One of the key traits of any successful gambler is being able to think about probabilities in a clear, rational way—not letting yourself be influenced by silly external influences like luck and superstition. However, while this may sound simple on the surface, you’ll see that most people suffer from a problem in their reasoning that’s often referred to as the gambler’s fallacy.

It’s safe to assume that most everyone understands the concept that the more times you run an event, the closer your results will be to their expected probability. This was proven by mathematician Jacob Bernoulli in the 17th century by tossing a coin many thousands of times and recording whether it landed on heads or tails.

In his Law of Large Numbers, Bernoulli concluded that the more times he tossed the coin, the closer to the percentages came to an even 50% each. However, the most important part of his results was the fact that, even though the percentages do start to equal out, at the same time there is a growth in the difference between the two outcomes.

Look at it this way—you toss a coin 10 times, and 9 out of the 10 times it lands on tails. This gives you 10% heads and 90% tails, with a difference of 9 in between the two. Now, after tossing the same coin another 9,990 times, you end up with 4,900 tails (49%) and 5090 heads (51%). As you can see, even though the two percentages are much closer after 10,000 tosses than they were after 10, there is now a much greater difference in between the two than there were in the first sample.

Variance in sports betting is very important for long term profitability and you can read more about that here.

To understand why this is important for gambling, let’s look back at the first 10 coin tosses. You toss the coin the first 9 times, and it lands on tails every time. So, if you had to bet on the outcome of the 10th toss, after tossing 9 tails in a row, which would you bet on—heads or tails? You’d probably pick heads like most people, mostly because you think it must be due—after all, the statistics usually even out, right?

Wrong. This is exactly what the gambler’s fallacy is—thinking that just because the same outcome has happened repeatedly, that the other outcome somehow suddenly has a better chance to occur. In truth, no matter what the previous outcomes were, you have a 50% chance of it landing on either heads or tails.

Games of chance such as this have no memory or record of the previous outcomes and they never matter for the outcome of the next game—no matter what your gut may be telling you.

The Gambler’s Fallacy in Real Life

The reason that Bernoulli should be important to a gambler is that his theorem teaches us that even though the results of an outcome should become proportional over time, we can’t use these results to determine the next outcome. And if you try to do so, you could end up losing a whole lot of money.

For those who enjoy slot machines, you’re probably familiar with the person who stands guard over a machine they’ve been pumping money into—not letting anyone else play it because they know it will soon payout. Six hours later, the same person is sitting at the same chair, still thrusting coins in the machine and mumbling to himself about how it will pay out soon—it just has to.

Don’t let yourself get suckered into this way of thinking. In gambling, nothing has to happen—it either does or it doesn’t, and nothing that’s happened before is going to change it. The sooner you realize this, the sooner you’ll be able to understand how the games work and start making more calculated risks based on odds.

This applies to other games as well. Take for instance the infamous 1913 case of a casino in Monte Carlo, which saw the roulette wheel land on black 5, 10, 15, 25 and then 26 times before finally hitting red. As you can imagine, the more times it hit black, the bigger and bigger bets people were putting on red in the thought that the streak just couldn’t go on. In fact, it was all random chance and each spin had the same chances as the next, but that didn’t stop a lot of people from losing a lot of money due to their irrational thinking. This incident is also the reason why it’s sometimes referred to as the Monte Carlo fallacy as well.

While all of these are bad, the worst of all is the gambler who thinks that he or she is due a win because they’ve been on a long losing streak.  Also having a winning run doesn’t mean you should start betting more. There is no such thing as a sure thing in gambling. It’s all down to chance and probability, but by understanding that, you can also learn to judge a good bet from the bad.

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