What is the Gambler’s Fallacy? Definition & Examples

The human brain is an amazingly complex instrument whose primary focus is arguably turning seemingly random events into order and, occasionally, beauty. Sorting through these constant stimuli to identify threats, find food, and generally make sense of the world is a daunting task.

In this mad rush to sort outside events into something resembling sense, the brain can sometimes make mistakes, and one of the more common is a misreading of randomness. From an evolutionary perspective, it stands to reason that the brain needs to make life-and-death decisions based on occasionally minimal data sets from past events.

So sometimes, we may believe that some small set of data points may indicate a broader truth or certainty of a future event when, in fact, a larger data set would show true randomness. When our brains trick us into believing that a truly random event is more or perhaps less likely to occur because of something that has happened in the past, we call that the gambler’s fallacy.

Probably the most straightforward example of the gambler fallacy to illustrate is that of the coin flip. If we flip a coin seven times and they all come up heads, should we be inclined to believe that the next flip is more likely to be heads, or conversely, should we believe that the coin is much more likely now to land tails? In either case, past events predicting future outcomes is a mistaken belief. The odds of the coin toss remain 50/50.

Occasionally, you may hear the gambler’s fallacy referred to as the Monte Carlo Fallacy. This is due to an infamous run of black numbers on a roulette wheel in Monte Carlo in August 1913. As the black numbers spun back to back climbed into the teens, bets that the next number would be red poured onto the table. Many of these gamblers apparently used the Martingale strategy, which calls for doubling your wager after every loss to have a winner eventually.

Once the string of black numbers reached into the 20s, the wagers grew at a frantic pace until finally, after 26 spins, red finally came, but much too late for many broke, bereft bettors. Roulette spins, like coin flips, is a trial of independent events. This erroneous belief that a red number was overdue would eventually become the most famous example of the gambler’s fallacy.

One of my favorite examples of the gambler’s fallacy was given by the man who many consider to be the father of the gambler’s fallacy, Pierre Simon Laplace, in an essay he wrote in 1796. In it, he mentions the anxiety of fathers in months when their pregnant wives are due if too many women in nearby towns have already given birth to boys, believing that this would harm their chances of having a boy as the number of boys birthed in the region reverted to the mean. Believing that the more births of girls there are, the more probable the births of boys are is another most famous example of the gambler’s fallacy at work, which is noted in many places and times in recorded history.

The gambler’s fallacy commonly presents itself as the belief that random events that have happened frequently in the past will be much less likely to occur in future events. This mistaken belief that past events influence random sequences is caused by cognitive bias in our overworked brains.

Sorting order from chaos can be helpful. Our brains have figured out that when we see storm clouds, it’s best to turn that boat around and come home, for instance. Our ancestors learned that it was time to plant or harvest when they saw certain signs in the heavens. However, this need to find order in chaos meets its match when it comes up against independent, random events that are not correlated.

Studies in the stock market have shown that many people sell hot stocks because they believe they are much more likely to fall after such a quick rise or even that bankers who approve loans are as much as 10 percent more likely to reject the next loan after approving the preceding one. The brain’s ordering mechanism prefers to find symmetry even in small numbers. And when those are independent events, we may be tricked into thinking that we can’t approve five loans in a row even if they all meet underwriting standards or that our beloved generationally owned stock has got to go because its price has risen too quickly.

Retrospective gambler’s fallacy is another interesting area of the gambler’s fallacy. If we use the random event of the coin flip and then use that data to extrapolate the unknown past events based on our available data, that is the retrospective gambler’s fallacy. If we are told that seven coin flips have produced seven heads, what do we believe the coin flip was that preceded this event?

Sometimes, our hard-working brains see a streak and believe it should continue. This can be thought of as the inverse gambler’s fallacy. For instance, I’ve spent over thirty years in the casino business, much of it around Baccarat players. In Baccarat, you may bet on either Player Or Bank. Due to the game’s rules, Bank is a bit more likely to happen. But you pay a 5% commission on winning bank hands. However, due to this minor tweak in the probabilities, I see many people betting against players’ streaks but betting heavily on bank streaks.

This sense that a small probability in favor of Bank will produce much longer Bank streaks than Player is an excellent example of the reverse position of the Gamblers’ Fallacy. Sometimes, we can be tricked into believing that something unlikely to continue will, in fact, go on much longer than it should.

