FRoulette - roulette analysis program
Most serious European roulette players have their own betting systems on which they place the most high hopes, and even those who at first bet “whatever they have to”, then look for consistency in the drawn numbers and try to bet on the most probable numbers, in their opinion. At the same time, some bet only on color, others on pairs, etc., because everyone has their own approach and strategy.
"FRoulette" is an automatic calculation of bets on roulette. As the name suggests, the program will help the player make correct and effective bets. It is designed to automatically calculate probabilities and bets for playing European roulette.
The program was written for European roulette because it is more common and humane in relation to its players. In addition, "FRoulette" is a full-fledged software extension of the Martingale gambling system with some of its own changes and additions, which are based on the experience of players, because it takes into account all 10 common types of bets, the following bets are considered by doubling, and also according to some algorithms you can calculate the bets at which you will win in any case, etc.
Roulette program features:
- automatic probability calculation for 10 types of bets at each stage of the roulette game;
- analysis of the size of the next bet, at which the winnings will be satisfactory;
- the choice itself winning bet after each number drawn;
- taking into account the minimum winnings that the player plans to receive after each bet;
- tracking maximum and minimum bets, balance, as well as the amount of current bets;
- change many settings to suit your own needs.
With all this, the program cannot guarantee the player a win with a 100% probability, because roulette was inherently designed in such a way that in the end the player could remain in the red (although with a serious approach the probability of winning can be increased to 99%).
So why not 100%? The answer is very simple: no matter how good the strategy and software are, nothing can save you from losing different series, but, nevertheless, this program can offer several of the most optimal ways out of the current gaming situation.
As a result, in addition to calculating probabilities and choosing the optimal bet, the player receives:
1. Saving time, because according to some strategies, manual calculations can take quite a long time, but software can be done in a fraction of a second.
2. Savings own strength and getting overall enjoyment from the game, because you won’t have to sit with a calculator and a piece of paper all the time, constantly writing something down.
3. Protection against mistakes that were made accidentally. For example, a player makes the next bet in such a way that it becomes the maximum allowable, but at the same time, so that absolutely all previous bets pay off. If the game is on long and a lot of bets have already been made, then the task becomes really difficult.

How to win at roulette?

Excitement, adrenaline, delight, disappointment and even despair. It's all roulette. They play roulette and win. They play roulette and lose, lose, lose... But everyone just wants to win. Let's talk today about how to win at roulette.

Is it possible to win at roulette?

How to win at European roulette? What about American or French? First you need to come to the understanding that roulette, like any gambling game, is subject to the theory of probability. After all, how a hypothetical player (each of us) dreams of winning: so he came to the casino and bet a thousand bucks, say, on 5. Yes! Now he has 36 thousand. I took them all and set them to 6. Yes! Now he has 1296 thousand. Lemon! He took it and put everything at 7. To the madness of the brave... Now he has 46... almost 47 million! If someone selflessly believes in their luck and has an extra thousand bucks, let them try, but just remember that the probability of winning in this case is 1 in 37 to the third power, i.e. 1 in 50653.

In roulette you can bet on one number (the probability of winning is 1 out of 37), on a group of numbers (from 1 out of 18 to 1 out of 3), on red/black, even/odd (1 out of 2). The lower the probability, the more win. The greater the risk, the more champagne! There are always players who want to drown in the effervescent sea, but they are in the minority. Most people are still more sober and play with small bets on equal chances. It would seem that with such a game everything should end quite acceptable. They lost their souls with sweet dreams, placed bets 3-5-10 times, and went home happy or not. About half lost, about half won.

However, human psychology plays a bad joke on people. For those who quickly lost their chips, it’s easier: they lost, gave up, and went home. But who started to win... He won the first bet, and a smile touched his lips. It's a small thing, but nice. I won the second, third - and the smile widened. Then he may have lost, but he won again. “And today seems to be a very successful day for me. Should I bet bigger?” - he thinks. And he puts it on. And he wins, and he loses, and he wins again. And, in the end, he bets everything and loses everything. How can this be, he thinks, this is unfair, after all, today is a good day for me, I have to recoup. And he goes to buy more chips. And again he plays until the end, that is, until he loses. Here's how to win at casino roulette. Like?

