Quite a complex guide unknown author about how to win at roulette in a casino online or offline.
What methods were used and on what factual material was this technique written?
This methodology was written over 4 years based on the following statistical material:
A) Games and statistical material in the following Moscow casinos: “Podkova”, “Grand”, “Royal”, “Golden Palace” - more than 10 thousand games of roulette and blackjack;
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; the results of more than 10 thousand games of roulette and black jet in the general room were recorded.
Myths of Internet casinos
Please read it carefully, because... It is this text that contains the raisins that I picked out from the article in order to prevent freeloaders from using this technique. What is not in the article will be noted: Highlight1, Highlight2…
You can skip this section now and move on 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 that is necessary in the game:
Myth No. 1 – the results of Internet games are completely random
Wording: The result of online games (roulette, blackjack, etc.) is absolutely random, because generator is used random numbers is an advertising bait based on your ignorance of special branches 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 connected in ANY WAY with other numbers in the sequence. The implication is that this sequence is INFINITE.
And any FINITE sequence is perfectly described by a polynomial (polynomial) of the nth degree, where n is the number of terms.
I translate from Russian into Russian: For example, you played 6 games of roulette (6 is a conditional number, so that any reader can verify in Excel that I am right). ANY dropped numbers can be perfectly described by a polynomial, with any accuracy. For example, one day the following sequence appeared: 29,10,26,2,33,22 (all numbers are black, see Figure 1) And it is absolutely EXACTLY described by a polynomial. ABSOLUTELY accurate:
It's 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. This illustration shows screenshots of the results of real roulette games in 3 casinos. Below are the results that ALREADY happened BEFORE the start of the game, the beginning of the games is marked with a red triangle. See how interesting it is?
Highlight1: On the middle indicator (with black background) last result before the start of the game, red, the number 9, came up, and a red-black transition took place (then the number 4, black, came up). This transition did not occur on other indicators.
Any Internet casino program has a single or multi-threaded pseudo-random number generator, which generates them according to some algorithm or several algorithms (you must agree, if there is a generation algorithm, what kind of randomness is there?).
Highlight2: It doesn’t matter to us at all whether the sequence is random or not – we care about winning. He has nothing to do with the sequence of numbers, it depends on the number of draws that took place. Next we will make sure that this is exactly the case. When you enter the game, a sequence of results begins to be generated. It is generated even if you do not play - go to the common room of any casino and check.
Moreover, every time you enter, this sequence is DIFFERENT (except for the case when someone else is playing in the common room).
Highlight3: And this is very important! These sequences more or less fit the definition of a random number sequence (less so if the casino owner begins to manipulate the generator). So it applies to them
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 general hall of the casino, and you see that the indicator shows that in previous drawings Red appeared 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 discussions refer to Cherny).
We do not consider other cases, because in most casinos the indicators only show the previous 10 results. We take into account the loss of Zero, 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 of the last red numbers is 18/37, or 0.4865 (there are 18 red numbers in roulette, 37 total numbers in roulette - another 18 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)…
Formula for the probability of getting red: VerKr=(18/37)^(n+1), where n is the number of identical colors drawn in a row before the start of the game, from 1 to 10);
Formula for the probability of getting red: VerKr when getting a Zero in previous drawings: Вн=(1/37)*(18/37)^(n+1), where n is the number of identical colors drawn in a row before the start of the game, from 1 to 9) ;
In the general casino hall, drawings are carried out without your participation - even if you do not bet, after 1 minute the roulette wheel begins to rotate. You are not playing yet, you are simply observing the results of the draw. Probabilities of getting a Red number when next draws(which you ONLY observe), depending on the results of previous draws, are shown in columns.
Highlight4: The results of the drawing do not depend on your bets - you do not place them at all!
Here's an explanation Highlights2! We don't care whether the sequence of numbers is random or not. It is important for us to make sure that the theoretical probabilities coincide with practice.
