Law of Large Numbers

Roulette and the Law of Large Numbers – Does it work?

It seems that the law of large numbers is the central theory of many roulette strategies. In this article, we’ll dive deep into the subject and see what the law of large numbers is. How does it apply to roulette, and can you use it to make money consistently?

The basic premise, engrained in the minds of gamblers, is that things tend even out to notice a trend in one direction we can bet on the opposite because it has to even out. Let’s see which part of this is true, which part is not, and which is a fallacy that’s causing many gamblers to go bankrupt while believing it.

 The Law of Large Numbers

 The Law of Large Numbers was first observed in the 17th century by Jacob Bernoulli, and it simply says that the larger the sample of an event, the closer it will be to its true probability. Using the simplest example, the more coin tosses you make, the closer the result will be to 50-50.

 In other words, the result will even out. The misunderstanding of this process is causing huge losses in gambling and is known as the Gambler’s Fallacy – also being the one fallacy among many fallacies in psychology and gambling to be the one that carries the title of being THE gambler’s fallacy.

 In 1913 in a Monte Carlo casino, black came up on a roulette table whopping 26 times in a row. People at the table noticed the trend after 15 blacks and started piling up their cash on red, being certain that the red is due at some point. After 11 more blacks, everyone at the table was bankrupt and the tale of Monte Carlo Fallacy – another name for the Gambler’s Fallacy – was born.

 There’s no memory of past events.

 If a coin flip landed on heads nine times, the gambler would say the next flip will be tails because it has to “even out”. However, it is supposed to even out over a huge number of tries, and not necessarily in the next flip. As a matter of scientific fact, the chance of a coin landing on heads after landing on heads nine times is exactly 50%. The coin has no memory of past events.

 Do coin flips even out or not?

 In theory – yes, they do. However, there’s a huge difference between a probability formula and actual real-life events, especially a single event in particular. The probability theory and The Law of Large Numbers can only be used to come up with certain estimates, but can not be used to accurately predict the outcome of a single real-life event in a long string of events.

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 In other words, the Law of Large Numbers is correct in that it accurately predicts the tendency of random events to even out as the sample grows larger, but it is not a guideline that dictates real-life events. It is used in mathematical theory and has no connection to our world.

 As seen in the example below, it took about 400 dice rolls for the average to even out, it then went the other way and evened out after some 50 rolls again, showing little variation from that point on. However, the crucial thing to understand here is that while we can see the overall tendency, it’s impossible to predict the outcome of the next event.

Law of Large Numbers

 At any given point in this graph, it would be impossible to predict what number would come up. We know the overall tendency is towards 3.5 as that’s the mathematical average between the smallest number, 1, and the largest number, 6. In the long run, it will go towards 3.5.

 But if it does correct itself, couldn’t I somehow bet on that?

 While the average does tend to even out, it is a fallacy if we think that after 10 odd numbers in roulette we, at some point, need ten more even numbers for the law to prove right, and that by knowing this we can exploit the laws of the universe to profit on gambling.

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 But the real effect is dilution. When you spin the roulette wheel 500 more times, the effect of your 10 odd numbers is diluted to almost nothing. Even if during those 500 spins the odd-even ratio is 250:250, with these 10 odd numbers added it becomes 260:250, so odd has an advantage of 50.98% to 49.02% for even numbers. And that’s close enough to be even. That’s how The Law of Averages works – by making your one spin insignificant.

Standard deviation

 There’s also a little thing called standard deviation, which says that our 50.98% – 49.02% is well within the expected. The standard deviation of a single roulette red/black bet is not 1-1 (0.50) as in a coin flip, but 18-37 (0.4865) so it is a bit more predictable than a coin flip. Standard deviation depends on the length of a sequence of events, but can only be calculated retroactively and in no way can it be used to predict the outcome of a next roulette spin. When one delves into the Law of Large Numbers, one should also know the other parts of math science, and not just cherry-pick the one that seems to benefit him.

Every roulette spin is individual

 It’s important to remember the key point from that 1913 Monte Carlo incident – any event can happen 26 times in a row regardless of what you desire. It is best to throw the entire idea of things “evening out” down the drain when gambling, as it can only lead to irrational decisions based on Gambler’s Fallacy. Every roulette spin is individual, and while things do tend to even out in the long run, there is no known way to profit on that.

 It is the casinos that profit from the Law of Large Numbers. The house edge on a single-zero roulette with standard rules is 2.70%, and with a very large number of spins and multiple bets per spin, the house is certain to make a profit. Plus a little bit extra from gamblers who think the ball remembers which pockets did it land on in the last 30 minutes or so.

 The one thing no one is talking about

 It is extremely egocentric to start counting the outcomes on the roulette table the moment you showed up. For all you know, the table could have had a million more reds than blacks since it was installed at the casino ten years ago, and it doesn’t matter one bit that you just saw eight blacks in a row. You might be on the wrong side of the Law of Large Numbers without even realizing it, as you have no possible way of knowing what the all-time average is.

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