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roulette, game of chance popular in gambling casinos, and in a simplified form elsewhere. In gambling houses the roulette wheel is set in an oblong table. Its outer area is marked off into 37 (in Europe) or 38 (in the United States) spaces, each of which has retaining walls so that a small ball may come to rest in one. The sectors, alternately red and black, are numbered 1 to 36; there is also a green (or sometimes white) 0 and in the United States an additional 00. On the table is an arrangement of red and black squares numbered in correspondence with the wheel. In addition, there are spaces for other types of bets: manque, that the winning number will be 1-18; passe, that it will be 19-36; pair, that it will be an even number; impair, that it will be odd; rouge, that it will be red; noir, that it will be black. All bets are placed against the house and are indicated by placing stakes on the layout. The croupier spins the wheel and tosses the ball onto it; its final place of rest indicates the winning bets. Many betting combinations are allowed, with varying odds and maximum stakes. Roulette dates from the late 18th cent.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Gambling game. After a small ball is released in the opposite direction of a revolving wheel, players make bets concerning which red or black numbered compartment the ball will enter as it comes to rest. Bets are placed on a table marked to correspond with the compartments of the wheel. Roulette (French: “small wheel”) emerged in the late 18th century in the casinos of Europe. All bets are placed against the “house,” or casino bank. Bets may be made until the ball slows down and is about to drop from its track into a compartment. Bets may be on a single number or various combinations of numbers that pay off at lesser odds if the winner is among them. Betting that red or black or that an odd or even number will come up are other options.

Learn more about roulette with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Roulette is a casino and gambling game named after the French word meaning "small wheel". In the game, players may choose to place bets on either a number, a range of numbers, the color red or black, or whether the number is odd or even. To determine the winning number and color, a croupier spins a wheel in one direction, then spins a ball in the opposite direction around a tilted circular track running around the circumference of the wheel. The ball eventually loses momentum and falls on to the wheel and into one of 37 (in European roulette) or 38 (in American roulette) colored and numbered pockets on the wheel.

The first form of roulette was devised in 18th century France. The roulette wheel is believed to be a fusion of the English wheel games Roly-Poly, Ace of Hearts, and E.O., the Italian board games of Hoca and Biribi, and "Roulette" from an already existing French board game of that name.

The game has been played in its current form since as early as 1796 in Paris. The earliest description of the roulette game in its current form is found in a French novel "La Roulette, ou le Jour" by Jaques Lablee, which describes a roulette wheel in the Palais Royal in Paris in 1796. The description included the house pockets, "There are exactly two slots reserved for the bank, whence it derives its sole mathematical advantage." It then goes on to describe the layout with, "...two betting spaces containing the bank's two numbers, zero and double zero." The book was published in 1801. An even earlier reference to a game of this name was published in regulations for New France (Canada) in 1758, which banned the games of "dice, hoca, faro, and roulette."

In 1843, in the German spa casino town of Homburg, fellow Frenchmen François and Louis Blanc introduced the single "0" style roulette wheel in order to compete against other casinos offering the traditional wheel with single and double zero house pockets.

In some forms of early American roulette wheels - as shown in the 1886 Hoyle gambling books, there were numbers 1 through 28, plus a single zero, a double zero, and an American Eagle. According to Hoyle "the single 0, the double 0, and eagle are never bars; but when the ball falls into either of them, the banker sweeps every thing upon the table, except what may happen to be bet on either one of them, when he pays twenty-seven for one, which is the amount paid for all sums bet upon any single figure."

In the 1800s, roulette spread all over Europe and the U.S.A., becoming one of the most famous and most popular casino games. When the German government abolished gambling in the 1860s, the Blanc family moved to the last legal remaining casino operation in Europe at Monte Carlo, where they established a gambling mecca for the elite of Europe. It was here that the single zero roulette wheel became the premier game, and over the years was exported around the world, except in the United States where the double zero wheel had remained dominant. Some call roulette the "King of Casino Games", probably because it was associated with the glamour of the casinos in Monte Carlo.

A legend tells François Blanc supposedly bargained with the devil to obtain the secrets of roulette. The legend is based on the fact that the sum of all the numbers on the roulette wheel (from 1 to 36) is 666, which is the "Number of the Beast."