Highlight5: It is especially important to understand that the probabilities, and not the next results themselves, depend on the results of previous draws.
This is precisely the main difference between a Player and capital letters(one for whom gaming is a way of earning money, a profession) from the player. The player bets on probabilities and understands that the result does not depend on his previous bets or previous results. Only the probability of the next result depends on previous results.
In other words, they understand the difference between theory and practice: probability is theory, result is practice.
Highlight6: A small clarification - in fact, the probability of previous and subsequent draws indicated in the table is absolute for infinitely large number pranks. We participate in a large, but finite number of drawings. And a probability of, for example, 48.65% is the most probable of the probabilities, the actual results fluctuate within a certain range. But we will apply a principle that will allow us to consider this probability as absolute.
Highlight7: Be sure to check these theoretical arguments - go to any casino!
For example, in the Planet of Fortune casino. All calculations are based on the example of this casino.
Myth No. 2 – md5 is ideal control of fairness in the game
Another myth: Many gambling establishments refer to md5 as the ideal control for game fairness. But…
“If it were possible to set different initial values of the MD5 registers of the processor from those inherent in the algorithm, then it would be possible to select two different messages ... such that the same digest could be built. What, in fact, was done in this cryptanalysis .... The author of the message, Hans Dobbertin, found that if we use the following initial values of the MD5 registers of the processor ... And set the value of the data block to be converted as follows .... Then the second message can be constructed 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 sequence of characters for which the MD5 will be the same.
The casino provides the player with the sequence and an MD5 hash to it. Having received a sequence, the player can calculate the MD5 from it and make sure that the resulting sequence matches what happened in the game. It turns out that a casino can create several different sequences with the same MD5 and use this to cheat.
And 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 is enormous in 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 “prance” with this: Before starting the game in the “randomness control” mode, you create (by pressing a button) a series of numbers that will appear sequentially 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 this really so? Can you check this? What follows is 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 generally accepted and widely used algorithm in the world. The essence of his work is that as a result of text processing, he produces a unique sequence of characters (the digital signature itself), which, with the slightest change in the source text, changes beyond recognition. It is impossible to find such text, when processed using the MD5 algorithm, the same digital signature will be obtained as when processing other 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 proved the fundamental possibility of such processing and cutting. If you can replace a sufficiently long sequence, then present a short one instead of a long one - even more so. You just have other numbers
don't see.
This suggests that, if the possibility of substitution and slicing exists theoretically, then casino references to honesty are a publicity stunt. They must prove that this sequence manipulation does not exist in their casino. And this is impossible to prove 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 quite long.)
Accordingly, the casino server may be guided in the game not by the sequence generated by the RNG, but by the balance of the given player. For example, so that he would be at a loss of -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 - the job is done! Honesty guarantees are 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 probability theory to the game of roulette
Many obvious misconceptions and simple mistakes wander from book to book, from century to century. For example, this:
When betting on a number, the casino pays out 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. When you lose, pay nothing but lose. 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 house (casino) advantage.
Let's calculate the advantages of the house. We subtract the fair win from the actual win, multiply by the probability of the number being drawn, and multiply by 100 to convert it into 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) one chip at a time, you will still lose 1 chip. To convert to a percentage, take the ratio of the result to the bet size and multiply by 100. The result is minus 1 chip, the bet is 37 chips. (-1) / 37 * 100% = -2.703%
Let me! With bets on a number, everything is clear - we placed 37 bets of 1 chip on all numbers and Zero - in any case, we got 37 if the payout is 36 to one + our bet. But what about the split? The payout is expected to be 18 to 1 + our bet. We decided to bet the same 37 chips - 2 chips for 18 splits and 1 chip for Zero. And the casino must rely on Zero - when ANY number comes up, we get 18x2+2 of our chips. We win + 1.
Similarly, for bets there are equal chances, per row, per dozen, per 6 in a line, per corner (square, corner, square) (do the math yourself).
