roulette
Roulette [ ruˈlɛt ] ( fr .: cog) is a traditional game of chance that is widespread worldwide and is mainly offered in casinos . The roulette called the game, the roulette is the roulette machine.
In roulette you bet on numbers or certain properties of numbers that are determined by the random run of a ball in a bowl.
history
The invention of roulette is often attributed to the French mathematician Blaise Pascal  but this is based on a misunderstanding: Pascal was one of the pioneers of probability and wrote his Histoire de la roulette and Suite de l'histoire de la roulette in 1658 , but act these writings not the roulette game, but from the French and Roulette called cycloid .
Italy of the 17th century is often cited as the country of origin , after all, Meyer's Konversationslexikon still referred to the large roulette with the 38 numbers 00, 0, 1–36 as Italian roulette around 1900  in contrast to the small or German roulette, which like the boules The game only knows 18 subjects. The roots of roulette, like those of the wheel of fortune, can be found in the medieval wheel of Fortuna .
Roulette came to France during the 18th century , where Louis XV. tried in vain to ban. In 1806, Napoleon Bonaparte only allowed gambling in the gambling houses of the Parisian Palais Royal , where roulette was played alongside Pharo and Rouge et noir and Trente et quarante until it was closed by LouisPhilippe I at the end of 1837 .
The time after 1837 was the heyday of the casinos of BadenBaden , Bad Homburg and Wiesbaden , where Fyodor Michailowitsch Dostojewski got to know roulette and fell for the game  the novel The Gambler was born from this experience .
In order to make the game in Bad Homburg more attractive and to give the casino a competitive advantage over the other casinos, François Blanc waived the double zéro in 1841 and thus reduced the casino’s advantage over the punchers , which the other casino operators soon followed suit Blancs followed. In the US, the double zero is still common today.
After the founding of the empire , all German casinos had to close at the end of 1872; they were not reopened until 1933 under the National Socialists .
The principality of Monaco benefited from the gambling ban in France and Germany . François Blanc took advantage of this opportunity and ran the Monte Carlo casino in its heyday.
Today roulette is played in casinos all over the world according to almost identical rules. Differences essentially only relate to whether or not Double Zéro is being played and to the rules for the event when the ball lands on Zéro.
The French roulette
The gaming table
French roulette is traditionally played on double tables: In the middle of a long table covered with green cloth (tapis) , the roulette wheel (cylinder) is embedded in a recess, to the left and right of it are the betting fields (tableau). Each table is looked after by eight employees of the casino , the cylinder is in the middle of four croupiers , another croupier sits at each head end and a separate chef de table is responsible for each half of the table .
Today, however, the game is mainly played at single tables , which are looked after by four croupiers: the roulette wheel is at one end of the table and there is only one tableau in the middle of the table.
The roulette machine (bowl) consists of a rotatable disc embedded in a bowl with 36 alternating red and black number compartments and a 37th, green compartment for zero ( Zéro ). The roulette bowl or cuvette used to be made of ebony , but today plastics are also widely used.
The winning number is determined with the help of a ball  previously made of ivory .
The course of the game
The aim is to guess in every single game (coup) which number the ball will fall on.
With the request "Faites vos jeux!" ("Make your games!", English "Make your bets!") The croupier asks the players for their bets. These are done with tokens . Either the player puts his chips on the tableau himself or he asks the croupier to do this for him and names (advertises) the number or group of numbers that he would like to bet on.
The stakes must be at least the minimum specified at each table and may not exceed the maximum , which varies depending on the type of bet .
If enough bets have been made, the croupier sets the roulette wheel in motion and throws the ball against the direction of rotation into the cylinder. You can still bet now. After the announcement “Rien ne va plus.” (“Les jeux sont faits.”, “Nothing works.”, English “No more bets.”) It is no longer possible to bet. As soon as the ball remains in a number compartment, the croupier says the winning number, its color and the other winning simple chances (see below) aloud, and points to the winning number with his rake (rateau) .
