How to guess what number will fall in roulette. Roulette random number generator

Two mathematicians, Michael Small and Chi Kong Tse, published a paper in which they proposed a roulette winning system. This news instantly spread across the Web and, being multiplied by natural lack of curiosity (only a few bothered to look into the note itself) and general illiteracy in the simplest issues of physics and probability theory, it grew to absolutely incredible proportions. On Lente.ru, for example, it became the most read news item for May 14. What exactly did the scientists do, and should they really, having discovered the secret of a gambling game in which millions lose, now be afraid for their lives? Let's figure it out.

From past

Roulette - perhaps one of the most popular games of chance today - first appeared in France. According to one version (given by Eric Bell in the book "Men Of Mathematics", published in 1937), Blaise Pascal had a hand in the invention of roulette. According to this version, the wheel with deflectors was supposed to be one of the parts of the perpetual motion machine that the scientist was working on. According to other versions, the game with the wheel was invented in Ancient China, a French monastery or in Italy. latest version remarkable in that it features a certain Don Pasquale (Don Pasquale), that is, a person with almost the same surname as Pascal's. However, "Don Pasquale" is also an opera buffa late XIX century, so the existence of an Italian mathematician with that name is in doubt.

Be that as it may, but at the end of the 18th century, roulette, also known as the ferris wheel (the sum of all the numbers on the disk is exactly 666), conquered France. This was partly due to the fact that the game looked much more honest - that is, more random - than others that existed at that time. In the very first version of roulette, there were 36 notches along the rim of the game wheel, in which numbers from 1 to 36 were placed - in the first version of roulette there was no zero sector. This sector, as will become clear from the mathematical model of roulette below, is needed in order for the casino to always win in a certain sense. This oversight (lack of zero) to early XIX century was corrected, and some time later, when the roulette reached the USA, the 38th sector appeared on the wheel - double zero, which almost doubled the average casino profit.

However, here too there is alternative version events: there is an opinion that the wheel with one zero was invented later than with two. They even name the specific names of the inventors of the "more honest roulette": Francois and Louis Blanc. Allegedly, they first introduced single-zero roulette at their casino in the German spa town of Bad Homburg in 1843. This hypothesis, however, was diligently spread by the brothers themselves, about one of whom there was a legend that he sold his soul to the devil, so this version raises serious doubts.

Rules of the game

So, let's turn to the basic rules of the game of roulette, which, with the exception of some minor nuances, have not changed almost since the end of the already mentioned 18th century. The main instrument of the game is the wheel. It is a kind of inclined funnel-shaped surface (usually not too high - the edges of the funnel should not block the movement of the ball from the participants in the game). A wheel is installed at the bottom of the surface, along the edges of which there are 37 (38 in the American version) sectors, also limited by deflectors. These sectors are marked with numbers from 0 to 36. Zero is colored green, while the remaining sectors are black or red (there are the same number of both colors). The numbers on the rim are not in order, however, there is more tradition than mathematics behind this. If you count clockwise from zero, then the numbers go in the following order: 0, 32, 15, 19, 4, 21, 2, 25, 17, 34, 6, 27, 13, 36, 11, 30, 8, 23 , 10, 5, 24, 16, 33, 1, 20, 14, 31, 9, 22.18, 29, 7, 28, 12, 35, 3, 26.

Players, who may be several, are allowed to make bets, and one bet can cover a group of numbers in the amount of 1, 2, 3, 4, 12, 18. The croupier spins the wheel in one direction, and lets a small ball go in the opposite direction on an inclined surface. Over time, the speed of the ball decreases and it falls onto the wheel, where it eventually ends up in one of the holes. After the ball has stopped, all players are paid out the winnings, and the casino takes the losing bets. The winnings are calculated using the simple formula (36 - n)/n to 1, where n is the number of numbers in the group the player bet on. In the rules of some casinos, the case of zero falling out is described separately: for example, a gambling house may not take all the bets of the players at once, but offer them a choice either to return half of the bet now, or to let it play again.

What are the stakes? According to a tradition that has nothing to do with mathematics, they are divided into internal and external. To place a bet, the player places a number of money chips on a fixed area of ​​the playing field. The field itself consists of many sectors. Its main part is occupied by numbers from 1 to 36, located in three sectors of 12 each, along with the fourth, entirely occupied by zero. This is the inside of the field. On its edges are placed special sectors, meaning outside rates. It is noteworthy that European roulette usually has large fields - because of their size, the croupier uses a special spatula to move bets around the table, while their American counterparts prefer to use their hands.