And all because such articles are written by order of casino owners, from the very beginning there is NLP (the logic is clearly lame, but they seem to criticize the casino - and the reader perceives the text uncritically). As a result, this is the conclusion drawn in this article (not substantiated by anything, by the way, except for obvious fraud):
It should be borne in mind that roulette has one advantage over the player - if the game is long enough, any betting system will LOSE.
Let's call a spade a spade: the casino wins IN ANY situation only if the player plays number, split and straight (the casino really "breaks" there). 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 player going overboard, wanting to quickly and easily “make money”, and starting to bet supposedly the most favorable rates- per room, split and street. In this case, he quickly loses. And the article unobtrusively pushes the player towards this.
Such juggling occurs due to an elementary substitution of concepts:
Subject of probability theory- This theoretical study such experiments in which, under the same conditions, the occurrence of mutually exclusive events is possible. Under the same conditions.
Do Internet Roulette have the same conditions? No, the number dropped 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 are rolled in a row, this EQUAL values DIFFERENT members of the sequence.
Are the conditions the same in real roulette? No, the number drawn is strictly determined physical properties wheel and roulette ball, psychophysiology, motor skills, skills, etc. of the dealer.
So they are trying to measure the current in kilograms, mixing 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 that old maids have many cats that eat mice and rats. More wild bees remain in this area (mice and rats destroy their swarms), clover is better pollinated, harvests are larger, cows eat better and produce more milk.
The wording is especially touching independent events.
There are no such events in probability theory. These pseudo-specialists are confusing independence random variables And mutually exclusive events (numbers appearing in each spin is mutually exclusive events, but all events are the occurrence of 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 table of European roulette. Note that we place bets on the table, and the numbers fall out in 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 there are 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 inconsistency of the arrangement on the table, there are only 4 red numbers in the middle column (by the way, there is such a paradox: we bet 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 equally probable bet on the 3rd column 5 units and on the 10 remaining red numbers 1 unit. (We closed all red numbers and 4 black ones, i.e. probability of success = 22/37). Why do we set 14 units in the first case, and 15 in the second? 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 covers a larger arc of the wheel than a bet on 4, 5, 6 (see for yourself how much distance is between the numbers). It's important to understand, that we bet not on numbers, but to 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 number dropped in each spin supposedly “has no memory” and does not depend on the previous spin.
Before the new spin, the wheel stopped in a certain position relative to
Dealer, What is the conclusion from this? The result of the subsequent 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 full revolutions along the stationary wheel plus a certain part of the revolution. Then the wheel made M full revolutions plus a certain part of the revolution and stopped in a new position relative to the dealer.
It’s the same on the Internet wheel - can there be a RNG algorithm that will correspond to the placement of numbers on a real roulette wheel?
Look - 10 black ones came up in a row. The player has last bid, he bet on red, doubling. Should he continue betting on red, or should he bet on even?
There is 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... Red arrows show the placement of results
previous spins.
It is clearly visible that the casino server in this game was not guided by the sequence generated by the RNG, but by the balance of the given player. Or the RNG generates a sequence in which the distribution of numbers is DIFFERENT from the distribution of numbers in real roulette.
Principle of the game and calculation of win-win bets
All roulette manuals say that when Any game, including the Red/Black casino always wins, because... There is also a chance of Zero falling out.
This is not true - no one is stopping us from betting on color and 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), given in advance, our winnings will always be greater than our bets and will always be maximum under the betting conditions of this casino. Let's call this principle Compensation for Zero. By the way, it is precisely this principle that allows us to consider the probability absolute - Zero sometimes falls out, and this is significant (see. Zest6).
Let's introduce the 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 bets “on equal chances” - from 1 to 50 to 1 to 80; ratio of minimum “even chance” bets to minimum rates“per number” - from 1 to 10.
To understand what winning or losing depends ONLY on this ratio, Let's consider n bets on Zero and black at the same time (a bet on color is more convenient - in all online casinos, indicators show red and black in color and the distribution of red and black on roulette is almost even.)