In the United States, the French double zero wheel made its way up the Mississippi from New Orleans, and then westward. It was here, because of rampant cheating by both operators and gamblers, the wheel eventually was placed on top of the table to prevent devices being hidden in the table or wheel, and the betting layout was simplified. This eventually evolved into the American style roulette game as different from the traditional French game. The American game developed in the gambling dens across the new territories where makeshift games had been set up, whereas, the French game evolved with style and leisure in Monte Carlo. However, it is the American style layout with its simplified betting and fast cash action, using either a single or double zero wheel, that now dominates in most casinos around the world.

During the first part of the 20th century, the only casino towns of note were Monte Carlo with the traditional single zero French wheel, and Las Vegas with the American double zero wheel. In the 1970s, casinos began to flourish around the world. By 2008 there were several hundred casinos world wide offering roulette games. The double zero wheel is found in the U.S.A., South America, and the Caribbean, while the single zero wheel is predominant elsewhere.

The pockets of the roulette wheel are numbered from 1 to 36, alternating between red and black. There is a green pocket numbered 0. In American roulette, there is a second green pocket marked 00. Pocket number order on the roulette wheel adhere to the following clockwise sequence:

Single-zero wheel: 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

Double-zero wheel: 0-28-9-26-30-11-7-20-32-17-5-22-34-15-3-24-36-13-1-00-27-10-25-29-12-8-19-31-18-6-21-33-16-4-23-35-14-2

The roulette table usually imposes minimum and maximum bets, and these rules usually apply separately for all of a player's 'inside' and 'outside' bets for each spin. For 'inside' bets at roulette tables, some casinos may use separate table chips of various colors to distinguish players at the table. Players can continue to place bets until the dealer announces "No more bets."

The cloth covering with the betting areas on a roulette table is known as a "layout." The layout is either single zero or double zero. The French style layout is a single zero, and the American style layout is usually a double zero. The American style roulette table with a wheel at one end is now used in most casinos. The French style table with a wheel in the centre and a layout on either side is rarely found outside of Monte Carlo.

0 | ↔ | 00 | |||

1- 18 |
1st 12 |
1 | 2 | 3 | ← |

4 | 5 | 6 | ← | ||

odd | 7 | 8 | 9 | ← | |

10 | 11 | 12 | ← | ||

red | 2nd 12 |
13 | 14 | 15 | ← |

16 | 17 | bgcolor="#ff0000">18 | ← | ||

blk | bgcolor="#ff0000">19 | 20 | bgcolor="#ff0000">21 | ← | |

22 | 23 | bgcolor="#000000">24 | ← | ||

even | bgcolor="#228B22">3rd 12 | 25 | color="#ffffff">26 | 27 | bgcolor="#228B22">← |

28 | color="#ffffff">29 | 30 | bgcolor="#228B22">← | ||

19- 36 | color="#ffffff">31 | 32 | color="#ffffff">33 | ← | |

34 | 35 | bgcolor="#ff0000">36 | ← | ||

↑ | ↑ | bgcolor="#228B22">↑ |

- Straight Up: a single number bet. The chip is placed entirely on the middle of a number square.
- Split: a bet on two adjoining numbers, either on the vertical or horizontal (as in 14-17 or 8-9). The chip is placed on the line between these numbers.
- Street: a bet on three numbers on a single horizontal line. The chip is placed on the edge of the line of a number at the end of the line (either the left or the right, depending on the layout).
- Corner (or square): a bet on four numbers in a square layout (as in 11-12-14-15). The chip is placed at the horizontal and vertical intersection of the lines between the four numbers.
- Six Line: a bet on two adjoining streets, with the chip placed at the corresponding intersection, as if in between where two street bets would be placed.
- Trio: a bet on the intersecting point between 0, 1 and 2, or 0, 2 and 3.

- 1 to 18: a bet on one of the first low eighteen numbers coming up.
- 19 to 36: a bet on one of the last high eighteen numbers coming up.
- Red or Black: a bet on which color the roulette wheel will show.
- Even or Odd: a bet on an even or odd number.
- Dozen Bets: a bet on the first (1-12), second (13-24), or third group (25-36) of twelve numbers.
- Column Bets: a bet on all 12 numbers on any of the three vertical lines (such as 1-4-7-10 on down to 34). The chip is placed on the space below the final number in this string.