First the losing stakes  the socalled mass  are collected; then all chances associated with the winning number are paid out.
The betting options
Simple opportunities
The most popular type of bet in roulette is betting on the simple odds. The numbers 1–36 are divided into groups of 18 numbers in three different ways, these are:
 Rouge ( Rot, Engl. Red ) and Noir ( Schwarz, Engl. Black ),
 Impair ( odd, Engl. Odd ) and Pair ( Straight, Engl. Even ) and
 Manque ( Low, English 1–18 ) and Passe ( High, English 19–36 ).
If you win, you get a 1: 1 win.
Multiple opportunities
 Plein, engl. Full number: You bet on one of the 37 numbers, the payout ratio is 35: 1.
 Cheval, engl. Split: You bet on two adjacent numbers on the tableau, e.g. B. 0/2 or 13/14 or 27/30, the payout ratio is 17: 1.
 Transversale pleine, engl. Street: You bet on the three numbers in a row of the tableau, e.g. B. 19, 20 and 21, the payout ratio is 11: 1. If you do not place the bet yourself and ask the croupier to place the chips, you always name the lowest and the highest number when you bet on a group of numbers. In this example "Transversale 1921".
 Les trois premiers, engl. First three: You bet on the first three numbers, ie on 0, 1 and 2; As with the Transversale pleine, the payout ratio is 11: 1.
 Carré, engl. Corner: You bet on four adjacent numbers on the tableau, e.g. B. 23/24/26/27. The corresponding advertisement reads “Carré 23–27”; the payout ratio is 8: 1.
 Les quatre premiers, engl. First four: You bet on the first four numbers, i.e. H. on 0, 1, 2 and 3. The payout ratio is 8: 1 as with the Carré.
 Transversale simple, engl. Six line: You bet on the six numbers of two consecutive cross rows of the tableau, e.g. B. on the numbers 4, 5, 6, 7, 8 and 9. The corresponding advertisement reads "Transversale 4–9", the payout ratio is 5: 1.

Douzaines, engl. Dozens: The numbers 1–36 are divided into three dozen, the win rate is 2: 1 each
 12 ^{P} , Premier, engl. First dozen. First dozen, numbers 112
 12 ^{M} , milieu, engl. Second dozen. Middle dozen, numbers 13–24
 12 ^{D} , Dernier, engl. Third dozen: last dozen, numbers 25–36

Colonnes, engl. Columns: Another division into three groups of 12 numbers each form the columns, the win rate is 2: 1 as with the dozen.
 Column 34: The first column contains the numbers 1, 4, 7, 10, ..., 34
 Column 35: The middle column includes the numbers 2, 5, 8, 11, ..., 35
 Column 36: The last column includes the numbers 3, 6, 9, 12, ..., 36.
 Remarks
 Winning stakes are refunded, i.e. H. For example, if you have placed € 10 on a square and won, you will receive an 8: 1 win, i.e. € 80 and the original stake, i.e. € 90 in total.
 The winning odds are generally calculated as follows: You divide the number 36  the calculation of the winning odds is as if there were only 36 instead of 37 numbers  by the number of occupied numbers and subtract one: There are four in a square Numbers occupied, the odds are therefore 36/4  1 = 8.
 The simple odds, dozens and columns are called low odds , and the other types of bets are called high odds.
Announcement games
Boiler games
In the kettle games , the player bets on numbers that are adjacent in the roulette cylinder. Kettle games are usually advertised, but there are also special fields for some of these types of games on many tables.
 Game with neighbors (Voisins): A player can bet on a number with up to four neighbors on either side, e.g. B. the announcement "7 with the two neighbors" (short: "722") means that the player bets on the numbers 18, 29, 7, 28 and 12 and needs five chips. The five numbers in this example are next to each other in the boiler (see picture).
 Zéro game: In the Zéro game, you place four tokens on the seven numbers 12, 35, 3, 26, 0, 32 and 15 that are adjacent to each other in the cauldron and include the zero. The chips are placed as follows: three Chevaux 0/3, 12/15 and 32/35, as well as a square on 26.
