10 Gambler’s Fallacy Examples

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.

Contents

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.

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.

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 previous events do not impact the current circumstances. This, therefore, illustrates the Gambler’s Fallacy’s flawed reasoning.

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. College Acceptances

Amy applied to 10 colleges, and she has already received acceptance letters from 7/10 of the colleges. Amy is still waiting to be accepted to the college she wants to attend, but she’s sure she’ll get in given that she’s been admitted to 70% so far.

We might think that Amy has good reason to believe that she will get in since she got into the other colleges, and therefore has a higher chance of getting into the remaining ones.

The point to be on the lookout for is why does Amy think she will get admitted to the other colleges? The fact that she got into the other 7, in and of itself, does not mean that she will get admitted to the remaining 3.

There is no causal relationship between getting into those other colleges and getting accepted to the one she actually wants to attend.

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 have a higher chance of succeeding this time, since what are the odds that they would fail twice?

In reality, the odds have to do with their level of preparation for the actual contents of the exam itself, not their performance on their last attempt. 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.