Bet name | Winning spaces | Payout | Odds against winning | Expected value (on a $1 bet) |
---|---|---|---|---|

0 | 0 | 35 to 1 | 37 to 1 | −$0.053 |

00 | 00 | 35 to 1 | 37 to 1 | −$0.053 |

Straight up | Any single number | 35 to 1 | 37 to 1 | −$0.053 |

Row 00 | 0, 00 | 17 to 1 | 18 to 1 | −$0.053 |

Split | any two adjoining numbers vertical or horizontal | 17 to 1 | 18 to 1 | −$0.053 |

Trio | 0, 1, 2 or 00, 2, 3 | 11 to 1 | 11.667 to 1 | −$0.053 |

Street | any three numbers horizontal (1, 2, 3 or 4, 5, 6 etc.) | 11 to 1 | 11.667 to 1 | −$0.053 |

Corner | any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21 etc. ) | 8 to 1 | 8.5 to 1 | −$0.053 |

Five Number Bet | 0, 00, 1, 2, 3 | 6 to 1 | 6.6 to 1 | −$0.079 |

Six Line | any six numbers from two horizontal rows (1, 2, 3, 4, 5, 6 or 28, 29, 30, 31, 32, 33 etc.) | 5 to 1 | 5.33 to 1 | −$0.053 |

1st Column | 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 | 2 to 1 | 2.167 to 1 | −$0.053 |

2nd Column | 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35 | 2 to 1 | 2.167 to 1 | −$0.053 |

3rd Column | 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 | 2 to 1 | 2.167 to 1 | −$0.053 |

1st Dozen | 1 through 12 | 2 to 1 | 2.167 to 1 | −$0.053 |

2nd Dozen | 13 through 24 | 2 to 1 | 2.167 to 1 | −$0.053 |

3rd Dozen | 25 through 36 | 2 to 1 | 2.167 to 1 | −$0.053 |

Odd | 1, 3, 5, ..., 35 | 1 to 1 | 1.111 to 1 | −$0.053 |

Even | 2, 4, 6, ..., 36 | 1 to 1 | 1.111 to 1 | −$0.053 |

Red | 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 | 1 to 1 | 1.111 to 1 | −$0.053 |

Black | 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 | 1 to 1 | 1.111 to 1 | −$0.053 |

1 to 18 | 1, 2, 3, ..., 18 | 1 to 1 | 1.111 to 1 | −$0.053 |

19 to 36 | 19, 20, 21, ..., 36 | 1 to 1 | 1.111 to 1 | −$0.053 |

Note also that 0 and 00 are neither odd nor even in this game.

In the early frontier gambling saloons, the house would set the odds on roulette tables at 27 for 1. This meant that on a $1 bet you would get $27 and the house would keep your initial dollar. Today most casino odds are set by law, and they have to be either 34 to 1 or 35 to 1. This means that the house pays you $34 or $35 and you get to keep your original $1 bet.

The house average or house edge (also called the expected value) is the amount the player loses relative to any bet made, on average. If a player bets on a single number in the American game there is a probability of 1/38 that the player wins 35 times the bet, and a 37/38 chance that the player loses their bet. The expected value is:

- −1×37/38 + 35×1/38 = −0.0526 (5.26% house edge)

For European roulette, a single number wins 1/37 and loses 36/37:

- −1×36/37 + 35×1/37 = −0.0270 (2.70% house edge)

The presence of the green squares on the roulette wheel and on the table are technically the only house edge. Outside bets will always lose when a single or double zero come up. However, the house also has an edge on inside bets because the pay outs are always set at 35 to 1 when you mathematically have a 37 to 1 chance at winning a straight bet on a single number. To demonstrate the house edge on inside bets, imagine placing straight $1 wagers on all inside numbers on a roulette table (including 0 and 00) to assure a win. You would only get back 35 times your original bet having spent $38. The only exception are the five numbers bet where the house edge is considerably higher (7.89% on an American wheel), and the 'even money' bets in some European games where the house edge is halved because only half the stake is lost when a zero comes up.

The house edge should not be confused with the hold. The hold is the total amount of cash the table changes for chips, minus the chips taken away from the table. In other words, the actual "win" amount for the casino. The Casino Control Commission in Atlantic City releases a monthly report showing the win/hold amounts for each casino. The average win/hold for double zero wheels is between 21-30%, significantly more than 5.26%/2.70% of all players money because players are making repeated bets after winning and losing portions of their total money. This is known in the casino gaming industry as "churning" and is especially true of slot machine players who statistically end up losing all their wagers.

A player with a certain total amount of money may not win or lose all their money instantly, such that the total of all bets they make will often be greater than the total of the money they actually started with. The house edge applies to each bet made; not the total money, which means the player can end up losing significantly more than 5.26% of his starting money. For example it is likely that a player with $100 making $10 bets on red will be able to bet more than 10 times, because sometimes he wins. He may end up betting a total of 20 times on red. This means the expected value is 20*$10*5.26% = $10.52, over 10% of his money is now in the 'hold' despite the game having a 5.26% house advantage. A player who continually bets until they run out of money will give the house 100% hold.