In fact, as it will become clear from the mathematical model, the roulette is designed in such a way that the casino does not care what bets the player makes - only the size of the bets matters. Moreover, using the above formula, you can allow players to bet on any combinations containing up to 18 numbers (this condition is necessary so that the win is related to the bet as an integer - paying out, for example, 1/35 of the bet may not be very convenient). However, according to a tradition that is already over 200 years old, bets are accepted only on certain fixed sets of numbers:

1. Direct bet (Straight Bet). This is simply a bet on a number, including zero. In this case n = 1 and the payoff is 35 to 1
2. A bet on two numbers (Split Bet). You can bet on two adjacent numbers on the table (including zero) - this, of course, is not all possible pairs. In this case n = 2 and the payoff is 17 to 1
3. A bet on three numbers (Street Bet). You can bet on three numbers in one column (zero, for obvious reasons, is not included). In this case n = 3 and the payoff is 11 to 1
4. Due to the peculiarities of the location of the zero, the trio bet (Trio) is distinguished separately - this is a bet on triples (0,1, 2) and (0, 2, 3). Here too n = 3 and the payoff is 11 to 1
5. Corner bet. They bet on four adjacent numbers on the table. In this case n = 4 and the payout is 8 to 1
6. Due to the special location of the zero, as in the case of the trio, there is a bet called the basket (Basket) - this is a bet on (0,1, 2, 3). The payout, as in the previous case, is 8 to 1
7. Two lines (Line Bet) - a bet on two adjacent columns, three numbers in each. Here n = 6 and the payoff is 5 to 1

Outside bets promise a much smaller win than inside bets:

1. Column (Column Bet) - bet on 12 numbers located in one line of the table. Winning equals double bet
2. Dozen (Dozen) - the bet is placed on three possible numerical intervals: from 1 to 12, from 13 to 24 or from 25 to 36. The win here is also equal to a double bet
3. Snake - the bet is placed on 1, 5, 9, 12, 14, 16, 19, 23, 27, 30, 32 and 34. The name becomes clear if you look at the location of these numbers on the table. This bet is not found in all casinos, and the payout, as in the previous two cases, is 2 to 1
4. Bets even-odd (guess the evenness of the dropped number), red-black (guess the color of the number), from 1 to 18, from 19 to 36 (in both cases, the player bets that the winning number will fall within the specified limits) bring a win equal to the bet . They are usually referred to as equal money (Even Money)

Now that the rules of the game are (more or less) clear, it's time to turn to ways to get around these rules, of which there have been many accumulated over the more than 200-year history of the existence of the casino. All these methods can be divided into two categories - theoretical and practical (of course, we are talking about methods that are not related to a direct impact on the croupier or the roulette wheel itself). Let's talk about theoretical methods first.

Probability and mathematical expectation

Roulette table and wheel
(Click to enlarge)

It is difficult to say what makes people believe in the existence of some mysterious algorithms that should ensure winnings at roulette. Perhaps not last role here plays the notorious sum of numbers, equal to 666, perhaps - banal ignorance in the field of probability theory, multiplied by faith in miracles (there are people who believe that MMM will defeat the laws of the market). Be that as it may, but rumors about the existence of such mysterious patterns have been circulating since the appearance of the game.

In order to understand what they are based on, it is necessary to briefly talk about the mathematical model of roulette. The space of possible outcomes consists of 37 elements, each of which has a probability of 1/37. Suppose a player bets on a group of n numbers. We make an equation for a random variable - it takes the value -m in the case when the number does not fall out of the group, that is, in 37 - n out of 37 cases (m is the size of the bet, and the minus sign shows that we are losing money), and (36 - n)m/n, when the number falls out of the group.

This value models the process of the game. For it, we can calculate the so-called mathematical expectation - a characteristic that describes the average value of a quantity. Without going into details (they can be found, for example,) let's say that it is equal to - m / 37, which is approximately -0.027m (by the way, in the case of American double-zero roulette, the losses are almost twice as much). Here you can see why the zero sector was added to the game - if it were not there, the mathematical expectation would be zero (in fact, this is due to the fact that the winning formula contains the number 36, and the sectors on the wheel - 37) and the game went would be on an equal footing with the casino, which, of course, is completely unacceptable for the latter.

The above mathematics is an illustration of the beautiful expression "You can win at roulette, never win." The construction of any roulette winning system is usually based on a simple consideration: in the general case, the player determines only one game parameter - the size of the bet. At the same time, due to the randomness of the process, he only has information about his own or other people's losses at the moment.

Three, seven, ace

Thus, any roulette winning strategy is essentially a recurrent sequence of bets m k , where each bet is defined as a function of bets with numbers less than k and the random variables they specify. It just so happens that mathematicians are usually expected to answer the question "How to win?", while she says that any strategy defined in this way for sufficiently long periods of time leads to a loss.