 Large series, series 0/2/3: The large series includes the seventeen numbers 22, 18, 29, 7, 28, 12, 35, 3, 26, 0, 32, 15, 19, 4, 21, 2 and 25 which are filled with nine chips as follows: two pieces each on the three numbers 0/2/3 and the square 25/29 and one piece each on the Chevaux 4/7, 12/15, 18/21, 19/22 and 32/35.
 Small series, series 5/8: The small series includes twelve numbers lying next to each other in the bowl, namely 27, 13, 36, 11, 30, 8, 23, 10, 5, 24, 16 and 33, those with six chips à cheval pointed, one piece each on 5/8, 10/11, 13/16, 23/24, 27/30 and 33/36.
 Les orphelins (dt. The orphans): The orphelins comprise those eight numbers that do not belong to either of the two series, that is 1, 20, 14, 31, 9, 17, 34 and 6. These numbers are either filled with eight tokens (Orphelins en plein) or filled with only five tokens, in the latter case one piece is placed en plein on the 1 and one each à cheval on 6/9, 14/17, 17/20 and 31/34 (the 17 is in two Cheval sets included).
Finals
Apart from these kettle games, the finals are also popular , which are sequences of numbers with the same final digit: For finals 3 you need four chips and thus bet on the numbers 3, 13, 23 and 33.
You can also play Chevaux finals, for the finals 2/5 you need four chips, which are set on 2/5, 12/15, 22/25 and 32/35 etc.
The Zéro
If the ball falls on Zéro, d. H. to zero,
 so the bets on the zero or those which contain the zero in a combination win, i.e. H. 0/1, 0/2, 0/3, 0/1/2, 0/2/3 and 0/1/2/3,
 all other multiple chances, i.e. transversals, dozens and columns lose, and
 the stakes on the simple chances are blocked, they are said to go en prison.
Example: A player bets on Impair, the ball falls to zero, the stake is now blocked. If the ball hits Impair in the next coup, the stake is released again, but the player wins nothing. On the other hand, if the ball lands on pair, the bet is lost.
If the ball lands on zero again in the next round, it is  according to the classic rules introduced by François Blanc  blocked for the two following rounds (double prison), in the event that zero comes three times in a row, that is Bet lost in any case.
A player can, if he does not want to block the stake, with the words “Partagez la masse, s'il vous plaît” reclaim half of his stake, the other half is then withdrawn by the casino. However, this option only exists if the stake is an even multiple of the minimum, i.e. H. if it can be halved exactly. There is also a corresponding possibility with Double Prison, whereby the player can reclaim a quarter of his stake. Another, albeit less wellknown option for the player is to have a blocked bet moved to another simple chance (e.g. from Impair to Pair), whereby the bet on the chosen chance is of course also blocked.
Some casinos have removed the prison rule. If the ball hits Zéro there , all bets on simple chances are immediately lost.
Bank advantage in French roulette
The casino secures its banking advantage through the Zéro .
Since the odds for the multiple chances bets are calculated as if the Zéro weren't there, i.e. H. As if there were only 36 instead of 37 numbers, the bank advantage with the multiple chances is ^{1} ⁄ _{37} = 2.70%. The payout ratio is 97.30%.
The following applies to the simple chances: In classic French roulette with the prison rule, the bank advantage is ^{1} ⁄ _{37} · ^{1} ⁄ _{2} = 1.35%; the payout ratio is therefore 98.65%. Without the prison rule, the bank advantage is twice as high and is then 2.70%, as is the case on all multiple chances.
If a player wins with a bet on a full number, it is customary to give a piece to the Tronc (fr. Sacrificial stock) with the words "Pour les employés" . Thus, the win rate for bets on the square is reduced from 35: 1 to 34: 1 and the average loss of the player doubles with this type of bet to ^{2} ⁄ _{37} = 5.40%. ^{}_{}
The maximum
The maximum stipulates that the casino never has to pay out more than a predetermined maximum amount for each individual win. The purpose of this rule is to ensure that the casino would not have to file for bankruptcy as a result of a single very large win by a player.