Let's start with equal bets: On Zero (StZ) = 1 unit; Per H (StCh) = 1 unit.
Winning on zero (Вз)=35 units; Win on black (HF) = 2 units. Loss (P)=2 units.
With n tending to infinity, the probability of getting a Zero (VerZ) = 1/37, the probability of getting a Black (VerCh) = 18/37, the probability of getting a Red (VerKr) = 18/37.
Our most probable win (NVV)=[(Vz)*(Ver3)+(Vch)*(VerCh)]*n=n*= n*, or n* 1.972973
Our most probable loss (NVP)=[(P)*(VerKr)]*n=n*, or n* 1.027027 Ratio (NVP)/(NVP)= 1.921053
Note that it is irrational to increase the bet on Zero, because in the case of (StZ)=N*(StCh), N>=2 Winning on black HF does not pay off the amount of bets.
Obviously, the maximum ratio (НВВ)/(НВП) = 1.998413 is achieved at the ratio (StZ)/(StCh) = 1/34
notice, that we have strictly proven the impossibility of losing in such a game scheme with n tending to infinity.
That is, theoretically, loss is excluded with such a game scheme.
I note that the player ratio (StZ)/(StCh) = 1/17. In this case, the winnings on Zero and Black exceed the bet amount by 34.
Independent formation of the probability of a favorable outcome
Betting on black and zero in a row is good, you say, but it happens that 9 or 10 results in a row come up when red comes up.
And you will be absolutely right.
And I'll be right. Here's what:
Nobody obliges you to play in all draws– remember, do real casinos require customers to play?
You can, upon entering the common room, wait for the favorable probability of the draws that have already taken place, or
Re-enter 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 plenty of other casinos.
This is an extensive way - to seize the moment, assuming that the sequence of numbers is close to a random sequence.
So, for simplicity, let’s assume that you need to earn money per day. And you will also start the game with a sum of money. Suppose also that you have a supply of money sufficient to fail once in a row and still win the next time and earn your own amount of money. To do this you need to have:
Suppose you want to earn money this way for 20 years. This turns out to be about 8000 days. This is how many times your scheme should work. Let us denote this number by the letter .
The probability of winning at roulette when betting on red/black is equal to , and, accordingly, the probability of losing in this case
Let another day of play begin. The probability that we will lose once in a row today (having spent the entire reserve) is equal to:
Well, and, accordingly, the probability that this unfortunate event will not happen today (that is, we, as prescribed by the strategy, will get our money and get out of the casino) is equal
But we need us to win every day, for days. The probability that we will never lose during these days will be equal to:
From here it is clear that there is always a chance of losing. The given formulas do not imply the probabilities of 0 or 1. But let’s try to extract something from the resulting formulas. Let's find, or more precisely, estimate the number . Let’s assume for simplicity that the probability of not losing in a matter of days is close to 1 (after all, this is what we are trying to achieve). That is:
Then, using (1), we get:
(2)
Let's take the logarithm of both sides of equality (2):
(Here we use what 
with and instead of the icon I just wrote )
Let us raise the exponents to powers equal to the left and right sides of (3) and equate them:
In expression (4), the exponential on the right can be expanded in terms of a small parameter:
Using (5) we can rewrite (4) as:
Or, remembering the definition:
Taking logarithms from both sides of equality (6) we obtain the following expression:
(7)
Let's take for example
Then, from formula (7) it follows that in order for the strategy to have a 99% probability of success over 8000 days of play, it must be equal to 18. Is this a lot or a little? That's a lot. This means that in order to make money every day at the casino, you need to have money in your pocket every day. This is already a huge amount. Do you want to earn 100 dollars every day in a casino for 20 years? Be kind: carry $260,000,000 with you every day.
Even if you have needed money. Let's estimate: in a year of playing in a casino you will earn money. And if you put the same money in the bank, let it be, for ease of calculation, at 3.125% per annum (3.125% corresponds to ). Then the earnings in the bank will be , which is 22 times more profitable than playing in a casino with the same amount of money in your pocket.
