# 10 Gambler’s Fallacy Examples

Reviewed by Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

The Gambler’s Fallacy describes an error in reasoning where the outcome of a random event is thought to be more (or less) likely than it really is. This misjudgment is based on the outcomes of previous, irrelevant events.

It’s called the gambler’s fallacy because often gamblers will make this mistake:

“The dice has landed on 6 five times in a row, so it’s likely to land on 6 again next time.”

The problem with this line of thinking, and what makes it fallacious, is that it looks to make connections between the outcomes of events where there are none to be found since the events themselves are random occurrences and up to chance.

The Gambler’s Fallacy is also referred to as the Monte Carlo Fallacy, or the Fallacy of the Maturity of Chances. It’s a sub-type of both the false cause fallacy and base rate fallacy.

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Meet the Peer Reviewer: The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. This article was written by Dr Dave Cornell and peer reviewed by Dr Chris Drew. Learn more about Chris Drew here

## Gambler’s Fallacy Examples

• If a roulette ball lands on black twenty-six times, people assume it will land on black the twenty-seventh time.
• If a coin landed on heads seven times, people assume it will land on heads the eighth time.
• If a woman had five girls, she assumes the next child will have to be a boy.
• If stocks have been going up for a week, then they will probably go up next week as well.
• If you had a bad year last year then this year will have to be a great year! What are the chances of having two bad years in a row?
• If you’ve been accepted into seven out of seven colleges so far, then you decide you’re probably going to be accepted into the eight as well.
• You saw someone win money on the slot machine next to you, so you snag it when they leave because you assume it’ll make you lucky as well.

## The Examples Explained

### 1. The Monte Carlo Incident

In 1913, at a casino in Monte Carlo, a game of roulette attracted a crowd because the ball landed on black twenty-six times in a row. People started placing bets on red, and their bets became bigger and bigger since they thought that the ball was bound to land on a red, as they’d all previously landed on black.

Despite everyone’s intuition that the next spin of the wheel would land on red, it didn’t, and people lost a lot of money on the gamble.

The gamblers likely didn’t realize it at the time, but they were committing an error in their logical reasoning known as the Gambler’s Fallacy. Roulette is a game of probability, and so the outcome of the last spin of the wheel has no bearing on the outcome of its subsequent spins. In a nutshell, this illustrates the flaw of reasoning with the Gambler’s fallacy.

### 2. Coin Toss

Coin tosses are a case in point of the Gambler’s Fallacy. Coin tosses are up to probability and each flip of the coin has a 50/50 chance of landing on either side. Each coin toss is an independent event.

The outcome of any one flip of the coin has no bearing or relevance on the next flip’s outcome, i.e., whether the coin will land on heads or tails.

Despite what we know of the coin toss, it’s still tempting to pick heads if the past 10 flips landed on tails. However, to choose heads for that reason is precisely what the Gambler’s Fallacy describes since each toss of the coin is an isolated incident, with no impact on the other.

### 3. Guessing the Sex of Your Baby

It’s not uncommon that a family has just boys or girls. If a couple is trying for a girl because they have 3 boys already, they might think that because they have 3 boys already, the odds of having a girl are now somehow higher.

Families might try for the opposite sex for family balancing purposes; and nowadays, there are options like pre-genetic implantation to select the baby’s sex.

We know that a baby’s sex is determined at the point of conception by its chromosomal makeup. The sex of a baby is not determined by the sex of the older siblings or other children in the same family.

To try to have another child because you think it could be a girl or boy is a case of the Gambler’s Fallacy error in logic.

### 4. Investing in Stocks

People that invest money in the stock market see that the value of their stocks fluctuates regularly. Stocks can skyrocket, remain relatively stable or drop in value completely.

The way stocks fluctuate in value influences people’s decisions on which stocks to purchase, avoid, and so forth.

If a stock increases in value, some people could feel inclined to sell because they don’t think it’s likely to continue to go up anymore, given it just went up significantly. Conversely, if the value of a stock drops significantly, some people hold because they think it is not likely to go down further.

Both cases and trains of thought are evidence of the Gambler’s Fallacy. Just because a stock decreases in its value, this does not mean it will not further decrease, and the same goes for the opposite.

You need to get more context to make a better decision.

Peer Reviewer’s Note: Of course, if you have knowledge of the economy or stock exchange, then you have more context to make future predictions, and therefore this instance wouldn’t be a Gambler’s fallacy. But for a layperson with no knowledge of the economy and stock exchange, they certainly may use the gambler’s fallacy to make investment decisions.

### 5. The Spelling Bee

Some kids sign up to compete in the Spelling Bee numerous times, despite not winning the tournament the previous year. Parents and kids say things like, “this is going to be my year!”