Probability theory

However, human genius does not want to accept defeat, and numerous “win-win” game systems appear. Probability theory itself was born as a game theory. Playing according to the system is the best answer to the question of how to win at roulette. The video will not help here, you need to understand the essence itself. Of course, you can use the system in a real casino, but the shine of lights, hot looks, and soft drinks that increase excitement do little to help this. Gambling is the enemy of the system. And sitting in front of a computer monitor, you can run any programs, generator random numbers, draw diagrams and graphs and whatever you want. And scrupulously move towards the goal.

It is simply impossible to list, let alone describe, all systems. And it’s not necessary, since they are all based on one thing. Namely, on the fact that the probability of any number, group, or color appearing is the same. For example, out of a hundred throws, the maximum probability of getting black and red is 50/50.

"D'Alembert" system

Let's consider one of the simplest and most reliable systems, namely the D'Alembert system. We always bet, for example, on red. Let's start with one chip. If you lose, we increase the bet by 1, if you win, we decrease it. Let's try.

• Let's put a chip on. Victory. Win 1. The cycle is completed.
• Let's put a chip on. Loss(-1). We bet 2. Loss (-3). We bet 3. Loss (-6). We bet 4. Win(-2). We bet 3. Win(+1). The cycle is complete. Winning 1.

It seems that the result is obvious, slow but sure. Everyone can practice, at least with cubes. But reality is unpredictable. The point is that the probability of the next throw is completely independent of the results of previous throws. And one day the number of losses will significantly exceed the winnings. As a result, the cycle will stretch for an infinitely long time, and the player may not have enough money for the next bet.

So is it possible to win at roulette? Can! If you do not play, then with a 100% guarantee you will win the money that you did not lose.

Many people, when starting to play roulette, remember that they once heard about the theory of probability.
Unfortunately, all this “probability theory” will not help when playing roulette, but will only cause harm.
Let's turn to probability theory.
"The theory of probability studies random events. Each random event is assigned a number, which is called its probability. This number characterizes the chances that the event will occur. If the number of repetitions of the experiment is increased indefinitely, then the relative frequency of the occurrence of the event will be stable to some fixed value and will deviate from it less and less often, the greater the number of experiments. This value is the probability of the event."

The above quote is taken from a textbook on probability theory; the formulas were simply thrown out.
What follows from this is only that probabilities can be used with an unlimited increase in the number of repetitions of the experiment. When we play roulette, we have a fairly limited number of repetitions of experience (roulette wheel rotations). For an unlimited increase in the number of experiments, we do not have an unlimited amount of money and time in reserve.
Apparently, in order to further confuse roulette players, mathematicians came up with the so-called “conditional probability.”

"Conditional probability estimates the chances of event A occurring when it is known that event B has occurred. Conditional probability is calculated using the formula P(A?B) = P(A) P(B)."

Let's look at an example of what will happen if we try to use the above formula.
Let's calculate the probability of getting five simple chances in a row (for example, 5 RED in a row).
We have 5 independent events(“the ball has no memory”), the probability of each of which is 18/37 = 0.49. Probability of a series of 5 RED = 0.49 * 0.49 * 0.49 * 0.49 * 0.49 = 0.03. Yeah, the probability is small, so we need to play against this probability, and we will win. Just how to play? Bet on BLACK five times? But a series of five hits on BLACK has the same probability as a series of five on RED.
Okay, we'll wait for a series of four strikes on RED, and then we'll bet on BLACK. We remember that the probability of 5 landings on RED in a row is very small.
We spin the roulette and finally RED, RED, RED, RED...
Now the moment has come when you need to bet on BLACK. But the probability of getting BLACK has not changed - the ball has no memory. All our calculations and expectations were in vain.
Such a “theory of probability” is also superimposed on the peculiarities of human physiology. Researchers William Gehring and Adrian Viloufbye from the University of Michigan found that losing engages part of the brain's emotion-perceiving area. This zone is a detector of everything negative, and the size of the loss does not matter, and the gain does not affect it. However, the brain takes into account previous experience. A series of losses causes a stronger reaction - as if the "loss detector" is established in the idea of ​​​​injustice. This reaction reflects the gambler's mistaken belief that the next time the roulette wheel will come up is black just because it was red 4 times in a row before.
"The brain believes that it must win - it expects everything to always work out average value", - Goering suggested.
Of course, it is not the theory of probability that is to blame, but its incorrect application. Probability theory is a mathematical science; it operates in the vastness of unlimited repetition of experiments. But it does not provide an answer in simple and specific situations. If we look at roulette theoretically, the advantage is 5.26% (wheel with two zeros) or 2.7% (wheel with one zero) of the bets made. This advantage makes roulette a theoretically losing game.
In fact, roulette is a game of luck and the player has a chance to win.
If there was no house edge and there was no zero, then the outcome of the game would be zero? (Theoretically this is true) No, you would still win or lose a lot more than 2.703%.
There is no need to challenge the casino's mathematical advantage. You cannot eliminate or change this advantage. If you want to do this, you will slowly but surely lose money. The mathematical advantage of a casino is the relatively small amounts of money that can be won or lost very quickly. Think of it as an unpleasant but acceptable tax or payment from the casino for the use of gaming equipment. Remember, you only pay the house edge when you win.