However, strategies "with a cliff" exist. The simplest of them is the so-called martingale (or martingale, d'Alembert martingale and others). So, within the framework of this strategy, it is proposed to always bet on equal money, for example, even or odd, doubling the bet with each move. If the first bet is m, then after k successive losses the bet will be 2 k m. If this bet won, then we returned the money and received 2 km profit. If we now add up according to the formula of a geometric progression all the money lost up to this moment and subtract them from the winnings, it turns out that our profit was only m, that is, equal to the initial bet.

This strategy, which has been known since the 18th century (it is noteworthy that, more than two centuries later, there are still people who tell the contents of this strategy as a revelation), there are two drawbacks: firstly, for a small win, we need a lot of money, and, secondly, in all modern casinos, without exception, the maximum bet size is determined for players. This makes martingale unprofitable stupidity. A modification of the martingale is the so-called Dutch system, in which rates increase by odd numbers - that is, if the rate was (2k - 1)m, then at the next step it should be (2k + 1)m. The maximum bet size interferes less with this system, but one win is not enough to cover all losses.

A whole class of methods based on an intuitive (and, of course, mathematically incorrect) concept of probability stands apart. The Biarritz system, for example, belongs to this class. Its essence is as follows: for 36 spins of roulette, on average, 24 numbers fall out. Accordingly, at least 12 numbers are played more than once. The method looks like this: the player watches the game without placing bets. As soon as a repeating number appears, he immediately bets the same amount on it 36 ​​times in a row. If during this time the number falls out only once, then the player will return the money, and if more, then he will be in the black!

Here, however, this fact brings up - each next rotation of the roulette wheel does not depend on the previous one, therefore this system is equivalent to a completely stupid and straightforward one - to bet on the same number 36 times in a row. The probability of getting a fixed number in a series of 36 spins is approximately 0.63 and does not depend on the number.

World Imperfection 1: Bad Wheel

The easiest way to win at roulette is an underbalanced wheel. This option is well described in Jack London's story "The Baby Dreams". One of the main characters in the story, Smoke, notices that the wheel next to the stove in the Antler Casino is behaving strangely. It turned out that it was warped, but the owners did not notice it. Thanks to his powers of observation, Smoke not only wins money, but later sells the "system" of the game to the owner of the establishment.

Shot from Raimondas Vabalas' film "Smoke and the Kid"

Most popular story one such claim to authenticity is the story of Mr. Jagger (in some sources he appears as William Jagger or Joseph Jagger). This gentleman, being a mechanic and an amateur mathematician, in 1937 in one of the casinos in Monte Carlo decided to use the imperfection of the then existing roulette mechanisms. Together with six assistants, he collected statistics for each of the six wheels in the casino hall for 5 weeks. Then, using this information, he began to win and took a total of 65 thousand francs from the institution.

A similar story, which happened, however, already in 1948 in Argentina, was described in Time magazine from 1951. Although there was not without an artistic touch: the main characters of the story were a Nazi sailor, several farmers, a waiter and speculators.

This method was brought to mathematical perfection in the 40s of the last century, when several mathematicians at once proposed convenient methods (tests) for analyzing roulette statistics for the presence of some technical defects. Needless to say, almost immediately these methods were adopted by casino owners.

Imperfect World 2: Determinism vs Randomness

The second, much more sophisticated way to beat roulette is related to the fact that, generally speaking, since the game is played by macro objects, it is impossible to talk about randomness in principle. That is, the mathematical model described above just describes the roulette quite well, while in fact, knowing the initial position of the ball, its speed relative to the wheel, and some other movement parameters should ideally allow us to predict where the ball will eventually land.

At the beginning of the last century, Henri Poincaré in his work Science and Methods studied the movement of a roulette wheel (albeit without a ball) and found that the position in which the wheel stops depends very much on the initial data. Hence, the great mathematician and physicist concluded that there can be no reasonable theory of predicting the position of the roulette wheel in principle. Later, the requirement of dependence on initial conditions appeared in chaos theory - in this sense, Poincare's work with roulette can be considered one of the first in this mathematical theory, which is so popular in non-mathematical circles.

In 1967, mathematician Richard Epstein in his book The theory of Gambling and statistical logic declared that knowledge of the initial angular velocity of the ball relative to the wheel makes it possible to predict in which half of this same wheel the ball will stop. Moreover, he showed that the task is to determine the moment when the ball leaves the inclined surface around the wheel - this happens at a constant speed, so it also does not need to be calculated. Then many experts concluded that even if such experiments were carried out, it was obviously impossible to do it in real time - at that time there simply were no suitable resources.

In 1969, Edward Thorpe published an article in the journal Review of the International Statistical Institute, in which he reported amazing fact. It turns out that the desire of the casino to reduce the systematic deviation from the ideal random statistics leads to the fact that it is easier to predict the movements of the ball. The fact is that when setting up the wheel axle is sometimes tilted. Thorpe showed that an inclination of 0.2 degrees was enough to create a large enough area on the funnel-shaped surface from which the ball never jumped onto the wheel. Moreover, using a portable computer to evaluate the speed allows you to bring the expectation of winnings to 0.44 of the bet! At the same time, the practical part of the study, which took place in Las Vegas, showed that, on average, a third of all roulettes satisfy the conditions considered in the Thorp problem.