That is, we see that in the game strategy described above, the law is hidden from the eyes of naive money makers large numbers. If you have a jar of jam, you can try a spoon - there will be almost as much jam in the jar as there was. But if you take a spoonful a day, the jar will still become empty.
As Augie Morosco said in the movie “Once Upon A Crime”: “There is no system in roulette, believe me... If you want to win at the casino, don’t go there.”
Is it possible to win at roulette on the Internet?
Yes, you can. The same goes for other gambling and lotteries. But usually in online roulette the casino wins. Because the rules of the game of roulette are designed in such a way that the player always has less chance of winning than the casino.
Let me give you an example. As is known maximum win is 1 to 36, and there are 37 numbers used (from 0 to 36). That is, if you bet 1 ruble on all numbers, then the costs will be 37 rubles, and the winnings will be only 36. One ruble will remain with the casino forever.
But don't despair. The chances of winning at roulette are always greater than at the lottery. In particular, in the USSR, in the DOSAAF lottery, only 50% was spent on paying out winnings.
And unlike any lottery, you choose the numbers you will bet on. Moreover, you can change these numbers during the game. This is what distinguishes roulette from “Gosloto 5 out of 36” and similar ones, where you can also choose the numbers on which you will bet, but only before the start of the draw.
Probability theory when playing roulette
The wonderful science of “Mathematics” is needed not only for counting change in the store. Everyone who received higher education, you probably remember one of the branches of higher mathematics - probability theory.
Probability theory is a branch of mathematics that studies the patterns of random phenomena: random events, random variables, their properties and operations on them. (material from Wikipedia)
In essence: random phenomena are described by law! This is what we need! After all, the numbers that appear when playing roulette are random (ideally, if you do not take into account the uncleanliness of the casino, a crooked table, a stuck roulette, an interested dealer, etc.) Thus, Knowing the sequence of numbers drawn, you can predict with a certain probability which number will be next!
Let's look at the simplest example.
Playing for “black” or “red” (even-odd, less than 18, more than 19).
At the beginning of the game. That is, if you have never spun the roulette before and, accordingly, not a single number has come up. The probability of “red” and “black” is 18/37 = 0.486. And the probability of Zero is 1/37 = 0.027.
If, for example, the result is “black”, then the chances of “red” in the next round increase. And they will be equal to 1 - 19/37 = 0.736. If black comes up twice in a row, then the chances of “red” increase to 1 - 19/37*19/37 = 0.865. Of course, this is not a 100% guarantee of winning, but there is a chance of success.
In order not to bore you with calculations, I will provide a table with the results.
Table 1. 
As you can see, the more blacks appear in a row, the higher the chances of red in the next move. BUT!!! The probability of getting red will never be 100% NEVER. In other words, there is no guaranteed win at roulette.
Roulette statistics
How many times in a row can “black” (or “red”, or even, etc.) appear? As many times as you like, at least 500. But according to statistics, everything is limited to 10 repetitions. History knows only a couple of cases when repetitions amounted to more than 10 balls in a row. Of course we are talking about honest casinos :)
Roulette tactics
The basic rule of playing roulette is to bet on those numbers that are more likely to appear. To do this, you must have statistics on the sequence of dropped balls. It is impossible to apply this tactic in a real casino. You will not be allowed to write anything down or calculate anything. Therefore, all of the above is true only for Internet roulettes in electronic virtual casinos.
Martingale method
The Martingale method is considered one of the win-win methods of playing roulette. I want to emphasize the word “win-win”. Not “winning” at all. Remember that all the advertised methods of playing roulette allow you not to lose longer, and, if possible, to win if you are lucky.
The essence of the method is to double your bets in case of loss.