There are different number series in roulette that have special names attached to them. Players at a table may bet a set amount per series (or multiples of that amount). The series are based on the way certain numbers lie next to each other on the roulette wheel. Not all casinos offer these bets, and some may offer additional bets or variations on these.

9 chips or multiples thereof are bet. 2 chips are placed on the 0,2,3 trio; 1 on the 4/7 split; 1 on 12/15; 1 on 18/21; 1 on 19/22; 2 on 25/26/28/29 corner; and 1 on 32/35.

6 chips or multiples thereof are bet. 1 chip is placed on each of the following splits: 5/8; 10/11; 13/16; 23/24; 27/30; 33/36.

A variant known as "Tier 5,8,10,11" has an additional chip placed straight up on 5, 8, 10 and 11; and so is a 10-piece bet.

This is also called the "Small Series" It includes the following wagers which are all Splits

- 5/8, 10/11, 13/16, 23/24, 27/30, 33/36

5 chips or multiples thereof are bet. 1 chip is placed straight-up on 1 and 1 chip on each of the splits: 6/9; 14/17; 17/20 and 31/34.

Any of the above bets may be combined, eg "Orphelins by 1 and Zero and the Neighbors by 1." The "...and the Neighbors." is often assumed by the croupier.

Nevertheless, the numerous even-money bets in roulette have inspired many players over the years to attempt to beat the game by using one or more variations of a Martingale betting strategy, wherein the gamer doubles the bet after every loss, so that the first win would recover all previous losses, plus win a profit equal to the original bet. This betting strategy is fundamentally flawed in practice and the near-universal long-term consequence is a large financial loss. Another strategy is the Fibonacci system, where bets are calculated according to the Fibonacci sequence. Regardless of the specific progression, no such strategy can statistically overcome the casino's advantage.

While not a strategy to win money, former Los Angeles Times editor Andrés Martinez described an enjoyable roulette betting method in his book on Las Vegas entitled "24/7". He called it the "dopey experiment". The idea is to divide one's roulette session bankroll into 35 units. This unit is bet on a particular number for 35 consecutive spins. Thus, if the number hits in that time, the gambler wins back the original bankroll and can play subsequent spins with house money. However, there is only a $(1\; -\; (37/38)^\{35\})$ * 100% = 60.68% probability of winning within 35 spins (assuming a double zero wheel with 38 pockets).

There is a common misconception that the green numbers are "house numbers" and that by betting on them one "gains the house edge." In fact, it is true that the house's advantage comes from the existence of the green numbers (a game without them would be statistically fair); however, they are no more or less likely to come up than any other number.

Various attempts have been made by engineers to overcome the house edge through predicting the mechanical performance of the wheel, most notably by Joseph Jagger at Monte Carlo in 1873. These schemes work by determining that the ball is more likely to fall at certain numbers. Claude Shannon, a mathematician and computer scientist best known for his contributions to information theory, built arguably the first wearable computer to do so in 1961.

More recently [[Thomas Bass, in his book The Eudaemonic Pie 1991 (published as The Newtonian Casino in Britain), has claimed to be able to predict wheel performance in real time. The book describes the exploits of a group of computer hackers, who called themselves the Eudaemons, who in the late 1970s used computers in their shoes to win at roulette by predicting where the ball would fall.

At least in the 1930s, some professional gamblers were able to consistently gain an edge in roulette by seeking out rigged wheels (not difficult to find at that time) and betting opposite the largest bets.

In the early 1990s, Gonzalo Garcia-Pelayo used a computer to model the tendencies of the roulette wheels at the Casino de Madrid in Madrid, Spain. Betting the most likely numbers, along with members of his family, he was able to win over one million dollars over a period of several years. A court ruled in his favor when the legality of his strategy was challenged by the casino.

In 2004 it was reported that a group of two Serbs and one Hungarian in London had used a laser scanner hidden inside a mobile phone linked to a computer to predict the sector of the wheel where the ball was most likely to drop. They were arrested, but released without charge as there was no proof they had technically interfered with casino equipment.

There are 18 red spaces on a roulette table with 38 total spaces. Dividing 18 by 38 yields a probability of landing on red of 47.37%. This probability can be used in a binomial distribution and made into an approximate standard normal distribution.