Since the last year didn’t go well, this year is bound to end with a better result, what are the odds that they won’t?

As it turns out, the Gambler’s Fallacy says otherwise, and to believe that this year is going to end up better simply because the previous year ended poorly is exactly what the Gambler’s Fallacy identifies as a flawed form of thinking.

The Gambler’s Fallacy tells us that these are separate events: the outcome of other events has no bearing or tie to the outcome of future events, unless of course, the students have changed their behavior in order to increase their chances of winning next year.

### 6. Sports Team Winning-Streak

Sports fans or people rooting for ‘their’ team to win can easily fall prey to the Gambler’s Fallacy.

Similar to the Spelling Bee example, people start forming beliefs on how a team will play or perform based on their previous performance and score.

They might think that because they’ve lost the last few games, this in and of itself means it is more likely that the team will win this one. If the team won the last few games, then some people might think they’re bound to lose this one as a result.

In reality, each game is an isolated event. The mere fact that you lost the last game doesn’t mean you’re sure to win the current game.

What does impact future events is the strength of the team, the quality of the coach, and related contextual factors.

But assuming the team will win or lose only based upon past events and not upon relevant contextual factors is entirely irrelevant. This, therefore, illustrates the gambler’s fallacy’s flawed reasoning when an ill-informed sports fan gambles on their team.

Peer Reviewer’s Note: Neil, a reader, commented in the comments section: “the performance of a sports team is not a random factor. A strong team will have a higher likelihood of winning than a weaker team in the same league“. Indeed, this is true. if you have more data that demonstrate an increased likelihood of winning this time over next time, you’re not using the gambler’s fallacy. However, if you make decisions only based upon past performance and no other factors, then you are using the gambler’s fallacy. Thanks for the comment, Neil.

### 7. The Fear of Flying

While it might strike some people as irrational, the fear of flying is common, generally speaking. It’s also understandable why some people are afraid of flying—it could be that they don’t fly often, or maybe they watched too many movies featuring plane accidents.

If a person flies frequently and still has never been in a plane accident, they might think that an accident is bound to occur since it hasn’t yet. This is more specific than the general fear of flying, and it is also a case of the Gambler’s Fallacy.

Any previous flight that the person had been on holds no relationship with the safety of his or her future flights.

### 8. Struck by Lightning

George is perhaps the most unfortunate person in the world – he’s been struck by lightning three times.

Interestingly, George has found that his friends don’t want to hang out with him during storms. They will cancel their meet-ups with him and his housemate even leaves their house and stays at a friend’s place on nights when there are storms.

They’re scared the lightning will strike George again, and they don’t want to be harmed as well.

This is, of course, a gambler’s fallacy, because there is no causal relationship between the three times George was struck by lightning in the past and future storm events.

### 9. Yahtzee

Yahtzee is a game of probability where players take turns rolling the dice to try and get a certain set of outcomes. The goal is to have the highest number of points by the end of the game. When a player gets a ‘Yahtzee,’ this means that all 5 dice are the same, and you get the most points.

Yahtzee is a very fun game, but if you’ve played it you’ll know that players start to get superstitious and have false hope. For example, if everyone else has already gotten their Yahtzee except for one player, that player might think that on their next roll they must get the Yahtzee.

That’s not how the game works, and the dice don’t recall the previous rolls’ results. This is another instance of the Gambler’s Fallacy, where wishful thinking replaces logical thinking.

### 10. Passing the Bar Exam

In most places, to become a licensed attorney it’s required to pass the bar examination. The bar exam is notoriously difficult, and some end up taking it more than once in order to get their license and be able to practice as an attorney.

There are multiple variations of the bar exam that are assigned randomly to students taking the test. Some students that re-take the exam might be under the impression that they will likely get variation B of the exam next time because last time they have variation A.

In reality, the odds of whether they get variation A or B the second time around is equal, assuming that variations A and B are distributed at a 50-50 ratio. This, again, shows the Gambler’s Fallacy and how it can lead to misleading and faulty judgments.

## Conclusion

It’s part of human nature to try and make sense of random occurrences by looking for patterns to explain them. The problem is that random events are just that—random. They do not conform to reason or logical processes and instead are up to probability and chance.

The problem that Gambler’s Fallacy poses is that it can cause people to make misguided and bad decisions. This is why it is important to recognize the fallacy, if it presents in your own thinking, and avoid making personal decisions on erroneous and flawed logic.

Dalia Yashinsky is a freelance academic writer. She graduated with her Bachelor's (with Honors) from Queen's University in Kingston Ontario in 2015. She then got her Master's Degree in philosophy, also from Queen's University, in 2017.

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.