The maximum bet for easy chances is generally 1200 times the minimum; The maximum stakes for the multiple chances are staggered so that the casino never has to pay out more than the maximum in the event of a win.
For a table with a minimum of € 10, the following maximums apply:
Bet type  Win rate  Maximum bet  Maximum profit 

Simple opportunities  1: 1  € 12,000  € 12,000 
Dozens, columns  2: 1  € 6,000  € 12,000 
Transversal simple  5: 1  € 2,400  € 12,000 
Carré  8: 1  € 1,500  € 12,000 
Transversal cord  11: 1  € 1,100  € 12,100 
Cheval  17: 1  € 700  € 11,900 
Plein  35: 1  € 350  € 12,250 
American roulette
In American Roulette, the game is handled at a faster pace. The tables are therefore a bit smaller so that every player can place their own seats and no advertisements are necessary. The croupiers' announcements are usually in English instead of French, the names on the tableau (here: Lay out ) are in English, and the arrangement of the betting fields is different. The croupier does not show the winning number with the rateau, but marks it with a small figure called Dolly.
In American Roulette, as it is offered in European casinos, the following Zéro rule applies to the simple chances : If the ball hits zero, half of the stakes are withdrawn.
A special feature of American Roulette is the ability to play with personal chips . These tokens have no value and are only given out at the table in different colors. Each player determines the value when buying, which is displayed for everyone to see. These chips can only be played on that table and must be changed back when the game is over at that table.
The game in the USA
American Roulette, as it is played in European casinos, differs from the game in the USA mainly in that the French roulette wheel with the 37 numbers 0, 1–36 is used in Europe. The numbers in the American boiler are not only arranged differently, the cylinder commonly used in the USA also contains the double zero as the 38th number .
The zero and double zero
If the ball hits zero, i. H. to zero,
 so the bets on the zero or those which contain the zero in a combination win, i.e. H. 0/00, 0/1, 0/2, 0/1/2, 0/00/2 and 0/00/1/2/3;
 all other multiple chances, i.e. transversals, dozen and columns lose, and likewise all bets on simple chances.
If the ball hits double zero, i. H. on the double zero,
 then the bets on the double zero or those which contain the double zero in a combination win, i.e. H. 0/00, 00/2, 00/3, 0/00/2, 00/2/3 and 0/00/1/2/3;
 all other multiple chances, i.e. transversals, dozen and columns lose, and likewise all bets on simple chances.
Bank advantage when playing in the USA
Due to the double zeros, the bank advantage in the USA is 2/38 = 5.26%, much greater than with roulette in Europe. The rule that the rates on the simple chances only lose half at a zero does not apply: In the USA, the stakes are collected in full.
In American roulette with Zéro and Double Zéro, however, there is no Tronc  so the expected loss of the player in the case of sets on a full number corresponds approximately to the ratios in classic roulette (5.26% compared to 5.40% in classic roulette), With all other betting options, of course, the European way of playing is much more advantageous for the player.
The bet on the five numbers 0/00/1/2/3 ( First Five ) is paid out at a ratio of 6: 1; the bank advantage here is 7.89%; this is the worst bet ever.
Game systems
Even older than roulette is the search for an infallible winning system in games of chance. The two oldest game systems, namely the Martingale and the Paroli game, have already been tried out with Pharo  with the same failure as with roulette.
Mathematical Systems
The classical or mathematical systems can be divided into the following groups
 Systems that always operate with stakes of the same amount, socalled mass égale : These systems each stipulate a mark that indicates which chance should be played. If one looks at the infinite sequences of coin tosses , sequences of rouge  noir or the sequence of numbers hit in roulette (the socalled permanences ), one finds certain regularities (cf. roulette laws ). However, these can not be used for winning strategies, since the individual coups are independent of one another , and so all these systems are worthless.