First time - 1 ruble (let it be a ruble, let's support a domestic manufacturer 🙂 (if you win - income 1 ruble and start from the beginning)
If you lose, then bet 2 rubles (if you win, income is 1 ruble and start from the beginning)
If you lose again, then we bet 4 rubles (if you win, then the income is 1 ruble and we start from the beginning).
More details in the table:
Table 2. 
That is, to win 1 ruble in 10 steps (we will assume that the maximum sequence of one color is 9) you must have 2047 rubles in your account! That is, you must have funds for such a bet. But the saddest thing is that the rules of many casinos have restrictions both on the maximum bet (for example, 1000 rubles) and on the ratio of the minimum to the maximum (usually 1:100). That is, if you started the game with a bet of 1 ruble, then your maximum bet will be 100 rubles. According to table 2, this is line 7. And the probability of winning, according to Table 1, will be 0.990584. And as you know, a sequence of one color can be continuous for 9 rounds in a row.
To at least slightly increase the probability of winning, it is more accurate not to lose until the 7th round. I slightly modified the method. The level of rates in which is shown in Table 3.
Table 3. 
As you can see, the income from this method is less. But the probability of losing is also lower. Now the bet threshold of 100 rubles is reached already in the 8th round, where the chances of success are higher.
How to use the Martingale method or the rules of roulette
It is necessary to analyze the dropped balls for compliance with the following sequences:
- Black (black-black - sequence of one color 2 times)
- Red (red-red - sequence of the same color 2 times)
- Color change (black-red-black - color change sequence 2 times)
- Even (2-12 - sequence of even 2 times)
- Odd (33-17 - sequence of odd 2 times)
- Parity change (28-5-14 - parity change sequence 2 times)
- Under (1-18) (11-8 - sequence “under” 2 times)
- More (19-36) (21-35 - sequence “more” 2 times)
- Shift “more-less” (27-4-19 – change “more-less” 2 times)
For example, the numbers fell 17-14-9
Let's analyze them.
17(black+odd+less)
14(red+even+less)
9(red+odd+less)
What do we see? There was a change of parity 2 times, 2 colors in a row (red) and 3 times the “under” was rolled. Thus best choice, according to Table 1, there will be a bet on “over”. If we lose, then we will use table 2 or 3 and place bets according to them. If we win, then we analyze the current situation.
For example, 23 was rolled.
And our sequence became 17-14-9-23.
We analyze.
17(black+odd+less)
14(red+even+less)
9(red+odd+less)
23(red+odd+more)
As you can see, there was “red” 3 times in a row and it makes sense to bet on black in the next round.
And so on. If we win, we analyze the sequence; if we lose, we use the Martingale method.
How much can you win at online roulette using the Martingale method?
As a rule, for 1 hour of play, income increases by 10-20%. With the restrictions imposed by casinos, losses are inevitable. In addition, the maximum income of 1 ruble does not contribute to quick enrichment.
Criticism of the Martingale method
Small income if you win.
Large amounts when betting.
Casino betting restrictions will not allow you to advance beyond the 7th round.
Alternative methods of playing roulette
By analogy with the game of half (black-red, even-odd). You can make tables of probabilities for playing by a third (columns and dozens). Where the winnings are greater and amount to 1 in 3. But the probability of winning is also less.
Criticism of roulette playing methods
One of the main arguments among critics is that the ball has no memory. And therefore, red, for example, can appear at least 500 times in a row. That is, the probability of getting a particular number is reset after each throw. In other words, if the probability of getting red is 18/37 = 0.486, then this value is constant from throw to throw.
From this they are trying to conclude that all methods of playing roulette are complete nonsense.
But statistics show that probability theory works great when playing roulette. And only restrictions in the rules of the game introduced by casinos do not allow turning gambling into a source of income.
How to win at roulette
By observing several simple rules You can make money at roulette. If you just sat down at the table, then miss a couple of ball throws. This will allow you to get a certain sequence of dropped numbers. And thereby push back the barrier of 7 or 8 games a couple of steps. By doing this, you increase the likelihood of your winnings. Don't be tempted to bet all your money, even if you see red 9 times in a row. If you are not sure what to bet on, then it is better to skip the move.
