The Gambler’s Fallacy: Why Past Results Don’t Predict Future Outcomes

The gaming table is the birthplace of countless legends and tales. Experienced players will know the soaring highs and crushing lows that games of chance bring, and can tell you tall tales of their exploits. They can boast of big wins, legendary winning streaks, or even exaggerate big losses, it is part of gambling folklore. But one of the biggest legends, or should we say myths, is the gambler’s fallacy.

This is one of the aspects of gambling that is inexplicable, and gamers can struggle to grasp it. Even the seasoned veterans who have seemingly seen it all can still fall prey to the fallacy. The underlying principle is extremely simple, but it can be hugely contradictory when comparing theory with real outcomes and results. Even if you haven’t heard of it before, you will probably recognise the instinct, and may have even done some reckless bets because of it. Here, we will break down how the gambler’s fallacy works, and the ways in which you can overcome it.

What is the Gambler’s Fallacy

The gambler’s fallacy is a cognitive bias in which players believe the previous result in a game can affect the next one. For instance, if the roulette ball lands 5 times in a row on red, then the black is “due”. Players will wait for the ball to land on black, believing that there is a stronger chance of the next spin landing on black instead of red. Now the fallacy can apply to virtually any game, from dice games like Craps to RNG-powered slot machines, and even in the skill based games such as poker.

Just to clarify and get it out in the open. The previous results have no bearing on what happens next in a casino game. The odds always remain the same, as does the chance of the bet winning. Most gamblers know this and expect a certain amount of variance to mix up the results and produce strange anomalies. Like the Banker Bet winning 4 times in a row in baccarat. We may accept the streak, putting it down to blind luck.

Yet these strange happenings can still play on our minds, and change our approach to the game. It may be the fear of missing out, or the quite rational belief that the results must balance out. Both can lead to some pretty dangerous assumptions. The kind of assumptions that some bettors act on impulsively and end up losing heavily.

The Monte Carlo System and Role of Variance

There is no better example of this than the 1913 Monte Carlo roulette bust, which created the Monte Carlo Fallacy. It is also called the Fallacy of the Maturity of Chances. At one of the roulette tables, the ball landed on black segments 26 times in a row. The chances of this happening are around 1 in over 68 million, and yet spin after spin, the ball kept landing on black. Gamblers flocked around the table, and millions of Francs were reportedly lost as the players upped the ante and bet on red.

The reasoning was that the streak was causing an imbalance in the overall results. After all, there is an equal chance of the ball falling on red or black, so it would be natural to assume the ball had to fall on black to make the real life results closer to their actual probabilities. Sure, the chances of the ball falling on black 26 times in a row are 1 in nearly 70 million before the wheel has been spun. But at the beginning of every round, the chances of the ball landing on black in that round are 18 in 37 (48.64%). No more and no less.

The house made a huge sum of money off the anomaly, and bettors were left holding their heads as they got suckered into what seemed a straight winner.

Our Perception of Randomness

The probabilities and house edge are easy to get hold of. To get the true odds probability, we divide the chances of winning by the chances of losing. For the house edge, we can compare the True Odds Probability [%] against the Implied Probability [%]. For the house edge, we just get the odds implied by the payout, and compare them against the true odds. The house edge is the discrepancy, the little invisible fee casinos charge to stay in business.

We have a range of calculators that can get the house edge and true odds for the following games:

• Baccarat
• Blackjack
• Craps
• Roulette
• Video Poker

Now we have no problem with assessing the probability of winning, but it’s the variance that can throw you off your guard. Variance is basically the measure by which the real life results differ from the statistical probabilities. Take a coin flipping game, for example. The perfect statistical results from 10 coin flips would be 5 heads and 5 tails.

With 5H and 5T from 10 flips, there is no variance. If the results brought 8H and 2T, then variance has come into play. All gamblers know about variance, and to varying degrees, they expect a certain amount to influence the results.

Variance vs Volatility

If you were to simulate millions of rounds of games, then, in theory, the variance should diminish. The results should closely resemble the true odds of each bet. However, this is not always the case. In the short run, variance is generally more prominent (again, it is also impossible to predict). For example, you could play 100 rounds on a 96% RTP video poker game, and win just 15% of your stake back. The short term variance has been high, and not in your favor. But then your 101st draws the 800x payout Royal Flush, and suddenly you are 785% in the green. The variance has suddenly taken a drastic turn for the better.

So variance is one thing that we cannot really explain. Another is volatility, a term attached to slot machines to describe the variance. A High Volatility slot machine generally pays out bigger amounts, but less frequently. Low Volatility games pay out more often, but in smaller increments. It has nothing to do with RTP. Volatility is a term that describes the variance in the game mechanics, but these can also be contradicted in the gameplay.

Why Players Fall for the Gambler’s Fallacy

The main reason why we struggle with the gambler’s fallacy is because of variance, recency bias, and also out of some gamblers’ conceit. Sure, you will not start with any biases, but as you game for longer periods of time, your mind can play tricks on you. The rush of dopamine and fluctuating cortisol levels in your body can be exhausting. Both mentally and physically. And experiencing dramatic highs or lows can spark biases as you play.

For instance, you notice patterns in the gameplay and assume you can predict what happens next. Another one is believing you are due the win. Especially during a seemingly endless losing streak. You don’t want to quit the game just yet, because you have sunk so much money into it. But it must be leading somewhere, so you keep going. In the hope that it will all pay off and you will return to your starting bankroll.

Loss aversion can also lead to the gambler’s fallacy. When the losses outmeasure the wins, not financially, but in the feelings they produce on you. You aren’t happy with smaller wins, but want to push for a bigger win, to get a more impactful hit of dopamine.

And the gambler’s conceit, a bias in which you think you can beat the house and quit while you are ahead. Sure, you are expecting variance, but you are waiting for the tides to turn in your favor. And once you are ahead, you will quit on a high. But you never know when you will reach the peak of your bankroll. If you just pass it and start losing, it doesn’t have the same “quit on a high” feeling. And you may chase the losses, however small they may seem in the grand scheme of things.

The Gambler’s Fallacy Outside Casino Gaming

The gambler’s fallacy can be found nearly anywhere, it is not reserved just for gambling. When you are hard on your luck, and feel you are due something, it is the gambler’s fallacy coming into play.

You can experience it when tracking the stock market, betting on sports, and even in your personal life. You’ve just quit 3 jobs in a row because they didn’t meet your expectations. So you must be due the real thing, right? The gambler’s fallacy can be extremely dangerous.

Prevention and Safer Gambling Practices

Overcoming the gambler’s fallacy is just as much about controlling your emotions as it is about financial management. You can set up reality checks, deposit limits, time-outs and other safer gambling tools to maintain control over your spending. Nothing beats making a fault proof bankroll, and sticking to a staking plan that you can sustain for longer periods of time. You can also set winning goals and loss thresholds, at which point you will stop after you cross.

Controlling your emotions is a lot harder. It is natural to feel that wins are due or read into patterns in games. But these are counterintuitive. Especially when you lose money on a specific game, and then refuse to quit because it will all but confirm that you fell victim to the gambler’s fallacy.

Staying calm and accepting losses is the toughest skill you will have to learn as a gambler. Though it is one of the most valuable. If you can learn how to lose, then you can enjoy the wins all the more. And you won’t use gambling as a means to make quick money or get a dopamine hit. No, you can then enjoy gambling as a risk taking game in which sometimes you win, other times you lose.