What Is Gambler's Fallacy?

In psychology and philosophy, Gambler’s Fallacy describes the common, mistaken belief that if a particular chance event has happened less than would have been expected, it will be more likely to happen in the future.

Which sounds quite complicated. So, as an example to illustrate the idea, imagine you’ve flipped a coin nine times, and it’s been tails every single time so far. Surely the streak is bound to end soon, right? If you’d call heads, reasoning that it’s more likely to fall on heads after such a long run of tails, you’ve fallen prey to gambler’s fallacy.

It’s an incredibly common psychological phenomenon, partly because human brains are programmed to look for patterns in everything, including matters of pure chance. And over the course of history, gambler’s fallacy has been responsible for people losing truly vast amounts of money.

Read on to find out why humans are so susceptible to the fallacy, and how you can avoid falling for it.

Why Is Gambler’s Fallacy A Fallacy?

A ‘fallacy’ is a philosophical term referring to a mistaken belief based on flawed reasoning - usually a belief that feels plausible or appears to be well-reasoned at first. Gambler’s fallacy can seem like common sense to a lot of people, and it can be difficult to convince them that it’s wrong, even when they understand the mathematics that underlies it.

In psychology, gambler’s fallacy has been studied extensively, and has been found to have effects far beyond the realm of gambling, with loan officers, umpires, stockbrokers and even judges at risk of making decisions influenced by this faulty reasoning.

It may seem obvious, but every coin toss - or other similar chance event - is completely independent of all other previous tosses of that coin. The chance of either heads or tails occurring will always be 50%, so long as it’s a fair coin.

This seems logical enough, but people run into trouble when unusually long strings of one result come along. We all know that if you toss a fair coin enough times, the results will average out to being 50% heads and 50% tails. So, if you’ve had an unusually long run of, say, heads, it seems like common sense that you’ll have to get tails, to balance things out.

But this principle works best for extremely large numbers. If you tossed a coin a million times, the results probably wouldn’t be far off 50/50 between heads and tails, and if you tossed it a billion times, they’d be closer still.

But that doesn’t translate to smaller numbers. If you toss a coin only ten times, you can’t expect it to come up heads five times and tails five times (although this is, of course, one of the possibilities). In reality, clusters happen all the time, and have no effect on the likelihood of the next toss having a particular outcome.

When you think about it, it seems clear that the coin can’t have any kind of memory of what’s gone before. Every time you toss a coin, you start from scratch with a 50% chance of heads or tails, no matter the previous results.

The Monte Carlo Fallacy

Gambler’s Fallacy is also known as the ‘Monte Carlo Fallacy’, thanks to a famous game of roulette from 1913, which featured an incredible run of black - 26 times in a row - and which took place at the Casino de Monte Carlo in Monaco.

After the first ten spins resulted in black, gamblers started to reason (incorrectly) that the ball was due to land on red, and began betting ever-increasing amounts of money accordingly. But the ball kept on landing on black, and gamblers’ losses kept mounting. By the time the streak finally came to an end, bettors had lost millions of francs - and the Monte Carlo casino, meanwhile, had made an absolute fortune.

Related Fallacies

Hot hand fallacy

Hot hand fallacy is what you might call the opposite of gambler’s fallacy. Hot hand fallacy refers to the belief that, if a gambler has been enjoying a run of good luck, they’re more likely to keep on winning. This can result in gamblers continuing to bet after winning significant amounts of money, believing that they’re bound to keep on winning - which is how many people end up losing all their winnings, and more.

Retrospective gambler’s fallacy

Based on the same principle as gambler’s fallacy, this refers to what a person might assume about past events, having seen only recent ones. For example, if someone rolled a pair of dice and got three double sixes in a row, an observer might assume that they had been rolling the dice for some time, because the outcome of a series of three double sixes is so unlikely.

When Is It Not Gambler’s Fallacy?

In some circumstances, someone can draw conclusions from the results of chance events without it being a case of gambler’s fallacy.

For example, if someone observes a series of coin tosses, notices that tails is coming up more frequently than heads, and concludes that the coin could be biased and thus more likely to fall on tails in the future, that would not be a case of gambler’s fallacy. Their conclusion is based on the actual evidence available, rather than a gut feeling about luck or chance.

They might well be wrong that the coin is biased, but because they are reasoning based on empirical evidence rather than an incorrect instinct, this wouldn’t be considered an example of gambler’s fallacy.