 Systems that operate with variable inserts, socalled progressions:
 In the Martingale games , the stake is increased in the event of a loss, the most important examples  because on the one hand historically interesting and on the other hand widespread
 the Martingale classique ,
 the Montante Américaine ,
 the Montante Hollandaise ,
 the progression d'Alembert ,
 the Fitzroy system and
 the Montant et Démontant system
 In the Paroli game , the stake is increased after a win.
 In the Martingale games , the stake is increased in the event of a loss, the most important examples  because on the one hand historically interesting and on the other hand widespread
In addition, many other  all unusable  game systems have been developed over the centuries. As one can generally prove with the help of the martingale theory , it is impossible to specify a game strategy that provides a positive expectation value for the player. This means that all progression systems are also worthless.
Comparison of the game systems
In relation to the expected value, i.e. H. the average profit of the casino per euro risked, the systems differ only insofar as
 in systems for simple chances, the expected value for the casino is 1.35% and
 for multiple chances systems for the casino 2.7%
due to the different treatment of single and multiple chances when Zéro occurs.
If one compares the systems that increase the stakes in the event of a loss (i.e. the various martingales) with the Masse égale game, the player increases the probability of completing a certain predetermined game route (e.g. 1000 coups) with a positive balance, At the same time, however, the risk of a total loss of the available gaming capital also increases.
In contrast, it is the other way around with the various forms of parole game. In this respect, the various systems do differ, but in the long term only the expected value is important and  apart from the special features mentioned above  it is the same for all systems.
The expected value, i.e. H. the advantage of the bank becomes more and more noticeable as the playing time increases. The best strategy to double your playing capital at roulette is therefore the bold strategy , the bold game : you bet all of the capital you intend to risk at once on one of the easy chances.
Physical systems
While the classical systems ignore the nature of the random mechanism  the systems for the simple chances can be played just as well in Trente et quarante  the following ways of playing try to profitably exploit the physical imperfections of the random mechanism: Joseph Jagger led the casino in 1873 MonteCarlo carried out a private investigation into whether the roulette games behaved as expected or whether there were statistically significant deviations due to inadequate calibration. For this purpose, he hired six people who each wrote down all the results of a day at a roulette game. While he found no deviations in five games, in the sixth game of roulette he was able to determine nine numbers that fell more frequently than statistically expected. With this knowledge, Jagger won up to $ 450,000. Despite countermeasures by the casino that put Jagger on a losing streak, he last had $ 325,000 in profit.
Boiler errors and search for favorites
No real roulette wheel has a perfect shape. Due to small imperfections in the manufacturing process and irregularities caused by wear and tear, the 37 numbers are not exactly as likely  some numbers are more likely than others. It is now important to recognize these favorites and then to bet on them. However, the purely random deviations, which would also occur when playing with an ideal wheel, far exceed the possible technical deviations, so that the numbers with a higher technical probability do not need to be hit more often in the long term. Many casinos also swap the roulette cylinders between tables on a daily basis to make it harder to find cup errors.
In any case, such circle errors would only be profitable for the players in the long term if a certain number known to the player occurs with a greater probability than ^{1} ⁄ _{36} instead of the correct probability ^{1} ⁄ _{37} , or in general if certain sectors of the circle occur with a much higher probability It should be taken that the systematic disadvantage of the player of 2.7% can be overcompensated. However, such gross manufacturing errors can be ruled out, especially since the boilers are carefully checked before they are used. In addition, the casinos also monitor the permanence of all cauldrons in order to be able to detect wear and tear or manipulation. Should a cauldron develop anomalies, the casino will determine this before it can be exploited by the players.