The hot hand fallacy is the belief that a series of winning bets will continue. Usually, as a result of luck or destiny or, more likely, a cascade of dopamine in the brain, leaving us feeling pretty good about our chances. We can see the hot hand fallacy not only in gambling but in the sports world where a run-and-gun basketball guard may drill shot after shot, or the unheard of PGA golfer comes from nowhere to sink putt after putt, or even on Wall Street where some young analyst runs the banks money into the billions in trading profits.

One of the more interesting things about the Hot Hand Fallacy is that there is some math behind it. Nigel Harvey and Juemin Xue published an article in Cognition showing that sports book winners were likelier to win their following bets. In fact, those gamblers who had won six bets in a row were almost a three-in-four favorite to win their seventh bet. Not only that, but the inverse was also true: if you lost six in a row, only about one in four betters won their seventh hand.

What’s going on here? Well, it’s our brain looking for order in randomness, but in this case, not true randomness. Sports events are not coin flips, and after a bit of digging, they were able to show that most of the effect was from winning betters becoming much more conservative in their bet selection as their winning streak went on. In contrast, the losing punters became increasingly aggressive in betting long shots and underdogs. This behavioral decision-making highlights the way we are conditioned to believe in streaks much more than it shows a problem with predicting random future events.

People struggle with probability—not just hard math-type probability but simple everyday determination of what is more likely. Studies by Tversky and Kahneman, two of the experts in the field, are littered with all the ways the human brain can trick itself. And it should surprise no one that numbers play an even more prominent role in confusing us about what is more likely.

One of the more common cognitive biases is anchoring. We can be fooled into assigning too much weight to the first numbers we are shown. For instance, a website may show you more expensive items at first, then much more reasonably priced ones. Due to anchoring, you will perceive these items as cheaper.

Another way our brain can mis-extrapolate numbers is through Prospect theory. Here, humans tend to prefer fixed outcomes over better probabilities. For instance, they would rather take $3 than a 10% chance of winning $50, even though probability theory tells us we should take the gamble over the long run.

The sunk cost fallacy is probably the only cognitive bias you may have heard regarding probabilities. It is one example of commitment bias, meaning that once we have committed to something, we are much more likely to stay with it despite rising costs or decreasing odds.

The most cited example of this fallacy is a dog of a stock. You bought it at $100, but now, after the earnings report, it’s at $70 and sliding lower daily. With the new info from the earnings call, you wouldn’t even buy the stock at $70, and yet you don’t sell; you’re going to wait until you break even. This refusal to take the pain of the loss and preference to stick it out is the sunk cost fallacy. What you’ve already invested in it plays a part in its worth today.

There are quite a few theories on why the gambler’s fallacy occurs, from people confusing random coin flips with what we would call an urn model—for instance, pulling seven red balls out of a bag containing an equal number of red and blue balls. Perhaps the brain uses a shortcut to compare something with which it has more experience, depleting a known resource, for instance, rather than true randomness. It would make sense that we would expect to see a blue ball next.

Others believe that the brain’s non-stop scavenger hunt for connections, which has pulled us up from the mud and put us on the way to the stars, confuses small sequences of numbers with much larger ones when it attempts to work out probability since it has so little experience with such vast data sets.

Whatever the reason, the gambler’s fallacy is real. It impacts many different aspects of our lives, so knowing when we may be misjudging a wager or, even more importantly, a life event without fully understanding the probabilities is essential. Below, we have listed some behaviors to watch for.

The first step is being aware of when you let cognitive bias start to slip in. Once you notice it, it becomes much easier for the more rationale part of your brain to take over and remind you that, yes, black can and does land 26 times in a row. The universe is weird and mysterious and no amount of lucky socks is likey to change what ever it has in store. And if you need to repeat to yourself dice don’t have memories, who would we be to judge.

Once gambling stops being fun and starts to turn into something else, it’s time to take stock of your situation. Be aware of the warning signs, set limits, and stick with them. Never bet more than you can afford to lose.

Check out our Responsible Gambling resources.

While technology has undoubtedly exacerbated problem gaming behaviors by making gambling easily accessible 24/7, it has also provided many new features that can help you slow or control your gambling spend or even time on your device. You can set daily, weekly, and monthly loss limits, daily and weekly time on device limits, and ask to be temporarily or even permanently excluded from that gambling app.

However, the best time to take full advantage of these features is when you sign up. If you wait until you have already lost too much, you haven’t done anyone any favors by believing you would stick to your budget without help. But it’s still better late than never to put some of these limits and locks in place regardless of your situation.

Land-based gambling still offers exclusion lists, but it lacks many of the other innovative safeguards we are seeing spring up in the online space. That doesn’t mean we won’t see some new legislation or technologies soon that might help people have more control over their gambling behavior.