Following the work of Thorpe, in 1977-1978, mathematicians Duane Farmer, together with Norman Packard, created a group whose goal was to win money for science from casinos. The group was named Eudaemons and used a 6502 processor-based computer that was hidden in the shoe of one of the band members. Of course, no mathematical article about this activity appeared, and everything that happened was described in the book "Newtonian Casino" (Newtonian Casino) by Thomas Bass, published in 1990.

Finally, last story this sort of thing happened in 2004, when three people described in the news as a Hungarian and two Serbs won £1.3 million at the Ritz casino in London. An ordinary laser scanner helped them do this, mobile phone and computer. The perpetrators were arrested, but the judge ruled that since they did not work on the casino equipment, the money was won fairly. The names of the characters were never revealed.

Truth or fiction?

The work by Michael Small and Chi Kong Tse, preprinted at arXiv.org, is essentially about a simple question: Is there any truth to the stories about the Eudaemons and the Ritz? Is it even possible to predict how the roulette will work in real time? Doubts about the reality of the described events persisted due to the insufficient mathematical validity of the statements (for example, in Thorpe's work, many calculations were left behind the scenes).

As part of the work, scientists built a fairly simple dynamic model movement of the ball in roulette (it must be said that there are more serious and realistic models, which, however, are more complex from a computational point of view), as well as a suitable software. The authors conducted experiments of two types - simple (without additional equipment on the table) and complex (a special chamber was installed directly above the wheel). For experiments, a standard wheel with a diameter of 820 millimeters called President Revolution was used.

Key Parameters Required for Small and Tse Analysis to Work
(Click to enlarge)

In both cases, the researchers had to determine five parameters. At the same time, the authors of the work, generally speaking, did not care about calculating these parameters secretly - all experiments were carried out in the laboratory and no one went to real casinos. At the same time, the researchers relied on some technical devices, the simplest of which can be considered a mobile phone. Be that as it may, but in such a simple mode, scientists managed to achieve a mathematical expectation of 0.18 of the bet (recall that the casinos themselves exist on a modest 0.027 of the player's bet).

From this, the researchers conclude that all the stories described may well be true. It is noteworthy that Farmer has already commented on the work and stated that the published approach is very similar to that used by members of the Eudaemons, with the exception of some details of the mathematical model - Farmer and colleagues believed that forces that stop the ball are not affected by the same forces that work in the work of Small and Kohn Tse.

Be that as it may, but protection from new system quite simple: you need to close the bets before you can calculate the speed of rotation of the ball and wheel. It is understandable, because physicists did not chase fabulous winnings - in this case they were interested in the question of veracity legendary stories. Thus, the conclusion, like 200 years ago, is still disappointing for players: the casino always wins.

A rather complicated guide by an unknown author on how to win at roulette in an online or offline casino.

What methods were used and on what factual material was this technique written?

This technique was written for 4 years on the basis of the following statistical material:

A) Games and statistics in the following casinos in Moscow: Podkova, Grand, Royal, Golden Palace - more than 10,000 roulette and blackjack games;

B) Games and statistical material in more than 20 Russian-language Internet casinos: Grand, Va-Bank, Sultan, Planet of Fortune, Chance, and others - 1024 games were played in each money and 1024 games for virtual chips in roulette and black jet recorded the results of more than 10 thousand games of roulette and black jet in the common room.

Myths of Online Casino

A big request to read carefully, because. it is in this text that the raisin that I picked out of the article is contained in order to prevent freeloaders from using this technique. What is not in the article will be noted: Zest1, Zest2…

You can skip this section for now and go to betting calculations, but then be sure to come back to it and read it - otherwise you will not understand the meaning of your bets.

I will note the main thing, what is needed in the game:

Myth #1 – The result of Internet games is completely random

Statement: The result of online games (roulette, blackjack, etc.) is completely random, because the random number generator is used is an advertising lure based on your ignorance of special sections of mathematics.

The fact is that there is still no theory of random numbers. There is only a definition - a sequence of numbers is called random if any of them is NOT related to other numbers in the sequence. This sequence is assumed to be INFINITE.

And any FINITE sequence is perfectly described by a polynomial (polynomial) of the n-th degree, where n is the number of members.