There are also gambling-related situations where the probabilities of events occurring aren’t independent of each other, and therefore where gambler’s fallacy cannot apply.

Take, for example, a game where you bet on the next card to be drawn from a pack of cards. If an ace is drawn from the pack, without being replaced, then the chances of an ace being drawn again are lower, because there are fewer aces remaining in the pack. This is the principle that gamblers use for card-counting in casino games like blackjack.

How Do Betting Sites Take Advantage Of Gambler’s Fallacy?

Although a betting site can’t explicitly lie to its customers to encourage them to keep betting - so they won’t say, ‘keep going, the ball’s sure to land on red next!’ - they can take advantage of gambler’s fallacy in more subtle ways.

For example, in games with random jackpot wins, they might indicate how long it’s been since the jackpot was last won to encourage gamblers to keep playing - even though, if the jackpot winner is determined entirely by chance, you’re no more likely to hit it when it’s been six months since the last win than when it was last won only a day ago.

And in slots games, if a gambler comes close to hitting a bonus, for example getting two out of three ‘scatter’ symbols, the final line will usually slow down drastically to build the gambler’s anticipation and hopes. This enhances the feeling of, ‘I was so close!’ and makes the gambler more likely to feel that hitting the bonus is just round the corner.

Non-Gambling Examples Of Gambler’s Fallacy

Although it’s called ‘gambler’s fallacy’, the phenomenon is by no means restricted to gamblers.

The financial industry can be particularly susceptible to gambler’s fallacy, with investors and traders frequently acting on the assumption that a certain stock must be ‘due’ to go up having been down previously, or vice versa. There will of course be other factors affecting the value of the stock, but financial decisions based purely on the idea that a trend in one direction must follow a trend in the other can have a dramatic impact on the world of finance.

People are also susceptible to gambler’s fallacy when it comes to predicting the gender of a child. If a couple has had several boys already, for example, they might expect to have a girl next. This phenomenon was described as long ago as 1796 by the French philosopher and mathematician Pierre-Simon Laplace.

He observed men who hoped for a son becoming extremely anxious when they noticed a larger number of boys than girls being born in a particular month, believing that the chances of their baby being a girl were greater, to balance out the boys that had come before.

Studies have also found that decision makers can be subject to gambler’s fallacy in some pretty high-powered situations. Asylum judges, for example, are less likely to approve an asylum claim if they have granted the two previous claims as well. In baseball, meanwhile, umpires are less likely to call a strike (when the ball was within the fair hitting zone for the batter, and the batter failed to hit it) if the previous two balls had been strikes.

How To Avoid Falling Prey To Gambler’s Fallacy

If you gamble regularly, it’s important to be aware of gambler’s fallacy to avoid being duped by it, but even if you stick to Matched Betting (which isn’t the same thing as gambling - to find out more check out our guide to Matched Betting) you still need to be conscious of it.

It’s surprisingly difficult to overcome the instinctive belief in gambler’s fallacy, even for people who understand the mathematics involved and the nature of probability.

Psychologists have found that the best way to resist the fallacy is to treat each event as if it is a beginning, rather than a continuation of prior events. For example, if as a matched bettor you’re given 10 free spins by a bookie, and don’t win on any of them, you might be tempted to keep trying with actual money, because surely you’re due a win after 10 successive failures.

However, as we’ve learnt in this article, this simply isn’t the case - your chances are no different from your very first spin, and you’d be much wiser not to risk your own money.

Similarly, if you place several matched bets and have a run of wins at the bookmaker, you might think it’s worth placing a couple of unmatched bets for real, as clearly you’re on a winning streak. But this would be an example of the hot hand fallacy, and again you’d be much wiser to stick to your usual Matched Betting, with its smaller, guaranteed profits.

Summary

Now that you understand how gambler’s fallacy works and why humans are so susceptible to it, you might feel confident that you won’t fall for it. However, that doesn’t mean you should allow yourself to become complacent.

It’s surprisingly difficult to identify one’s own flawed thinking, so, especially when Matched Betting or making any sort of financial decision, you should be careful to examine your own thoughts and instincts objectively.

It’s also a good idea to be open to criticism from others, because people are often much better at spotting fallacies in others than in themselves. If someone points out that your reasoning might be flawed, listen to them! They might not turn out to be right, but you’ll be better off for having taken the time to consider the way you’re thinking, and whether it’s as rational as you believe.