Casino in 1913. On this particular late summer night, the roulette ball fell into the black 26 times in a row. The gambler's fallacy is a belief in negative autocorrelation of a non-autocorrelated random sequence of outcomes like coin flips. For example, imagine Jim repeatedly flipping a (fair) coin and guessing the outcome before it lands. If he believes in the gambler's fallacy, then. In 1913, gamblers at the Monte Carlo Casino lost millions of francs at the roulette table. The ball would land on black, and the gamblers would bet on red. The ball would land on black again, and the gamblers would continue to bet on red. The ball landed on black 26 times in a row. The probability of that happening was 1 in 66.6 million. Gamblers fallacy originated from the roulette of Monte Carlo. The most well-known example this phenomenon happened from the game of roulette in the Monte Carlo Casino on August 18, 1913,5 as soon as the ball dropped in black 26 times in a row. What About the Gambler’s Fallacy and the Game of Roulette? Roulette is perfect for understanding how to disprove the Gambler’s Fallacy. In fact, most roulette betting systems are products of the Gambler’s Fallacy. When you bet on a single number in roulette, you can easily calculate the probability of winning that bet.

A classic example of the Gambler’s Fallacy is when parents who’ve had children of the same sex anticipate that their next child ought to be of the opposite sex. The French mathematician Pierre-Simon Laplace (1749–1827) was the first to document the Gambler’s Fallacy. In Philosophical Essay on Probabilities (1796,) Laplace identified an instance of expectant fathers trying to predict the probability of having sons. These men assumed that the ratio of boys to girls born must be fifty-fifty. If adjacent villages had high male birth rates in the recent past, they could predict more birth of girls in their own village.

There Isn’t a Lady Luck or an “Invisible Hand” in Charge of Your Game

The Gambler’s Fallacy is what makes gambling so addictive. Gamblers normally think that gambling is an intrinsically fair-minded system in which any losses they’ll incur will eventually be corrected by a winning streak.

In buying lottery tickets, as in gambling, perseverance will not pay. However, human nature is such that gamblers have an irrational hunch that if they keep playing, they will eventually win, even if the odds of winning a lottery are remote. However, the odds of winning the jackpot remain unchanged … every time people buy lottery tickets. Playing week after week doesn’t change their chances. What’s more, the odds remain the same even for people who have previously won the lottery.

Gambler’s Fallacy Coaxed People to Lose Millions in Monte Carlo in 1913

The Gambler’s Fallacy is also called the Monte Carlo Fallacy because of an extraordinary event that happened in the renowned Monte Carlo Casino in the Principality of Monaco.

On 18-August-1913, black fell 26 times in a row at a roulette table. Seeing that that the roulette ball had fallen on black for quite some time, gamblers kept pushing more money onto the table assuming that, after the sequence of blacks, a red was “due” at each subsequent spin of the roulette wheel. The sequence of blacks that occurred that night is an unusual statistical occurrence, but it is still among the possibilities, as is any other sequence of red or black. As you may guess, gamblers at that roulette table lost millions of francs that night.

Gambler’s Fallacy is The False Assumption That Probability is Affected by Past Events

The Gambler’s Fallacy is frequently in force in casual judgments, casinos, sporting events, and, alas, in everyday business and personal decision-making. This common fallacy is manifest by the belief that a random event is more likely to occur because it has not happened for a time (or a random event is less likely to occur because it recently happened.)

• While growing up in India, I often heard farmers discuss rainwater observing that, if the season’s rainfall was below average, they worry about protecting their crops during imminent protracted rains because the rainfall needs to “catch-up to a seasonal average.”
• In soccer / football, kickers and goalkeepers are frequently prone to the Gambler’s Fallacy during penalty shootouts. For instance, after a series of three kicks in the same direction, goalkeepers are more likely to dive in the opposite direction at the fourth kick.
• In the episode “Stress Relief” of the fifth season of the American TV series The Office, when the character Jim Halpert learns that his fiancee Pam Beesley’s parents are divorcing, he quotes the common statistic that 50% of marriages wind up in divorce. Halpert then comments that, because his parents are not divorced, it is only reasonable that Pam’s parents are getting divorced.

The Gambler’s Fallacy is a Powerful and Seductive Illusion of Control Over Events That are Not Controllable

Don’t be misled by the Gambler’s Fallacy. Be aware of the certainty of statistical independence. The occurrence of one random event has no statistical bearing upon the occurrence of the other random event. In other words, the probability of the occurrence of a random event is never influenced by a previous, or series of previous, arbitrary events.

Idea for Impact: Be skeptical of most judgments about probabilities. Never rely exclusively on your intuitive sense in evaluating probable events. In general, relying exclusively on your gut feeling or your hunches in assessing probabilities is usually not a reason to trust the assessment, but to distrust it.