I translate from Russian into Russian: For example, you played 6 games of roulette (6 is a conditional number so that any reader can be convinced in Excel that I am right). ANY numbers that have fallen out are perfectly, with arbitrarily accurate, described by a polynomial. For example, once such a sequence fell out: 29,10,26,2,33,22 (all numbers are black, see Figure 1) And it is absolutely EXACTLY described by a polynomial. ABSOLUTELY accurate:

Important to understand general principle: The more games played, the more random the outcome. The smaller it is, the less random it is. The closer to the beginning of the game, the more random the result. At the very beginning of the game, he ABSOLUTELY not random.

I will illustrate with an example. In this illustration - screenshots of the results real games roulette in 3 casinos. Below are the results that ALREADY happened BEFORE the start of the game, the start of the games is marked with a red triangle. See how interesting?

Highlight1: On the middle indicator (with a black background) last result before the start of the game - red fell out, the number 9, and the red-black transition took place (then the number 4 fell out, black). On other indicators, such a transition did not occur.

Any online casino program has a single or multi-threaded generator pseudo-random numbers, which generates them according to some algorithm or several algorithms (agree, if there is a generation algorithm, what kind of accident is there?).

Zest2: It doesn’t matter to us at all whether the sequence is random or not - the win is important to us. He has nothing to do with the sequence of numbers, it depends on the number of draws that have taken place. Next, we will verify that this is the case. When you enter the game, a sequence of results begins to be generated. It is generated even if you are not playing - go to the common room of any casino and check it out.

Moreover, with each new entry of yours, this sequence is DIFFERENT (except when someone else is playing in the common room).

Zest3: And this is very important! These sequences more or less fit the definition of a random number sequence (less so if the casino owner starts manipulating the generator). So they apply
Theory of Probability and Mathematical Statistics.

Let me explain with an example:

Consider the probabilities of getting "Red" n times in a row. Red / Black is convenient for learning - in all casinos, indicators show Red in one column, Black in another, and highlight Red in red - you can't go wrong.

You entered the common hall of the casino and see that the indicator shows that in previous draws Red fell out from 1 to 10 times in a row. (If the last number drawn or several numbers in a row, including the last one, were Black, then
further considerations refer to Cherny).

We do not consider other cases, because in most casinos, indicators only show 10 previous results. The loss of Zero is taken into account, i.e. if we see the sequence: Kr, Kr, Kr, Kr, Zero, Kr, Kr, Kr, Kr, Kr - we consider it as a sequence - 9 red numbers in a row plus Zero.

The probability of getting 1 last red number is 18/37, or 0.4865 (there are 18 red numbers in roulette, there are 37 numbers in total in roulette - 18 more black numbers + Zero (0)). We do not consider roulette with two Zeros), the probability of getting the last 2 red numbers is (18/37)^2, or 0.2367%, etc. (see table, column 2 Probability, in %%)

The probability of getting 1 last red number plus Zero is (18/37)*(1/37)…

The formula for the probability of falling red: VerKr=(18/37)^(n+1), where n is the number of identical colors in a row before the start of the game, from 1 to 10);

The formula for the probability of a red drop: VerKr when Zero was dropped in previous draws: Vn=(1/37)*(18/37)^(n+1), where n is the number of identical colors dropped in a row before the start of the game, from 1 to 9) ;

In the general hall of the casino, drawings are conducted without your participation - even if you do not bet, after 1 minute the roulette wheel starts to rotate. You are not playing yet, you are just watching the results of the draw. Probabilities of getting a Red number next draws(which you ONLY watch), depending on the results of previous draws, are shown in columns.

Zest4: The results of the drawing do not depend on your bets - you don't bet them at all!

Here is the explanation Raisins2! We don't care if the sequence of numbers is random or not. It is important for us to make sure that theoretical probabilities coincide with practice.

Zest5: It is especially important to understand that the probabilities, and not the next results themselves, depend on the results of previous draws.

This is the main difference between the Player and capital letter(the one for whom the game is a way of earning, a profession) from the player. The player bets on probabilities, and understands that the result does not depend on his previous bets, nor on previous results. Only the probability of the next result depends on the previous results.

In other words, they understand the difference between theory and practice: probability is theory, outcome is practice.

Zest6: A little clarification - in fact, the probability of previous and subsequent draws, indicated in the table, is absolute for an infinitely large number of draws. We participate in a large but finite number of draws. And the probability, for example, 48.65% is the most probable of the probabilities, the actual results fluctuate in some range. But we will apply a principle that will allow us to consider this probability as absolute.

Zest7: Be sure to check these theoretical arguments - go to any casino!

For example, in the Planet of Fortune casino. All calculations are given on the example of this casino.

Myth #2 – md5 is the perfect fairness control in the game

Another myth: Many gambling establishments refer to md5 as an ideal game fairness control. But…

“If it were possible to set different initial values ​​of the MD5 registers of the processor from those that are embedded in the algorithm, then it would be possible to select two different messages, ... such for which the same digest can be built. What, in fact, was done in this cryptanalysis .... The author of the message, Hans Dobbertin, found that if you use the following initial values ​​​​of the MD5 registers of the processor ... And set the value of the data block for transformation as follows .... Then the second message can be built from the first using formulas…Then MD5(IV,X)=MD5(IV,X').»

