A man named Jacob Bernoulli established The Law of Large Numbers in the 17th century. Bernoulli showed that the larger the sample of an event, like a coin toss, the more likely it is to represent its true probability. 400 years later that theory has been used in reference to something called Gambler’s Fallacy, which highlights the struggles that bettors in general have had with grasping the concept. Here is a look at Gambler’s Fallacy and the Law of Large Numbers.
The Law Of Large Numbers
A fair coin toss is the perfect example to use when it comes to the Law of Large Numbers because there is a 50-percent chance that heads comes up and a 50-percent chance that tails comes up with every turn. Bernoulli calculated that as the number of coin tosses increase, the percentage of heads and tails results grows closer to 50-percent. However, Bernoulli’s calculations also showed that while the distribution will be even, the expected deviation could actually be quite large. While it might seem like a simple concept, it has led to one of the biggest mistakes that gamblers continue to make because of their inability to understand the impact of the statistical deviation.
The Gambler’s Fallacy
If you tell somebody that the coin has a probability of landing on heads 50-percent of the time and tails 50-percent of the time, they will often make the mistake of believing that the results should even out on a small sample size. However, if you flipped a coin 10 times in a row, there is still a very realistic possibility that the result includes more of one outcome. Tails is just as likely to come up eight times in 10 flips as it is four times in 10 flips, but that is a concept that most casual gamblers fail to understand. The coin doesn’t remember the outcome on every flip so it has no way of evening out the results on its own. The reality is that the potential outcome for heads or tails is 50-percent every single time and that number does not change from one flip to the next.
It’s extremely important to remember that while the probability for two outcomes could be even it doesn’t necessarily mean the actual outcomes will be. In 1913, a roulette table in a Monte Carlo casino saw black come up 26 times in a row. That has led to the Gambler’s Fallacy also being referred to as the Monte Carlo fallacy but the reality is that the outlook is the same regardless of what you call it. This theory can be applied to roulette just the same as it can with sports betting or slots or any other type of wager. While the odds of an outcome could differ, the reality is that the probability of each outcome does not determine what the outcome is as much as outline the chances for each of the possibilities. Gambler’s Fallacy is still a huge issue with casual sports bettors but understanding the problem and how it works will go a long way to avoiding making the same mistakes over and over again.