Wondering what to read next?

In 1913, gamblers at the Monte Carlo Casino lost millions of francs at the roulette table. The ball would land on black, and the gamblers would bet on red. The ball would land on black again, and the gamblers would continue to bet on red.

The ball landed on black 26 times in a row. The probability of that happening was 1 in 66.6 million. To this day, it’s a shocking moment in gambling history.

The 27th time, can you guess what the probability of the ball landing on black would be?

1 in 2, or 50/50.

This doesn’t seem right, but it is. And the people who would have bet on black, after the ball landing on black 26 times in a row, would still only win double what they bet.

This video is all about the Gambler’s Fallacy, and how we convince ourselves that things will “even out” on the gambling table and in other change occurrences.

What Is The Gambler’s Fallacy?

Put yourself in the gamblers at Monte Carlo’s shoes. The ball lands on black. The ball lands on black again. The ball lands on black for a third, fourth, fifth time.

At some point, you’re going to feel sure that the ball will land on red next. There’s a 50/50 chance that the ball will land on red at any given time or on black at any given time. So after a streak of the ball landing on black, you may start to think that the ball has to land on red next.

This is the gambler’s fallacy. It’s a bias in which we let past events influence our decisions and predictions about what will happen next. But this bias is based on fallacy, or a mistaken belief.

The reality of the situation is that the ball has a 50/50 chance of landing on black every single time you play roulette. Each action is independent of the actions before it. Sure, the chances of the ball landing on black 26 times in a row are way smaller than the chances of the ball landing on black twice or three times in a row, but that doesn’t mean that the ball will land on red based on those chances.

The gambler’s fallacy often leads people astray while they’re in the casino. Think of all of the people who continued to bet on red at Monte Carlo. I’m sure some of those gamblers put a lot of money on red, thinking that somehow their chances at winning big were larger just because the ball kept landing on black.

But this doesn’t just happen at the roulette table. Many people will stay at the slots for hours, believing that although they lost time after time again, their chances of winning will somehow increase.

Examples

But the gambler’s fallacy isn’t just a phenomenon that occurs within the walls of a casino. In the “real world,” this logical fallacy can have some pretty serious effects on the ways people make decisions and conduct business.

Take loans. Approving or rejecting loans can sometimes feel like a gamble to loan officers. Studies show that loan officers are more likely to reject a loan that is sitting in front of them if they had approved the last loan that came across their desk. Researchers think that 5% of loans are affected by this fallacy.

This can have a huge impact on a person’s ability to buy a house or start a business, but further research shows that this fallacy can have an even more significant impact. Asylum judges are not immune to the gambler’s fallacy. Data shows that they are more likely to approve a person’s application if they had denied the previous application, and vice versa.

Explanations

The gambler’s fallacy goes beyond how we make decisions - some argue that it affects how we make sense of the world. Remember, the gambler’s fallacy is a bias that is influenced by past events. We may link our decision to stay at the slots because of past events. But we may also explain what is happening now based on what happened in the past.

We use the gambler’s fallacy to establish patterns. We may get sick and blame it on the bread that we ate before. If we get sick a second time after eating bread, we are very likely to believe that we have an intolerance or allergy involving gluten. But connecting our stomachache to what we ate before isn’t always based in logic or correct probability. Just like connecting the ball landing on red to the ball landing on black before (or vice versa) isn’t always based in logic. Independent events are just that - independent events.

Be Aware of Gambler’s Fallacy

I’m not saying that people with stomach aches shouldn’t write off certain foods or that you should go to the casino and only bet on one color or number. But I am telling you about the gambler’s fallacy so you can be more aware of if you’re using it in your life.

Logical fallacies affect the way we make decisions, form arguments, and predict what is going to happen in the future. Since these fallacies are based on falsehoods, the results may not be so great. The more you are aware of these logical fallacies, the easier it will be for you to step back, make a proper assessment based on facts, and make better sense of what is going on around you.

Quiz

Let’s test your knowledge on the Gambler’s Fallacy.

Question 1:

A coin has been flipped 12 times. 10 of those flips have resulted in “heads.” What is the likelihood that it’s going to be tails the next time you flip it?

Answer:

50/50

Question 2:

Roulette Strategy Gambler's Fallacy

True or False: The Gambler’s Fallacy is just limited to gamblers.

Answer:

False. Everyone is affected at some point by the Gambler’s Fallacy. It’s a common bias that all humans experience.

Last question:

Roulette Gambler Fallacy Definition

The Gambler’s Fallacy is a _____ fallacy that we should be aware of when making judgements and decisions.

Roulette Gambler Fallacy Example

Answer:

Logical