And here are the essential practical advice: If you know the MD5 hash of the password and the original sequence, then in a reasonable time you can generate a character sequence for which the MD5 will be the same.

The casino provides the player with a sequence and an MD5 hash to it. Having received the sequence, the player can calculate the MD5 from him and make sure that the resulting sequence corresponds to what happened in the game. It turns out that the casino can create several different sequences with the same MD5, use this to cheat.

It doesn't matter what you get BEFORE the game - the sequence itself or the key to it. It is important that the sequence itself has a huge length - billions and billions of digits, and the key shows you ONLY the results of your games,
let's say 100 or 1000.

For example, in loto.ru they “prancing” like this: Before starting the game in the “random control” mode, you create (by pressing a button) a series of numbers that will sequentially fall out on the roulette wheel during your game.

But they don't say how many of these numbers you create. They announce that from 5 to 50 - but is it really so? Can you check it? Further, even more interesting - highlighted in bold:

In our case, this is the MD5 algorithm (RSA Data Security, Inc. MD5 Message-Digest Algorithm). This is a universally recognized and widely used algorithm in the world. The essence of his work is that, as a result of text processing, he gives a unique sequence of characters (actually an EDS), which, with the slightest change in the source text, changes beyond recognition. Can't find text like this. when processed by the MD5 algorithm, the same digital signature will be obtained as when processing another text. And before the game, you are shown exactly the digital signature obtained as a result of processing the sequence of numbers you created using the MD5 algorithm.

Hans Dobbertin just proved the fundamental possibility of such processing and cutting. If it is possible to replace a sufficiently long sequence, then present a short one instead of a long one - all the more so. You are just other numbers
don't see.

This suggests that if the possibility of substitution and slicing exists theoretically, then the casino's references to honesty are a publicity stunt. They must prove that this sequence manipulation does not exist in their casino. And it is impossible to prove this without independent competent verification.

For example, for roulette: instead of the actual sequence of numbers, you can always be presented with pieces from this sequence, made up of results (after all, the sequence contains all the numbers from 0 to 36, and their sequence is long enough.)

Accordingly, the casino server can be guided in the game not by the sequence generated by the RNG, but by the balance of this player. For example, to make him lose -3%. After the game, the numbers of the actual results are matched with the numbers from the sequence, a key is compiled that opens only the numbers of the actual results from the sequence sent to you, and - it's done! Guarantees of honesty concocted. You open the sequence with the key you received after the game and see that everything is fair.

Myth No. 3 - about the applicability of the theory of probability to the game of roulette

Many obvious misconceptions and simple errors wander from book to book, from century to century. For example, this:

When betting on a number, the casino pays out a win of 35 to 1, and there are 36 numbers and zero on the table. This means that when you win, you give part of your winnings to the casino. You don't pay anything for a loss, except for the loss. If the game were fair, the casino would pay out 36 to 1 when betting on a number. All "mathematical" systems will lose during a long game due to the advantage of the house (casino).

Let's calculate the advantages of the house. From the actual win, subtract the fair win, multiply by the probability of the number coming up, multiply by 100 to convert to a percentage. So we have: [ 35/1 - 36/1] x 1/37 x 100 = -2.703%, against the player. Simply put, if you close all the numbers (including zero) by one chip, you will still lose 1 chip. To convert to a percentage, we take the ratio of the result to the size of the bet and multiply by 100. The result is minus 1 chip, the bet is 37 chips. (-1) / 37 * 100% = -2.703%

Allow me! With bets on the number, everything is clear - we placed 37 bets of 1 chip on all numbers and Zero - in any case, we got 37 if the issue is 36 to one + our bet. But what about the split? It is supposed to give out 18 to 1 + our rate. We decided to bet the same 37 chips - 2 chips for 18 splits and 1 chip for Zero. And the casino should rely on Zero - when ANY number falls out, we get 18x2 + 2 of our chips. We win + 1.

Similarly, for bets equal chances, on a row, on a dozen, on 6 in a line, on a corner (square, corner, square) (calculate for yourself).

And all because articles of this kind are written ordered by casino owners, from the very beginning there is NLP (the logic is clearly lame, but it seems that the casino is being criticized - and the reader perceives the text uncritically). As a result, this is the conclusion made in this article (unfounded, by the way, except for obvious juggling):

It should be borne in mind that roulette has one advantage over the player - with a sufficiently long game, any betting system - LOSES.