Doing so indicates that, if one were to spin the wheel 38 times, there is a 99% probability that the ball would land on red at least 10 times. There is an 83% probability that in 38 spins, the ball will land on red at least 15 times. Out of 38 spins, there's a 50% chance that 18 will be red.

However, the break-even point is 19 spins, since the bet on red is 1:1, and the probability of 19 or more red spins in 38 has been claimed to be only 37%. This indicates the difficulty of winning by only betting on red. Yet, the foregoing analysis would appear faulty, as, by symmetry considerations alone, the probability of 19 or more black spins in 38 should also be 37%, then, leaving a hard-to-swallow 26% chance of exactly 18 red and 18 black. A straightforward binomial expansion (momentarily neglecting green outcomes) of (0.5 + 0.5)**36 reveals that the chance of 18/18 is far less than 26%, indeed, it is precisely equal to 36!/(18!18![2**36]).

The results occur because, as indicated by the 18 divided by 38 equals 47.37% figure, the ball will land on red less than half the time. This percentage applied in the binomial and standard normal distributions creates the vast divide in probability from 18 red spins to 19 red spins out of 38 spins.

Biased wheels: Section betting

- In 1982, several casinos in England began to lose large sums of money at their roulette tables to teams of gamblers from the USA. Upon investigation by the police, it was discovered they were using a legal system of biased wheel-section betting. As a result of this, the English roulette wheel manufacturer John Huxley manufactured a roulette wheel to counter-act the problem.

The software is designed for use at online casinos using a random number generator (RNG), most of these software applications claim to be exploiting a flaw in the RNG. Whilst the software is able to perform more complex calculations, you can never hope to beat roulette every time, at the very most you could hope to minimize your losses.

- In 1873, the Englishman Joseph Jaggers made the first famous roulette biased wheel attack. Mr. Jaggers with a team of six clerks, clocked all the wheels at the Monte Carlo casino and found one wheel to show significant bias. In their attack exploiting this flaw they won over $325,000, an astronomical sum in 1873.
- In the summer of 1891 at the Monte Carlo casino, a part-time swindler and petty crook from London named Charles Wells, broke the bank at each table he played over a period of several days. Breaking the bank meant he won all the available money in the table bank that day, and a black cloth would be placed over the table until the bank was replenished. In song and life he was celebrated as "The Man That Broke the Bank at Monte Carlo." He later admitted that it was all luck, and he eventually ended up in jail for many years because of his fraudulent schemes.
- In 2004, Ashley Revell of London sold all of his possessions, clothing included, and brought US$135,300 to the Plaza Hotel in Las Vegas and put it all on "Red" at the roulette table in a double-or-nothing bet. The ball landed on "Red 7" and Revell walked away with his net-worth doubled to $270,600.
- In the 1942 film Casablanca, Rick's Café Americain has a trick roulette wheel. The croupier can cause it to land on 22 at will. Rick (Humphrey Bogart) urges a Bulgarian refugee with whose case he becomes sympathetic to put his last three chips on 22 and motions to the croupier to let him win. After the man's number dramatically comes up, Rick tells him to let it all ride on 22 and lets him win again. Although the details are not mentioned in the film (the croupier only notes that they are "a couple of thousand" down), it appears that Rick has given the man 3885 ((3*36*36)-3) francs.
- In the music video for "Palace & Main" by Kent, guitarist Harri Mänty goes to Las Vegas and bets the entire video budget on black. He wins, and the profits were donated to charity.
- In the third part of the 1998 film Run, Lola, Run, Lola uses all her money to buy a 100-mark chip. (She is actually just short of 100 marks, but gains the sympathy of a casino employee who gives her the chip for what money she has.) She bets her single chip on 20 and wins. She lets her winnings ride on 20 and wins again, making her total winnings 129,600 marks (29,600 more than her smuggler boyfriend owed his boss, Ronnie). The odds of two consecutive wins on the same number on a European roulette wheel are exactly 1369-to-1 against.
- In the South Park episode "Red Man's Greed", the town, facing destruction at the hands of Native Americans, bets $10,000 to raise money to save themselves. They win, but let it ride, and lose all of it.
- Near the beginning of the 1973 film The Sting, Johnny Hooker (Robert Redford) takes his share of the money conned from a numbers runner and loses nearly all of it on a single bet against a rigged roulette wheel.

- Russian roulette
- Straperlo
- The Red Snake Roulette Bet
- Smart Live Casino
- Live Roulette TV
- Eudaemons
- Bauernroulette

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