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Your Guide to the Gambler’s Fallacy

Gamblers Fallacy

Most gamblers have all sorts of peculiar beliefs that simply don’t hold up to scrutiny. Whether it’s blowing on dice or carrying a lucky rabbit’s foot, these seemingly harmless superstitions have no place in reality.

When playing games of chance, success is really just a matter of probability and variance. Yet even players who know this often fall for the gambler’s fallacy, which is essentially the false belief that events have a way of balancing out. Unfortunately, even the most level-headed people fall victim to the gambler’s fallacy while betting, and even in life at large!

What is the Gambler's Fallacy?

The gambler’s fallacy is a psychological phenomenon that’s the false belief that random events will balance each other out. Based on the “law of averages”, it is the mistaken notion that a particular outcome or event is inevitable or certain, simply because it is statistically possible.

One of the main elements of this misconception is that past results could help you predict future ones. As a result, you might believe that because a certain number hasn't appeared on the roulette wheel, it is overdue and is more likely to appear.

There's also the reverse fallacy, such as seeing multiple wins with the same result and assuming that number is “hot” and will appear more often.

As such, the gambler's fallacy is based on two key elements:

  • Odds must balance out during a specific period
  • Previous results will impact future outcomes

Gambler's Fallacy Examples

Gamblers Fallacy

The simplest gambler’s fallacy example is flipping any coin you want, as long as it’s fair. If you flip it 10 times in a row, you'd expect it to land on heads 5 times and tails 5 times. Yet if you do this experiment, you might get 8 heads and 2 tails, or 6 heads and 4 tails.

Does that mean the coin is rigged? The fact is when flipping a coin, every toss is an independent event. It’s entirely unconcerned and fully unaware of what happened on the previous flip.

If you enjoy gambler's fallacy real life examples, this one really gained prominence after an episode at the Monte Carlo Casino in 1913. But on this infamous night, the spinning roulette wheel had the ball land on black a whopping 26 times in a row.

Bettors lost millions believing that red was overdue. In reality, every spin is a random event bound by the laws of physics. If a game is fair, every spin should be entirely independent and unrelated to what happened before.

Players Win or Lose with Variance, Casinos with Probability

Most gamblers know that casinos take in more money than they pay out. Even when the games are fair, the rules give the casino a slight advantage, which is known as the house edge. In roulette, the casino pays even money for winning bets on red or black but still holds a 2.70% advantage since the ball can also land on 0, which is green.

That seems reasonable, but it raises questions for bettors who are afflicted by the gambler’s fallacy. How can the casino expect to make a profit if every event is independent? The answer is variance and it may appear a little contradictory at first glance.

While random events are independent, when the sample size is large enough the effects of variance, which is a measure of how much an outcome differs from what you might expect, are reduced. In other words, over time the probabilities are true.

It’s important to understand that this sample size is larger than your individual playing session. It could take thousands upon thousands of roulette wheel spins before red and black even out.

This is why a game with high variance, also sometimes called volatility, can be so rewarding or so frustrating. Casinos make their money because with so many players enjoy games, they work out to almost infinite games and can reap the rewards of the house edge.

Players make their money when the variance works in their favour, like when a progressive jackpot lands in a slot game. But you could just as easily play for hours, days or weeks and never hit the jackpot, no matter how “overdue” it may seem to players lured in by the gambler's fallacy.

The Truth About Betting Systems

Gamblers Fallacy

Whether you play roulette, baccarat, craps, or other games of chance, you’ll probably encounter a variety of popular betting systems. The Martingale method is by far the most popular technique, which requires you to double your previous bet whenever you lose.

The Martingale has two fundamental flaws. The first is that if your losing streak is long enough, you’ll eventually hit the table limit since you need to keep upping your wager. The second problem is that it is based on the gambler’s fallacy. It falsely assumes that events will balance themselves out in the short term, which we know isn’t true.

Of course, these betting systems aren’t all bad. Betting systems force you to take a disciplined approach when placing wagers. Be that as it may, it’s important to measure your expectations and understand the fundamental flaws in this approach.

When it comes to the gambler's fallacy, statistics are used incorrectly. Each event is distinct, and the probability of a given outcome remains the same with each experience. If your betting system has you change your bet based on previous outcomes, it is based on the gambler's fallacy and is inherently flawed as anything other than a bankroll management system.

Conclusion: Avoiding the Fallacy

Although just about everyone will admit that coins have no memory, people still believe in the gambler’s fallacy. What’s worse is that this false believe is even more prevalent in the heat of the moment. When you’re trying to win money, it’s easy to get wrapped up in the apparent magic of the roulette wheel.

If you’ve fallen for the gambler’s fallacy, you’re not alone. Most people including skilled gamblers continue to believe that past events have influence on future outcomes. By merely acknowledging that this is failed reasoning at best, you are already several steps ahead of the game.

Looking for patterns and trying to make sense of your world is human nature, but you shouldn’t let it undermine your bottom line. Acknowledging the existence of the gambler’s fallacy is the first step to avoiding it.

Frequently Asked Questions About The Gambler's Fallacy

What is the gambler's fallacy?

The gambler's fallacy is the mistaken belief that events will balance out in the short term, thus making previous results impact future outcomes.

What is an example of the gambler's fallacy?

A common gambler's fallacy example is when a flipped coin shows heads three times in a row. With a fair coin, the odds are just as likely with the fourth flip that the result will be heads or tails.

What are the gambler's fallacy statistics?

Gambler's fallacy statistics, also known as the law of averages, assumes that just because something is statistically possible, it is inevitable. Yes, there is a 50/50 chances a coin will land on heads vs tails, but to infer that this will have any impact on a specific flip of the coin is a fallacy.

What are the gambler's fallacy variations?

There is also the inverse or reverse gambler's fallacy. This is the mistaken belief that because a result has happened a number of times, it will continue to be successful. Also called hot hands or a hot machine, this is when players assume a slot will payout more because it has paid out a lot with recent spins, or that a lucky number in roulette will continue to appear more often.

What's the difference between the gambler's fallacy and Monte Carlo fallacy?

They are the same thing! The gambler's fallacy has many names, including the Monte Carlo fallacy, and the fallacy of the maturity of chances, which is quite the mouth full.