Let's call a spade a spade: in winning the casino IN ANY scenario, only if the player plays for a number, split and straight (there the casino really "breaks down"). In all other options, the chances are equal, and in some cases the player has long-term advantage in front of the casino.

On the contrary, the casino is interested in the gambler going too far, wanting to make money FAST for easy money, and began to bet supposedly the most favorable rates- per room, split and street. In this case, he quickly loses. And in the article, unobtrusively, the player is being pushed towards this.

There is such a juggling due to an elementary substitution of concepts:

The subject of probability theory- This theoretical study such experiments in which, under the same conditions, the onset of mutually exclusive events is possible. Under the same conditions.

Are the conditions in Internet roulette the same? No, the loss of a number is strictly determined by the algorithm and settings of the pseudo-random number generator. There is a generated sequence of n numbers, and 2 spins in a row are just the values ​​of DIFFERENT members of the sequence with numbers m and m+1. Even if 2 Zeros fell out in a row, these are EQUAL values ​​of DIFFERENT members of the sequence.

Are the conditions in real roulette the same? No, the drop of a number is strictly determined physical properties roulette wheel and ball, psychophysiology, motor skills, skills, etc. croupier.

So they are trying to measure the current strength in kilograms, they interfere with red and sour.

The connections between such phenomena are studied by a completely different science - mathematical statistics.

A textbook example - in the 19th century in England, a connection was established between the milk yield of cows and the number of old maids in a given area. It turned out the old maids have a lot of cats that devour mice and rats. There are more wild bees in this area (mice and rats destroy their swarms), clover pollinates better, crops are larger, cows eat better and give more milk.

Especially touching wording independent events.

There are no such events in probability theory. These pseudo-specialists confuse independence of random variables and mutually exclusive events (loss of numbers in each spin is mutually exclusive events, but all events are ANY number from 0 to 36 in one back refer to the distribution of ONE random variable).

Let's explain with an example:

Here is the wheel and the table European roulette. Note that we place bets on the table, and the numbers fall into the holes of the wheel.

Obviously, there is no correspondence between the arrangement of numbers on the table and on the wheel- on the wheel between 0 and 1 23 numbers, if you count clockwise, between 1 and 2 - 20 numbers, between 2 and 3 - 29, between 3 and 4 - 6. And on the table - they are nearby.

Due to the discrepancy between the location on the table in the middle column, there are only 4 red numbers (by the way, there is such a paradox: we put 10 units on red and 1 unit on 4 black numbers 6, 15, 24, 33. From the point of view of probability theory, this is equiprobable bet on the 3rd column 5 units and on the remaining 10 red numbers 1 unit each. (We closed all red numbers and 4 black ones, i.e. probability of success = 22/37). Why, in the first case, we put 14 units, and in the second - 15? Or why are there only 8 even red numbers?

Due to the inconsistency of the location, it follows, for example, that a bet on 1, 2, 3 captures a larger arc of the wheel than a bet on 4, 5, 6 (see for yourself what the distance between the numbers is). Important to understand that we put not on numbers, but on certain sectors of the roulette wheel.

Based on the fact that the angular and linear speeds of the ball are many times greater than the speeds of the roulette wheel, it can be VERY roughly assumed that the loss of a number in each spin supposedly “has no memory”, does not depend on the previous spin.

Before a new spin, the wheel has stopped in a certain position relative to
croupier, what is the conclusion from this? The result of the next spin depends on the position in which the wheel stopped in the previous spin and the number of revolutions of the ball. We can assume that the ball has made N complete revolutions along the stationary wheel, plus a certain part of the revolution. Then the wheel made M full turns plus some part of the turn and stopped in a new position relative to the croupier.

Similarly, on the Internet wheel - can there be such an RNG algorithm that will correspond to the placement of numbers on a real roulette wheel?

Look - 10 blacks fell out in a row. The player has the last bet, he bet on red, doubling. Should he continue to bet on red, or bet on even?

Obviously, a clear shift not only to black, but also to the lower half of the roulette wheel (the top number on the indicator is the last result, the second from the top is the penultimate one ... The red arrows show the placement of the results
previous spins.

It is clearly seen that the casino server in this game was guided not by the sequence generated by the RNG, but by the balance of this player. Or the RNG generates a sequence in which the distribution of numbers is DIFFERENT from the distribution of numbers in a real roulette.

The principle of the game and the calculation of win-win bets

In all manuals on playing roulette it is said that when Any game, including the Red / Black casino is always a winner, because. There is also the possibility of a Zero drop.

This is not true - no one bothers us to bet on color and on Zero SIMULTANEOUSLY.

We have a completely different task - to calculate the bets in such a way that, given the probability of a favorable outcome (the color we need), our winnings will always be greater than our bets and will always be the maximum under the betting conditions of this casino. Let's call this principle Zero compensation. By the way, it is this principle that makes it possible to consider the probability as absolute - Zero sometimes falls out, and this is essential (see Fig. Zest6).

