Critical Thinking and Learning Site

Gambler’s Fallacy


Gambler’s Fallacy

You see the lottery numbers. Some of them haven’t shown up for some time, so you go and play those numbers, believing that there is a greater chance of winning. Well, there is not, you are just victim of the Gambler’s Fallacy.

You are at the supermarket, you are waiting on the line, and you see the line near you going faster. You consider changing lines, but after that, you think that if I go to that line, it will happen what happens all the times, that line will go slower and the one I am now will go faster. Well there is not any kind of rule for that, it is pure randomness, (except if there is a cashier who is doing a better job, or a faster barcode machine exists)

You are playing the dice, and someone has two times in a raw sixes, you think that it can’t happen a third time. The person is rolling the dice, and there comes a third pair of sixes. You think that something is going on, the guy can’t continue like that. Well, it might happen again a fourth time.

What we think

We believe in a way, that if something quite lucky and with low or high probabilities of happening happens, the next events will be different. We think that the universe will collide so that things will come to a probability balance. If we toss a coin and it happens too many times in a row heads, we tend to believe that one of the next tosses will be tails. We believe that the probability of that happening is actually higher. If we hear on the news that two planes crashed, then we think that the chances of a similar event for a third time are lower.

What is the reality

The reality is that in real random events, in events that there are no external factors affecting their probability of happening, after series of events (e.g., after some coin tosses), the probability of happening the same event is equal; it doesn’t change. This means that if you have 10 heads in a raw, the likelihood of an 11th head coming is the same as the probability of tails coming.

How it works

Gambler’s fallacy is the belief we have, that previous events affect future ones. We believe that if something that has a fixed probability of happening happens for a period with a low or high probability, from some point on there will be a correction and there will be reverse events.

There are two ways Gambler’s Fallacy is functioning.

The first contains most of the examples I have mentioned so far, in these events the probabilities are independent of one another. For example, when you toss the coin two times, the second time is not affected at all by the first toss. So on every occasion, the probability of something happen is 50%.

The second occasion is when events are dependent. Imagine a basketball club that has a 70% average of winning games, and let’s say there are another 10 games for the end of the season. If this team loses 3 games in a raw (meaning the 30% of the last ten), someone might assume that it will win the remain 7, or at least most of them to be on it;s average. The thing here is that 3 losses in a row, might be a result of bad team’s shape, or the injury of some of the major players.

Examples and experiments

There is a very particular story of Gambler’s fallacy. It was the 18th of August, at a casino in Monte Carlo. The ball on a specific roulette started falling on black in a series of throws. From about the 15th through, people started gathering on the table, and beating huge amounts on the red. This series continued, the ball made a 26th series of black, and people kept betting on red, on the thought that this would stop. The result was that the Casino made an enormous amount of money until the 27th game.  

To illustrate further Gambler’s Fallacy, and how people perceive randomness, will have a look at 2005 and the Apple presentation of smart shuffle. Shuffle for those who don’t know, is the random play of songs in a playlist. What actually happened is that in random series of songs, it can occur in a playlist two or three songs from the same artist or album to replayed in a raw. This was something that some customers didn’t like; they considered that the shuffle wasn’t actually random. So then Apple made a smart shuffle, so that same artist’s song didn’t play on a raw, which actually wasn’t random.

Gambler’s Fallacy in everyday life

In a very recent research by Kelly Shue, Daniel Chen and Tomas Moskowitz( Decision-making under the gambler’s fallacy: Evidence from asylum judges, loan officers and baseball umpires, January 12, 2016), it is shown how the gambler’s fallacy can affect people in their decision making. In the paper, what is actually appears about the fallacy, is that people are influenced in their decision making when there is a stream of similar events. To be more precise, it was shown in the study, that there is 3,3% higher probability of rejecting an asylum application if there previous one was accepted. This means that, although there might be an application that is Ok with all the criteria for asylum, there is a slightly less probability to be accepted. If there is a sequence of more decisions on the same direction, this could become even higher than 3.3.

The other thing which was tested was how loan officers judge an application and if that judgment is biased based on previous decisions. It was found that there is up to 9% negative autocorrelation. That practically means, that if there is a series of successfully granted loans, although a loan might apply all the criteria to be granted to, about one out of ten will be rejected, due to bias.

A very interning part would be to examine what is the situation in other areas of everyday life, as more general decisions by judges, or how the examiners correct papers, or even how random checks by police or at airports are taking place.

How to avoid it

Well, it is tough to prevent this fallacy. The best think you can do, is to try and consider each event as a separate one. To illustrate that with the toss coin example, do not think of the previous results, believe that this toss is one event with 50-50 chances whatever the choice you make. Do not bother yourself on whether you should change the line at the supermarket. It might be bad luck, which causes you to go slower. Check what are the variables, do people have more products, does everything on the line work fine? You can’t predict a problem with a credit card that might delay you. Do not believe that in every random thing, there is a logical universal rule behind it. It could be just random.

Another way to protect from Gabler’s Fallacy is to pay attention to the laws of probability. You do not have to go in great depth, but if you have a basic understating of how probability works, it will help you to be more reasonable.

How to gain from Gambler’s Fallacy

Well if you are not a gambler there are not a lot of things that you can do to gain from this. The most important part is to try to figure the things that are truly random in your everyday life, and stop trying to take some action or make a calculation that you believe might affect them. This will just put you in a calmer sense of mind, and it might give you a little more clear mind to consider and analyze more important things, not the choice of a line at the supermarket or the selection of lottery numbers.

Other than that, there is a gray area which is on the borderline of ethics depending on the way you use it. If you are doing something good in a raw, and this is by sheer luck, you can use it to persuade people to support you in what you are doing, whether they are customers, friends, investors, etc. Of course, if things turn bad and you don’t deliver, you can lose their faith and gain their anger. You’ve been warned!

Bonus  funny tips

Actually, in head or tails, the Probability is not exactly 50-50. To begin there is a possibility that the coin is not in good shape after long time use. Some alternations, even minor, in the original shape could change the probability shifting to tails or heads.

Other than that, actually there is a 51% chance for the coins to come up the same side we had them before flipping. That means if you start tossing a coin with tails there is 51% probability to end up tails. In the following research Dynamical Bias in the Coin Toss, it is showed that, if the coins instead of tossed is spun, the probability of ending the heavier side of the coins down (not both sides, have the same weight), can increase much more than 50%.

Also, there is 1 in 6000 chances for a nickel to land on edge as show on the Probability of a tossed coin landing on edge” research (The research studies the Us nickel). I would like to try that out, but of course, that doesn’t mean that in 6000 throws I would get what I want.

Finally, if we leave the coins to fall to the floor, a randomness depending on the floor is added.


Most of the times the Gambler’s Fallacy can lead to the Hot Hand Fallacy.




Interesting article? Subscribe for more!

About the author

By Plato
Critical Thinking and Learning Site

Latest Stories