The casino wants you to play forever because, ultimately, the casino has the advantage.
Your goal is to win more money in fewer spins and have clear criteria for when to stop. Will help you win more money in fewer spins good system playing roulette, but to determine the criteria for when to stop -

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

From the past

Roulette - perhaps one of the most popular games of chance today - first appeared in France. According to one version (cited 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 become 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, that is, a man with almost the same surname as Pascal. However, Don Pasquale is also an opera buffa late XIX century, so the existence of an Italian mathematician with that name is doubtful.

Be that as it may, but in late XVIII 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 seemed much more honest - that is, more random - than others that existed at that time. In the very first version of roulette, there were 36 grooves along the rim of the playing wheel, in which numbers from 1 to 36 were placed - in the first version of roulette there was no sector zero. This sector, as will become clear below from the mathematical model of roulette, is needed so that, in a sense, the casino always wins. This oversight (lack of zero) to early XIX centuries were corrected, and some time later, when 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 an alternative version of events: there is an opinion that the wheel with one zero was invented later than with two. They even call specific names inventors of "more honest roulette": Francois and Louis Blanc. They allegedly first introduced single-zero roulette at their casino in the German resort 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 practically since the end of the already mentioned 18th century. The main instrument of the game is the wheel. It represents some inclined funnel-shaped surface (usually not too high - the edges of the funnel should not block the movement of the ball from the game participants). At the bottom of the surface there is a wheel, along the edges of which there are 37 (in the American version 38) sectors, also limited by deflectors. These sectors contain numbers from 0 to 36. Zero is colored green, while the remaining sectors are black or red (the same number of both colors). The numbers on the rim are not in order, however, this is more likely to be tradition than mathematics. If you count clockwise from zero, the numbers are 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, of whom there may be several, are allowed to place bets, and one bet can cover a group of numbers in the amount of 1, 2, 3, 4, 12, 18. The dealer spins the wheel in one direction and shoots a small ball along the inclined surface in the opposite direction. 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 stops, all players are paid their winnings, and the casino takes the losing bets. Winnings are calculated using a simple formula (36 - n)/n to 1, where n is the number of numbers in the group on which the player bet. In the rules of some casinos, the case of a zero is described separately: for example, a gambling house may not take all the players’ bets at once, but offer them the choice of either returning half of the bet now or letting it be played again.

What are the rates? According to tradition, which has nothing to do with mathematics, they are divided into internal and external. To place a bet, a player places a number of chips, representing money, 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 in each, along with the fourth, entirely occupied by zero. This is it inner part fields. Along its edges there are special sectors indicating external bets. It is noteworthy that European roulette usually features large fields - due to their size, the dealer uses a special spatula to move bets around the table, while their American colleagues prefer to use their hands.

In fact, as will become clear from the mathematical model, 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, it is possible to allow players to bet on any combination containing up to 18 numbers (this condition is necessary so that the winnings are correlated with 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 dates back more than 200 years, bets are only accepted on certain fixed sets of numbers:

1. Straight Bet. This is simply a bet on a number, including zero. In this case n = 1 and the winnings are 35 to 1
2. Bet on two numbers (Split Bet). You can bet on two adjacent numbers on the table (including zero) - these, of course, are not all possible pairs. In this case n = 2 and the winnings are 17 to 1
3. 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 winnings are 11 to 1
4. Due to the peculiarities of the location of the zero, a trio bet is distinguished separately - this is a bet on triplets (0,1, 2) and (0, 2, 3). Here too n = 3 and the winnings are 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 arrangement of the zero, as in the case of the trio, there is a bet called a basket - this is a bet on (0,1, 2, 3). The winnings, as in the previous case, are 8 to 1
7. Two lines (Line Bet) - a bet on two adjacent columns, three numbers in each. Here n = 6 and the winnings are 5 to 1