Kettle watching
From the exact speeds of the ball and the turnstile, as well as the exact starting positions of the same, it can theoretically be calculated exactly in which compartment the ball will fall, or guess the sector of the roulette cylinder into which the ball is likely to fall. Just as no soccer or tennis player actually calculates the path of the ball in a mathematical sense , but develops a very good feeling for the path of the ball, there are also roulette players who want to develop and use similar skills. The later a player bets, the sooner he can guess the sector and then quickly bet on these numbers in front of the Rien ne va plus .
Guessing the boiler sector is of course complicated by the fact that the ball as soon as it approaches the center through diamondshaped obstacles (obstacles) is disturbed in its course. In addition, the casino has a very simple countermeasure at its disposal: If a player seems to be gaining an advantage in this way, future coups will be canceled accordingly early. H. the Rien ne va plus follows immediately after the ball is thrown, and subsequent bets are not accepted.
Throwing distance game
The throwing distance player assumes that every croupier has his own individual and uniform throwing technique, so that  depending on the direction of rotation or throwing  between the throwing point of the ball relative to the turnstile and the compartment in which the ball comes to rest, there is always approximately the same number of Fields. Therefore, after throwing the ball, the player quickly bets on the number and its neighbors determined in this way.
In contrast to the mathematical systems, no evidence of their unsuitability can of course be provided for the physical systems. However, this does not mean that longterm profits can actually be achieved with the help of these systems (see, for example, the explanations on the topic of boiler errors and the search for favorites ).
Roulette variants
 Boule and the mechanical horse roulette Petits chevaux
 Sandown
 Wheel of fortune
 Multicolore
Also:
 Russian roulette
 English roulette is another name for the Hoggenheimer card game of chance .
literature
history
 Oskar Becker, Jos. E. Hofmann: History of Mathematics. Bonn 1951
 Thomas Bronder: Game, chance and commerce: theory and practice of the game of money between mathematics, law and reality. Springer, Berlin Heidelberg 2016, ISBN 9783662488287
 Rudolf Neuhäuser: Epilogue to The Player by Dostoyevsky . dtv, Munich 1981
 Hans Ernst Schmitt: A roulette professional tells. RoProfVerlag, Munich 1990
 Alexander B. Szanto: Roulette, TrenteetQuarante, Baccara, Black Jack. Perlen Series, Volume 645, Vienna 1977
 Ralph Tegtmeier : Casino. The world of casinos  casinos of the world. DuMont, Cologne 1989
Mathematical Systems
 Alexander B. Szanto: Roulette, TrenteetQuarante, Baccara, Black Jack. Perlen Series, Volume 645, Vienna, 1977
 M. Jung: Roulette played the right way  system games that brought wealth. FalkenVerlag, Niedernhausen / Ts 1987 (very widespread, but not a recommendation, just an example from the wealth of system books)
 Claus Koken: Roulette. Computer simulation and probability analysis of game and strategies. 2nd, improved edition. Oldenbourg, Munich 1987, ISBN 3486204440 .
Physical systems
 Pierre Basieux: Fascination with Roulette. Printul, 1999, ISBN 3925575286 (phenomena and case studies)
 Pierre Basieux: The taming of fluctuations. Printul, 2003, ISBN 3925575316 (throwing distance games, physical prediction methods, statistical effects)
 Pierre Basieux: Roulette in Zoom. Printul, 2003, ISBN 3925575200 (anatomy of the ball barrel)
 Pierre Basieux: The world as roulette. Rowohlt, 1995, ISBN 3499197073
 Thomas A. Bass: The Newtonian Casino. Penguin, London, 1990 (first published as "The Eudaemonic Pie", Houghton Mifflin, 1985)
 Edward O. Thorp : The Physical Prediction of Roulette . Woodland Hills, 1982
Web links
Individual evidence
 ↑ MatheGk 13 Kolleg St. Blasien: Blaise Pascal. In: www.joergrudolf.lehrer.belwue.de. Retrieved May 30, 2016 .
 ↑ cf. the books by Szanto and Tegtmeier mentioned in the bibliography
 ^ Lester Dubins, Leonard Savage: How to Gamble If You Must . McGrawHill, New York / London 1965