Instead of an epilogue
You can win at roulette. At the very least you don't have to lose. But the crumbs earned are not worth the time spent on them. That is, you cannot count on playing roulette as a source of permanent income. Moreover, at the slightest deviation from the rules and recommendations described in this article, you will quickly lose.
The rules of roulette were developed by people well versed in mathematics. And mathematics is a science. Believe that knowledge ordinary person It’s not enough to come up with a technique for winning at roulette. Methods and programs that are widespread on the Internet are created with the aim of profiting from those who want to get rich by playing roulette.
Modern roulette rules are designed so that the casino always wins. As one of my friends says: “You can only win at a casino if you have more money than the casino, but then why go to the casino?”
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 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, 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 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 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 “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 participants in the game). 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, the player places a number of chips, representing money, on a fixed area 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 the inner part of the field. Along its edges there are special sectors indicating external bets. It is noteworthy that European roulette usually has large fields - due to their size, the dealer uses a special spatula to move bets around the table, while their American counterparts 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:
- Straight Bet. This is simply a bet on a number, including zero. In this case n = 1 and the winnings are 35 to 1
- 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
- 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
- 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
- Corner Bet. They bet on four adjacent numbers on the table. In this case n = 4 and the payout is 8 to 1
- 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
- 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:
- Column Bet - bet on 12 numbers located in one row of the table. Winning is equal to double bet
- Dozen - a bet is placed on three possible numerical intervals: from 1 to 12, from 13 to 24 or from 25 to 36. The winnings here are also equal to the double bet
- 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
- 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. Space possible outcomes consists of 37 elements, the probability of each of which 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 winning system at roulette is usually based on a simple consideration: 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 the random variables specified by them. 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, in which bets are increased by odd numbers - that is, if the bet was (2k - 1)m, then at the 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.
Apart from this there 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 later sells the game “system” to the owner of the establishment.
Still from Raimondas Vabalas' film "Smoke and the Kid"
The most popular story of this kind that claims to be reliable 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 and in total took away 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 is played 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. Hence, the great mathematician and physicist concluded that in principle there could be no reasonable theory for predicting the position of the roulette wheel. 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 an 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! Wherein practical part A study carried out 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, scientists built a fairly simple dynamic model of the movement of a ball in roulette (it must be said that there are more serious and realistic models, which, however, are more complicated 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 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
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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, 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, 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.
Every player, both beginner and experienced, wants to guess winning number while playing roulette. Not 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 an analysis of European roulette, proposed an effective gaming system. A preprint of the study is posted on the university website in the archive section, which is available for free downloading.
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:
- You should analyze how the ball and the wheel move. They can be affected numerous factors. This is a labor-intensive process that requires concentration and attention when calculating the trajectory of the elements. It is important to remember how the roulette was turned before the start of the game, in particular which sector. Using this method, you can increase the likelihood of winning. It is worth keeping in mind that it does not provide a 100% guarantee. Also note that it only works in land-based casinos. This method is ineffective in virtual games.
- You need to place bets in sequential order on one sector. Winners large sums players claimed that this was due to persistence. They always bet on one number. It is worth noting that this method has high risks.
- You need to find a roulette wheel that has defects. It is worth noting that in real casinos the wheels may become “crooked” over time. In this case, you can see that some numbers appear noticeably more often than others. IN virtual game This 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 watch the game over a certain period of time, and then you can bet on the numbers that came up most often.
- Place bets not on one roulette number, but on a whole series. According to professional players, this increases the possibility of winning, because there is a greater chance that the ball will fall out within one series rather than within one number.
- You need to choose one gaming system and stick to it. If you use several tactics at the same time, the likelihood of losing increases significantly. It is recommended to choose the most time-tested system and stick to it throughout the game. For example, you can bet exclusively on odd numbers or on the color red. You can use Hook's 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 a casino.