External bets promise much smaller winnings than internal ones:

1. Column Bet - bet on 12 numbers located in one row of the table. Winning is equal to double bet
2. Dozen - a bet is placed on three possible numerical ranges: from 1 to 12, from 13 to 24 or from 25 to 36. The winnings here are also equal to the double bet
3. Snake - a 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 winnings, as in the previous two cases, are 2 to 1
4. Bets even-odd (the parity of the number drawn is guessed), red-black (the color of the number is guessed), from 1 to 18, from 19 to 36 (in both cases the player bets that the winning number will fall within the specified boundaries) bring a winning equal to the bet . They are usually referred to as Even Money.

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

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 winning at roulette. Perhaps the notorious sum of numbers equal to 666 plays an important role here, 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, 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, the probability of each of which being drawn is 1/37. Suppose a player bets on a group of n numbers. We create an equation for a random variable - it takes the value -m in the case when a 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 a number is dropped from the group.

This value models the game process. 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 roulette with double-zero, the losses are almost twice as large). Here you can see why the zero sector was added to the game - if it had not been there, the mathematical expectation would have been equal to zero (in fact, this is due to the fact that the number 36 appears in the winning formula, and there are 37 sectors on the wheel) and the game would go on 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 wonderful expression “You can win at roulette, but you can never win.” The construction of any system for winning at roulette is usually based on a simple consideration: in the general case, the player determines only one parameter of the game - the size of the bet. At the same time, due to the randomness of the process, he only has information about his own or others’ losses at the moment.

Three, seven, ace

Thus, any strategy for winning at roulette 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 specified by them random variables. It just so happens that mathematics is usually expected to answer the question “How to win?”, while it says that any strategy defined in this way for sufficiently large periods of time leads to loss.

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

This strategy, known since the 18th century (it is noteworthy that still, more than two centuries later, there are people who tell the contents of this strategy as a revelation), has two disadvantages: 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 a money-losing fool. A modification of the Martingale is the so-called Dutch system, within which the bets are increased by odd numbers - that is, if the bet was (2k - 1)m, then by next step it should be (2k + 1)m. The maximum bet size is less of a hindrance to this system, but one win is not enough to cover all losses.

What stands apart is a whole class of methods based on an intuitive (and, of course, mathematically incorrect) idea of ​​probability. For example, the Biarritz system belongs to this class. Its essence is as follows: for 36 spins of roulette, on average 24 numbers appear. Accordingly, at least 12 numbers are played more than once. The method looks like this: the player watches the game without making 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 appears only once, the player will return the money, and if more, then he will be in the black!

Here, however, the following fact brings us down: each subsequent rotation of the roulette does not depend on the previous one, so this system is equivalent to a completely stupid and straightforward one - betting on the same number 36 times in a row. The probability of landing 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 with an underbalanced wheel. This option is well described in Jack London's story "The Kid Dreams". One of the main characters of the story, Smoke, notices that the wheel located next to the stove in the Deer 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 also later sells the game “system” to the owner of the establishment.

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

Most popular story This kind of story that claims to be authentic 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 imperfections of the then existing roulette mechanisms. Together with six assistants, he collected statistics on each of the six wheels on the casino floor for 5 weeks. Then, using this information, he began to win in total took 65 thousand francs from the establishment.

A similar story, which happened, however, already in 1948 in Argentina, was described in Time magazine in 1951. Although it 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 proposed convenient methods (tests) for analyzing roulette statistics for the presence of certain 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 takes place with macro objects, it is impossible to talk about randomness in principle. That is, the mathematical model described above simply describes roulette quite well, while in fact, knowing the initial position of the ball, its speed relative to the wheel and some other parameters of movement should ideally allow us to predict where the ball will ultimately land.

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

In 1967, mathematician Richard Epstein wrote in his book The theory of Gambling and statistical logic announced 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 demonstrated that the problem boils down to determining 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 counted. Then many experts concluded that, even if such experiments were carried out, it was obviously impossible to do this in real time - at that time there were simply no suitable resources.

