Our Reader Den developed his own system. He has been playing in accordance with it for years at least two or three times per week. "Sometimes I'm nervous, but I never left a casino in the red in the previous year", - he says. Has Den really found a way to beat the casino? Is it theoretically possible? Let's find this out.

## Conspiracy Theory

I have noticed that all of the major sites operating in the field of gambling focus on the fact that it is impossible to beat the casino while playing roulette. It has been proven mathematically that players, who use any system while playing roulette, will surely lose in the long run.

It is always suspicious when everyone says the same thing. What are the benefits obtained by casinos from this negative information that is constantly present on gambling resources? Do they tell the truth? After all, if you repeat a lie long enough, it becomes accepted as truth.

Once upon a time there was a myth that a person would never be able to fly. Everyone supported it! However balloons appeared and undermined this faith. In the end, on December 17, 1903 this myth was finally dispelled by the Wright brothers whose Flyer was able to fly 14 seconds for a total distance of 39 meters. Thus, a few seconds dismantled the centuries-old myth.

To be sure, this article is not intended to completely destroy the myth concerning the impossibility to win while playing roulette, but I hope it will make you think. I offer our dear readers to test the system described below and make their own conclusions.

## Things that are Familiar to Everyone

Anyone can win money at the roulette table. Unfortunately, it is possible only in the short run, since casinos always win over the long run. Therefore, every player wants to outwit a casino and elaborate a system that will help users to make a profit for a quite long period of time. Many systems have been elaborated since the time when roulette appeared. Each of them allows players to make the same conclusion: casinos always win. However there are some systems that allow users to win more frequently than lose.

Let’s firstly discuss a little bit of theory. If you toss a coin, you have a 50% probability that heads will come up. A 50% probability is also observed for tails. (In fact, because of the coin topography, one side is heavier than the other, so that a slight deviation from 50% will be observed. However we will not take into consideration this argument.) Thus, if you toss a coin one thousand times, tails will come up 500 times and heads will appear 500 times. Therefore, many players believe that if heads show up many times in a row, the probability that tails appear becomes higher. In fact, it is a misconception. Every time when you toss a coin, heads or tails come up on a 50 probability.

Exactly the same situation is observed in roulette: even if red comes up 10 times in a row, the probability that red appears in the 11th spin will be the same as in the first one: 18/37. There is no law proving that black must automatically show up after ten appearances of red numbers. However there is a law of large numbers. According to it, if you increase the number of trials, the average of their results becomes more accurate and does not depend on luck. In other words, we can say that:

- Red numbers come up in 10 spins in a row;
- The red/black ratio in one hundred spins can be roughly 40-60;
- It becomes closer to 500-500 in 1,000 spins;
- If there are higher orders of magnitude, the difference between the appearance of red and black numbers is so insignificant that it is supposed to be a statistical error.

## System

My friend Den says that he does not like games of chance but loves money. He regularly attends Las Vegas casinos and plays in the following way: he just stakes on dozens. Numbers from 1 to 12 form the first dozen. The second dozen includes numbers from 13 to 24. Numbers from 25 to 36 form the third dozen (although, users can form their own dozens.)

If he wins, he gets three bets. When he does not win, one bet is lost. According to the probability theory, he must win in 32.43% of cases. You may ask why this probability is not equal to 33.33%? - The roulette wheel has 37 numbers but not 36. The 37th additional number is zero. It provides a house edge of 2.7% and removes 0.9% of the probability to win.

Den bets only when one of the dozens did not win during the recent five spins. He knows that the outcome of each round is independent of others, but he still plays in this way. When we asked him about this, he replied: "I become calm." Well, let’s assume that it is a struggle with negative emotions :)

If he wins, he waits for the next opportunity to bet. If he loses, he makes bets in the following way:

As we can see, his scheme is similar to Martingale. So, he has to take serious risks to win a considerable amount. However I know what makes Den limit his session to 15 rounds: he has never made the highest possible bet for several years.