If you or someone you know is experiencing any of the symptoms of disordered gaming, please know that you are not alone, and that help is available.

National Problem Gambling Helpline: (1-800-GAMBLER)If you use the link, this number can be used for calls, texts, or chats. It is staffed by trained professionals who can answer your questions about your or your loved one’s behavior, how to get help, and all of the resources available to help. The calls are confidential, and there is no charge.

Gamblers Anonymous GA is a group of former compulsive gamblers and those still struggling with gambling addiction that relies on meetings and sharing of experiences to help people get help. This talk-based approach has been a generally successful approach for many faced with gambling disorders. Again, there is no charge.

GamTalk offers some of the same features as Gamblers Anonymous but through an online community instead of real in-person meetings. They have a large group of people who have vast experience in dealing with gambling issues. They can help put you in touch with people in your community, and their online support group can also help.

State-Specific Resources: (feel free to add more)

http://ccpg.org

The Connecticut Council on Problem Gambling can also be an excellent resource for Nutmeg State residents.

http://gamblinghelplinema.org/

The Massachusetts Problem Gambling help site has lots of information and resources for residents.

http://www.mdgamblinghelp.org/

If you are in Maryland, you can reach out to the Maryland Gambling help website, which offers chat as well as phone numbers for resources available in Maryland communities

http://1800gambler.net

West Virginia’s riff on the national helpline is .net, not .com. The website has great information for West Virginia residents seeking help with gambling problems.

https://oasas.ny.gov/hopeline

New York State has an award-winning website for when you are ready to get help for disordered gaming. It offers libraries of info on the topic, phone, and internet links for local resources, and the ability to connect you with professionals that can help today.

Do you have more questions about the gambler’s fallacy, or are you wondering about responsible gambling practices? Read the common questions and answers we’ve compiled below.

The easy answer is, of course, that with training and awareness, it is easy to overcome the gambler’s fallacy and be aware when we are starting down that slippery slope. The more complex answer is that our brains have developed this order from chaos mechanism over millions of years and that it is pernicious. Once we start to notice it, we will see it everywhere, and the fact is that it can hide deep down in our fundamental unconscious. We must be very aware and honest with ourselves to avoid it altogether.

The belief that very small sets of numbers will behave the same as large ones is the main culprit, but this is mostly caused by the brain often having only small data sets to act on. In this case, truly random events are neither more nor less likely to happen due to past events, but our brain looks for patterns in this short bit of randomness and decides that this is more likely to happen than that. This is best summed up by the reminder that “the dice have no memory,” meaning simply that past random events have zero bearing on future ones.

There are many. But to be honest, casino gambling itself is undoubtedly the greatest gambler’s fallacy. If we consider roulette an easy proxy for most casino games, with its even money payoff on the 18 red or black numbers interlaced on the wheel but then note the two extra green numbers, it should be evident to anyone that the odds are nowhere near 50%. The belief that, over time, you can overcome those two extra green numbers, or more generally, the house edge, to win more wagers than you lose is not only at the heart of today’s commercial gambling but also the finest illustration of the gambler’s fallacy.

If it is indeed a random event, then yes. But sometimes events we believe are random, which everyone believes are random, are not. In my personal experience in the casino world, I have personally witnessed a gambler beat a roulette wheel for over a quarter of a million dollars not once but twice by betting a section of the wheel that was biased.

I’ve seen video surveillance of a team that had hacked old slot machines and discovered the pseudo-random number generator that makes the slots appear random but actually tells them what to do next. Using software tucked away somewhere in Russia, they could broadcast video of the machine play, infer where they were in the very long string of PRNG cycles, and then tell the player the exact time to hit the spin button for a win.

Our cognitive processes are constantly at war with randomness, and sometimes, they find striking ways to beat it that may not be apparent to everyone.

Systematic effects can alter so-called random events, but they are not related to the actual gambler’s fallacy. For instance, the biased wheel discussed above caused systematic effects that made the wheels no longer truly random and introduced errors into our random sequences, changing the probability.

Another example is blackjack. If blackjack had a truly infinite number of decks, the game would not be beatable. But because we deplete certain cards out of the deck, the deck composition changes, which means that sometimes the advantage lies with the player, which turns out to be an excellent time to bet more. This systematic error is caused by the substitution of finite cards for true randomness.

The Inquirer is not an online gambling operator, or a gambling site. We provide this information about sports betting for entertainment purposes only.