In 1969, Edward Thorpe published an article in the magazine Review of the International Statistical Institute, in which he reported amazing fact. It turns out that the casino's desire to reduce systematic deviation from ideal random statistics makes it easier to predict the movements of the ball. The fact is that when adjusting, the wheel axle is sometimes tilted. Thorpe showed that an inclination of 0.2 degrees is enough to create a large enough area on the funnel-shaped surface from which the ball never jumps onto the wheel. Moreover, using a laptop computer to estimate the speed allows you to bring the expected 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 Thorpe’s problem.

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

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

Fact or fiction?

The work of Michael Small and Chi Kong Tse, a preprint of which is available on arXiv.org, essentially addresses simple question: Is there any truth to the stories about Eudaemons and the Ritz Hotel? How possible is it to predict the performance of roulette in real time? Doubts about the reality of the events described remained 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, the scientists built a fairly simple dynamic model of the movement of a ball in a roulette wheel (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 suitable software. The authors conducted experiments of two types - simple (without additional equipment on the table) and complex (a special camera was installed directly above the wheel). For the experiments, a standard wheel with a diameter of 820 millimeters called President Revolution was used.

Basic parameters required for Small and Tse analysis to work
(Click to enlarge)

In both cases, the researchers needed to determine five parameters. At the same time, the authors of the work, generally speaking, did not care about counting 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 mathematical expectation at 0.18 of the bet (remember that the casinos themselves exist at a modest 0.027 of the player’s bet).

From this, 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 Eudaemons, with the exception of some details of the mathematical model - Farmer and his colleagues believed that stopping the ball is influenced by forces other than those that work in the work of Small and Cohn Tse.

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

People come to gambling for various reasons. Today, you don’t even have to leave your home to do this. Just turn on your computer and use the services of an online casino. Someone wants to tickle their nerves and test their luck. Someone, on the contrary, seeks to relieve nervous tension. A separate category of casino visitors are people who want to make money. One of the most popular games- roulette. And, sooner or later, all players begin to wonder: “How to beat roulette in a casino?” Is there a way to stay ahead? In fact, the idea of ​​making money this way is not new. Since this game can be predicted within certain limits, it is mathematically possible to calculate the probability of winning.

Types of roulettes

Today there are two types of roulette - European and American. The casino profit is 2.7% and 5.3% respectively. The principle of the game in both versions is the same: there is a wheel with numbered cells, and there is a ball. The player needs to guess the number or color of the sector where the ball will land. Based on the above figures, it is already clear that it is easier to beat a casino at roulette if you choose a table with a European version of the game. There are many methods and ways to beat the casino at roulette. All of them are equally applicable to both real gambling establishments and their online competitors. All these methods are mathematically justified and fair only if the casino plays fairly and there are no blocks on a series of identical bets. But, as you know, any gambling is a scam and a risk. And you need to outsmart fate. Otherwise, how to win at casino roulette?

Martingale method

The simplest and most common way to beat roulette. The essence of the method is as follows:

1. Select the minimum bet with which to start the game.

2. After each loss, we double the amount so that when you win, the profit is equal to the initial bet.

3. Did you win? Great! We immediately return to the minimum bet.

The method is old, it was invented back in the 18th century, but even today it has not lost its relevance. After all, everything that we have that is new is long-forgotten old. In each cycle of the game, you must bet on one of the options - red or black, and in no case change your choice when increasing the bets.

Is it possible to beat an online casino at roulette using this method? Most likely not, because everyone knows it, and the rules of the game can take into account its application. First of all we're talking about on limiting the number of identical bets. That is, at a certain move in the series it will be impossible to bet on the same sector. Also, some casinos limit in their rules maximum amount- 10-100 initial bets.

Fibonacci method

The method is similar to the previous one. How to beat roulette in a casino with its help? It is enough to follow the following rules:

1. You need to select a minimum bet.

2. After each loss, we increase it by a multiple of the Fibonacci series (for those who don’t remember, it’s 1-1-2-3-5-8 and so on).

3. If you win, you do not need to return to the minimum bet - you need to step back two numbers in the Fibonacci series.

4. The game cycle ends as soon as you return to the minimum.

You must bet on the same color in each series - black or red.

The main difference between this method and the previous one is that the probability of reaching the maximum bet is much lower, due to which the series can be significantly extended. Also, each game can end with either a negative balance or a positive one.

