The law of large numbers explains why persistence leads to success for those who know how to take advantage of opportunities in sites for betting . Let's apply the law of large numbers to a very common gambling game, which is Roulette. This is an exciting game that you can find in casinos and gambling halls. The game of Roulette is a wheel with 37 numbered slots from 0 to 36. 18 odd-numbered slots like 1, 3, 5, ... 35 are black. 18 even-numbered slots like 2, 4, 6, ... 36 are red. The number 0 is a special number and is green.

Let's illustrate with a popular variation of Roulette called European Roulette.

The rules of the game are as follows: You can bet a certain amount of money, let's say $10, on odd numbers - the black slots. If the wheel lands on a black slot, you win $10. Conversely, if the wheel lands on a red slot or the number 0, you lose $10.

With these rules, you can see that we are at a disadvantage! You only win when it lands on 18 out of 37 slots. Therefore, the probability of winning is only 48.6%. The house has the edge.

This is an example of European Roulette. In American Roulette, an additional green slot with double zero (00) is added. The odds further favor the house. Our chances of winning now decrease to 18 out of 38, which is approximately 47% in a single game.

Looking at this, you might think: 47% is still a significant number. I still have a chance to make money if I'm lucky!

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But let's think for a moment and apply what we have learned about the law of large numbers. If your number of plays is small, let's say 10 or 20 plays, your chances of winning are still relatively high. But what if you play 1,000 times or 10,000 times?

The law of large numbers shows us that as the number of plays increases, the winning ratio will converge to the probability, which is 47%! Roulette plays, just like flipping a coin, are independent of each other, so the law of large numbers can be fully applied.

By playing more, it becomes certain that you will win approximately 47% of the plays and lose in the remaining 53% of the plays. You will definitely lose money if you play too much!

Mathematics can be used to calculate the probability of losing in the game. Image: localcast-app.com

At this point, it is important to note that I am not saying that if you play more, the likelihood of losing the next round will be higher. The probability of winning in a single round is constant and independent, which is 47%. But when considering the total of all plays, your chances of losing money will increase as the number of plays increases.

In fact, I can use mathematics to calculate the probability of you losing in this game.

If you play only one round, we know that the probability of winning the bet is 47% and the probability of losing is 53%.

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Next, if you play 100 rounds, what is the probability of losing after 100 plays?

I need to calculate the probability of you having fewer than 50 wins. The number of wins in 100 plays follows a probability distribution called the binomial distribution. The details of this distribution will be discussed in Chapter 10 of this book. What you need to know here is that we can use the binomial distribution to calculate the probability of the number of wins in the game.

We can use a function in Excel for