The system for playing roulette Thomas Donald

The main provisions of this system are as follows:

• For the game you need to have a capital of 3,000 times more than the initial acceptance rate you accepted.
• Every time you lose a bet, you need to increase the next one bet. Having won the bet, the next one needs to be reduced by one bet.

The system is based on the position accepted by the author that during a certain period of time - day, week, month, year - the number of losses and winnings is approximately equal. The author promises to win if the player will use his system for such lengths of time, subject to two additional conditions:

- Do not play if you can not freely dispose of the time within the term chosen by you or with money in the amount of 3000 times the rate you have accepted;

- Do not play on other people's money and on money borrowed.

Let's try to test how the system "Thomas Donald" worked in practice, if the events developed in full accordance with the theory of probability (personally I have never played on this system, so I myself am interested to see what happens).

Suppose we always put on red. Of the 37 spins, the red should fall 18 times, the same number of times black should fall out, and 1 time must drop the zero. Let red and black alternate this way: 5 times red, 5 times black, 4 times red, 4 times black, 3 times red, 3 times black, 2 times red, 2 times black, then one after the other. See Table 2.

Pay attention: by the result we played a draw, although we had 1 less winnings than losses. In addition, we distributed the fallout of red and black in a completely unprofitable way: all the first 5 wins were at the same rate. If we started with five blacks in a row, then the next 5 wins would bring us not 5 bets, but 20 (6 + 5 + 4 + 3 + 2).

Continuing our research, we will try to improve the system of Thomas Donald, recalling that in it the bet is always made on one of three "simple chances": red-black, even-odd, more-less. Let's say you play the red and the initial bet is the ruble. Then the system is based on a very simple rule: after falling out of black, the rate increases by ruble, and after red decreases. (We forgot about the zero for a while and decided to play as if in a toss.)

But there is an exception to this rule. What happens if you bet a ruble and win? According to Thomas Donald, the rate should remain unchanged; Neither zero nor negative rates do not exist. And, actually, why, we thought. Also have tried. It turned out interesting.

What is a zero rate, it is understandable: the next run of the roulette you miss. A negative bet is a bet on black, but in both cases the value of the next bet is determined literally by T. Donald. Let, for example, with the first three starts of the roulette all the time fall red. After the first launch, we won the ruble, the second time "set zero", and the third - minus 1 ruble, i.e. Ruble to black (and lose). Before the 4th launch we must lower the bet to minus 2 rubles. We put 2 rubles for black.

It can be proved that if from 2N starts of the roulette the red and black rolls drop N times, then the payout will be exactly N rubles. Regardless of the number of red (and, therefore, black) reds, the "invariance property" is executed: the sequence in which the red alternates with the black one, does not affect the payout size.

Suppose roulette is launched 36 times. Your income (positive or negative) is shown in Table 3. For example, if the red has fallen 20 times, you will win 14 rubles. It is curious that the income distribution is symmetric with respect to the middle of Table 3.

Table 3 shows only those cases when the frequency of falling red and black differ slightly (with other "hands" you will lose big). It was on the proximity of these frequencies that T. Donald was counting, we just followed in his footsteps and "aggravated" the system. To finish the picture, let's recall the zero.

According to T. Donald, with the dropouts of zero, the next bet should be increased. In our modification, it should be increased modulo. In other words, if the rate is positive, it should be raised to the ruble, if it is negative, it should be lowered. Unfortunately, the appearance of a zero violates the beautiful property of invariance, and it is impossible to determine your income unambiguously. We confine ourselves to the case, when out of 36 launches of roulette zero falls exactly once.

Let the rate at the loss of zero was positive. Then the zero is completely equivalent to black, so the revenue is determined by the same table. For example, with 20 drops of red, 19 black and one appearance of zero, the winnings will be 14 rubles. Just do not think that the zero does not affect anything: it reduces the expected number of fallouts of red.

Zero can fall and with a negative bet. Now it is equivalent to red. If the red dropped 20 times, then because of the zero number of his appearances is actually 21. According to Table 3, instead of 14 rubles. We win 6. But if the red dropped less than 18 times, your income increases.

Finally, the zero can appear at zero rate. You can do anything: when you raise the bet, the zero will be equivalent to black, while decreasing - to red. But still look at the background: if the red dropped out more often than black, it's worth to increase the rate, if less often - on the contrary. Thus, you seem to bring together the frequency of loss of both colors. Mr. Donald would be pleased.

For goodbye, we want to warn you once again: do not play on someone else's or borrowed money, and do not believe in any systems without checking, all question, recount all the results themselves. It will be much more pleasant for us if you share your winnings with us than if you report a loss.

In conclusion, we quote a letter from Fyodor Mikhailovich Dostoevsky, written to his wife from Hamburg.

FMDostoyevsky - AGDostoyevskaya:
"... Hello, my angel, Anya ... And here is a game that I could not tear myself away from." Here is my observation, Anya, the final: if you are sensible, that is, be as marble, cold and inhumanly cautious, Without any doubt, you can win as many as you like, but you have to play a lot of time, many days, content with small, if not lucky, and not rushing for chance. "