Let's calculate the probability of the fact that a certain dozen shows up at least once in 15 spins.

- The probability that a dozen comes up is 32.43% or 0.3243;
- The probability that a dozen does not come up is 100-32.43%=67.57% or 0.6757;
- The probability that a dozen does not come up 15 times in a row is 0.6757 to the power of 15 = 0.0028 or 0.28%;
- The probability that a dozen appears at least once in 15 spins is 1-0.0028=0.9972 or 99.72%.

Thus, according to the law of large numbers, he wins $1 or $2 9,972 times in 10,000 gaming sessions (note that we are talking about sessions but not spins. Each session can consist of 15 spins.) The winning may vary from 9,972 to 19,944 dollars. He may lose 709 dollars 28 times. That is why the total loss may be equal to 19,852 dollars. As a result of 10 thousand sessions, Den will probably be in the red, but there is a small probability to make a profit: if you will win $2, instead of $1, in each session.

## Light Version

However 709 dollars is a considerable amount of money, and it is a pity to lose it. Taking a look at the table, you may notice that if you reduce the session to 11 spins, you will have to risk only 139 dollars. It does not seem to be a true disaster to lose 139 dollars. Let's calculate probabilities for 11 rounds:

- The probability that a dozen comes up is 32.43% or 0.3243;
- The probability that a dozen does not come up is 100-32.43%=67.57% or 0.6757;
- The probability that a dozen does not come up 11 times in a row is 0.6757 to the power of 11=0.0134 or 1.34%;
- The probability that a dozen appears at least once in 11 spins is 1-0.0134=0.9866 or 98.66%.

Thus, 9,866 sessions will be winning and 134 will be losing out of 10,000 ones. The won amount will vary from 9,966 to 19,732 dollars. The lost sum will be equal to 134х139 = 18,626 dollars, i.e. if you reduce the number of spins to 11, the probability to win rises by 1%. However you risk losing an amount that is five times less than in 15 spins. The theoretical probability to be in the black is observed even for 11 spins.

## Pros and Cons of the Den’s System

Den answers tricky questions well:

I perfectly understand that casinos always win and do not pretend to hit the gold mine. I understand that in accordance with the theory I must lose, but fortunately, this has not yet happened. The theory is an interesting thing, but I win money and spend it. I renovated my house and purchased a good car. I can also afford to buy different things. Even theoretically, it seems to be quite difficult to lose all of these things, since I do not make such big bets.

He says that he has never suffered from the table limits, which usually reach a few thousand dollars. He also says he reached the 14th round only once. However he lost in the 13th round in the previous year, since he did not have enough money to make a bet. "I was relaxed -. Dan laughs -. I went to the casino with three hundred bucks in my pocket and forgot my card at home."

Playing in accordance with this system, it is really impossible statistically to beat the casino playing roulette in the long run. The same is true for any other tactic. However the great advantage of the system is the fact that you will win almost every time while playing roulette, making a profit. The disadvantages of the Den"s system are quite low winnings compared to the bets. The other disadvantage is a greater impact of losing sessions on your bankroll compared to the winning ones. In addition, it is important that you should have enough money to be able to wager in the 15th round. However let's hope that you will never have to do this.

## Conclusions

This system is very pleasant for the players, because it allows winning always. However this tactic will require a great discipline and attention to follow the scheme and avoid confusing betting amounts. Ultimately, you will lose from the theoretical point of view. However this sum will be insignificant. You also have a theoretical chance to win in the long run if your winnings will always be equal to $2. To be sure, this is unlikely, but the probability that you lose, for example, in ten or twenty sessions is vanishingly small.

This article is not a guide to action. It is rather food for thought. Feel free to investigate the efficiency of this system. And only after that you should start playing for real money. Keep in mind that gambling can be addictive, and this can be devastating for you and your life. If you are not sure that you can resist gambling addiction, you should not even try to gamble.

We have a request. If someone decides to try this betting system, please share information about your results in the comments to this article!