Labouchere system

This is a fairly simple game strategy. It also answers the question: “How to beat roulette at an online casino?” Using this method, you can quite easily control your bets and keep track of your winnings.

The essence of the method is as follows:

1. We will use the game on equal chances: black-red, even-odd and the like.

2. At the very beginning of the game, you need to come up with a random number from 1 to 9; optimally if there are 4-6 numbers (for example: let our row be 4-1-7-3).

3. We determine the bet by adding the extreme numbers of our series (in our case it is 4+3=7).

4. If we win, the last numbers are crossed out (we are left with 1-7). If the row ends, then a new list is invented.

5. In case of loss, you need to add to the amount equal to the lost bet (for us it is 7, and the row will look like this: 4-1-7-3-7, which means the next bet is 4+7=11).

There is also "Reverse Labouchere". In this case, if you win, the last bet is added, and if you lose, the last numbers of the series are crossed out.

"Three for three spins" system

How to win at roulette following this strategy? Much easier and faster than previous options. The idea is to place three bets simultaneously in one spin. The game series lasts three spins.

The likelihood that you can beat roulette using this method is very high, but also minimum bid has a higher size - a multiple of 17. You need to bet in a ratio of 9:6:2 on the following positions:

• 9 units - for “smaller”;
• 6 units - for the third dozen;
• 2 units - for the corner of the numbers 19, 20, 22, 23 or 20, 21, 22, 24.

In this case, with a bet on 17, the winnings will be - 18. In one spin you can win one unit (with a bet on 17 - 1, with a bet of 34 - 2). You can also lose in this case: if you get zero or the numbers 21 and 24 (depending on the selected corner).

The chances of winning with such a game are very high, much greater than when using the previous three methods.

System "Dozen and a half"

The essence of the method is as follows:

• We expect the non-winning numbers 19, 20, 21, 22, 23 and 24 to appear;
• skip one spin;
• We place equal bets on the lower number and on the third dozen;
• if the smaller number is rolled out, we return the bet; if the third dozen is rolled out, we return one and a half bets;
• after winning, we continue to wait for the numbers from point 1 to appear; if we lose, we increase the bet using the Martingale method.

It is worth noting that if a “zero” appears, the player also loses his bet.

System "31"

This is the most convenient game when betting on even odds. How to beat roulette in a casino this way? You need to follow the instructions:

1. The initial bet is 1 on even odds.

2. If you win, we double it.

3. In case of loss, we increase the bet according to the progression 1-1-1-2-2-4-4-8-8. If we win a spin, we return to the initial one.

Minimum amount of funds for this method games - $31. This amount will allow you to withstand ten losing spins. It should be noted that this is quite unlikely, but also possible.

If you win twice in a row, you should return to your initial bet. This will reduce the risk of completely losing all your money at roulette. After all, winning generates excitement and the erroneous belief that luck is on your side.

Albert Suarez system

The essence of the whole game is as follows.

1. Collect statistics of the last 75 spins.

2. Based on the results of the games, we determine the missing numbers. If there are none, then we take statistics from another table.

3. We bet one chip on the numbers that did not appear during the next 37 games.

4. When a number appears, we increase the bet on it by one chip. But you don’t have to do this, but always set it the same way.

5. Over the next 37 spins, one of the numbers will appear at least twice, and you can make an excellent profit on this.

Belle's repeating number system

The method is very similar to the one described above. Because it also uses statistics from previous games. The method looks like this:

1. We skip a series of spins until a number appears twice.

2. As soon as this happens, we place 1 bet on this number for the next 37 spins.

3. If during a series a certain number appears twice, we begin to bet on it too.

4. If this number does not appear again in 37 spins, then we make the following selection according to statistics.

These are just a few of the most popular and simple ways How to beat roulette in a casino. There are still a huge number of them: different in terms of minimum financial support for one game series, differing in their complexity. Nothing will prevent you from developing your own way of playing roulette - it will only increase the likelihood of winning.

It is worth noting that the casino administration knows about everyone known methods achieving regular winnings at roulette. It is in their interests to protect themselves from clients who use these methods. This is the goal of the administration as real gambling establishments, as well as online casinos. Therefore, an integral companion of any successful player, just like a hundred or two hundred years ago, is luck, without which gambling difficult to win.