Let's introduce a definition: win-win game is a game in which the most likely win is greater than the most likely loss.

Most casinos have a STANDARD ratio of minimum and maximum rates"for equal chances" - from 1 to 50 to 1 to 80; the ratio of the minimum bets "for equal chances" to minimum rates"per number" - from 1 to 10.

To understand what win or lose depends ONLY on this ratio, let's consider n bets on Zero and black at the same time (betting on color is more convenient - in all online casinos, indicators show red and black in color and the distribution of red and black on the roulette table is almost even.)

Let's start with equal rates: On Zero (StZ) = 1 unit; On H (StCh) \u003d 1 unit.

Winning at zero (Vz)=35 units; Winning on black (Wh) = 2 units. Loss (P) = 2 units.

With n tending to infinity, the probability of hitting Zero (VerZ)=1/37, the probability of hitting Black (VerCh)=18/37, the probability of hitting Red (VerR)=18/37.

Our Most Likely Payoff (NVV)=[(Vz)*(Vp3)+(Vp)*(Vpp)]*n=n*= n*, or n* 1.972973

Our Most Likely Loss (MOP)=[(P)*(VerKr)]*n=n*, or n* 1.027027

Note that it is irrational to increase the bet on Zero, because in the case of (St3)=N*(StCh), N>=2 Winning on Black Black does not cover the amount of bets.

Obviously, the maximum ratio (NVV) / (NVP) \u003d 1.998413 is achieved with the ratio (St3) / (StCh) \u003d 1/34

notice, that we have rigorously proven the impossibility of losing with a similar game scheme with n tending to infinity.

That is, losing is theoretically excluded with such a game scheme.

I note that the player's ratio (StZ) / (StCh) \u003d 1/17. In this case, the winnings on Zero and Black exceed the sum of bets by 34.

Independent formation of the probability of a favorable outcome

Bets in a row on black and Zero are good, you say, but it happens that 9 or 10 consecutive results drop out when red falls out.

And you will be absolutely right.

And I'll be right. Here's what:

Nobody obliges you to play in all draws- remember, do you real casinos require customers to play?

You can enter the common room to wait for a favorable probability of already held draws, or

Restart the game, changing the sequence– remember, in real casinos you can play at any of the tables.

The fact that some casinos simply throw you out of the game (for example, "All In", "Fortune") if you do not play is a way for casino owners to reduce your chances of winning. But there are many other casinos out there.

This is an extensive way - to seize the moment, assuming that the sequence of numbers coming up is close to a random sequence.

Programs for calculating bets in roulette

This is a convenient roulette simulator that allows you to test game strategies before you start using them in an online casino. Just imagine how much it will save you time and, most importantly, money!

Every player, both beginner and experienced, wants to guess winning number playing roulette. Not so long ago, a work was published that allows you to increase your advantage in the game to eighteen percent. The authors of this mathematical work were scientists from Cornell University, who, based on the analysis of European roulette, proposed an effective gaming system. A preprint of the study is posted in the archive section of the university's website, which is available for free download.

It is important to consider that this is not the only way to succeed in the game. There are several more options for how you can guess the number in roulette:

1. You should analyze how the ball and the wheel move. They can be influenced by many factors. This is a time-consuming process that requires concentration and attention when calculating the trajectory of the elements. It is important to remember how the roulette wheel was turned before the start of the game, in particular, which sector. Using this method, you can increase the probability of winning. It is worth bearing in mind that it does not give a 100% guarantee. Also note that it only works in land-based casinos. In virtual games, this method is inefficient.
2. You need to bet in sequential order on one sector. Players who won large sums claimed that this was due to perseverance. They always bet on the same number. It should be noted that this method differs high risks.
3. You need to find a roulette wheel that has defects. It is worth noting that in real casinos the wheels can become “crooked” over time. In this case, you can see that the loss of some numbers occurs much more often than others. In a virtual game, a similar pattern can be traced due to errors in the operation of the system responsible for generating random numbers. To see this pattern, it is better to carefully observe the game for a certain period of time, and then you can bet on the numbers that most often fell out.
4. Bet not on one roulette number, but on a whole series. According to professional players, which increases the possibility of winning, because more chances that the ball will fall out within one series, rather than one number.
5. You need to choose one game system and stick to it. If you use several tactics at the same time, then the probability of losing increases significantly. It is recommended to choose the most time-tested system and not deviate from it throughout the game. For example, you can only bet on odd numbers or in red. You can use the Hook method or the system developed by Thomas Donald.

All of the above methods have been tested by numerous experienced gamblers who know the intricacies of roulette. By choosing the most suitable option among them, you will no longer face the problem of how to guess the number in the casino.