Roulette

18th century E.O. wheel with gamblers

The first form of roulette was devised in 18th century France. Many historians believe Blaise Pascal introduced a primitive form of roulette in the 17th century in his search for a perpetual motion machine.[1] The roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game Biribi.[2]

The game has been played in its present form since as early as 1796 in Paris. An early 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 (Québec) in 1758, which banned the games of "dice, hoca, faro, and roulette".[3]

The roulette wheels used in the casinos of Paris in the late 1790s had red for the single zero and black for the double zero. To avoid confusion, the color green was selected for the zeros in roulette wheels starting in the 1800s.

In 1843, in the German spa casino town of Bad 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, there were numbers 1 through 28, plus a single zero, a double zero, and an American Eagle. The Eagle slot, which was a symbol of American liberty, was a house slot that brought the casino extra edge. Soon, the tradition vanished and since then the wheel features only numbered slots. 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".[4]

1800s engraving of the French roulette

In the 19th century, roulette spread all over Europe and the US, 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.

Early American West Makeshift Game

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, that the wheel was eventually 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. The American game was 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.

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. In 1996 the first online casino InterCasino made it possible to play online roulette for the first time.[5] By 2008, there were several hundred casinos worldwide offering roulette games. The double zero wheel is found in the U.S., Canada, South America, and the Caribbean, while the single zero wheel is predominant elsewhere.

The sum of all the numbers on the roulette wheel (from 0 to 36) is 666, which is the "Number of the Beast".[6]

Roulette with red 12 as the winner

Roulette players have a variety of betting options. Placing inside bets is either selecting the exact number of the pocket the ball will land in, or a small range of pockets based on their proximity on the layout. Players wishing to bet on the 'outside' will select bets on larger positional groupings of pockets, the pocket color, or whether the winning number is odd or even. The payout odds for each type of bet are based on its probability.

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 roulette table chips of various colors to distinguish players at the table. Players can continue to place bets as the ball spins around the wheel until the dealer announces no more bets or rien ne va plus.

Croupier's rake pushing chips across a roulette layout

When a winning number and color is determined by the roulette wheel, the dealer will place a marker, also known as a dolly, on that winning number on the roulette table layout. When the dolly is on the table, no players may place bets, collect bets, or remove any bets from the table. The dealer will then sweep away all other losing bets either by hand or rake, and determine all of the payouts to the remaining inside and outside winning bets. When the dealer is finished making payouts, the marker is removed from the board where players collect their winnings and make new bets. The winning chips remain on the board.

The pockets of the roulette wheel are numbered from 0 to 36.

In number ranges from 1 to 10 and 19 to 28, odd numbers are red and even are black. In ranges from 11 to 18 and 29 to 36, odd numbers are black and even are red.

There is a green pocket numbered 0 (zero). In American roulette, there is a second green pocket marked 00. Pocket number order on the roulette wheel adheres to the following clockwise sequence in most casinos:

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

Triple-zero wheel

0-000-00-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-18-29-7-28-12-35-3-26

French style layout, French single zero wheel

The cloth-covered betting area on a roulette table is known as the layout. The layout is either single-zero or double-zero. The European-style layout has 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.

In roulette, bets can either be inside or outside bets.[8]

The expected value of a $1 bet (except for the special case of Top line bets), for American and European roulette, can be calculated as

${\displaystyle \mathrm {expectedvalue} ={\frac {1}{n}}(36-n)={\frac {36}{n}}-1,}$

where n is the number of pockets in the wheel. The initial bet is returned in addition to the mentioned payout. It can be easily demonstrated that this payout formula would lead to a zero expected value of profit if there were only 36 numbers. Having 37 or more numbers gives the casino its edge.

Top line (0, 00, 1, 2, 3) has a different expected value because of approximation of the correct ​6 ¹⁄₅-to-1 payout obtained by the formula to 6-to-1. The values 0 and 00 are not odd or even, or high or low.

En prison rules, when used, reduce the house advantage.

The house average or house edge or house advantage (also called the expected value) is the amount the player loses relative for 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 his 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)

For triple-zero wheels, a single number wins ​¹⁄₃₉ and loses ​³⁸⁄₃₉:

−1 × ​³⁸⁄₃₉ + 35 × ​¹⁄₃₉ = −0.0769 (7.69% house edge)

The presence of the green squares on the roulette wheel and on the table is technically the only house edge. Outside bets will always lose when a single or double zero comes up. However, the house also has an edge on inside bets because the pay outs (including the original player's bet) are always set at 36 to 1 when you mathematically have a 1 out of 38 (1 out of 37 for French/European roulette) 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 (including 0 and 00) to assure a win: you would only get back $36, having spent $38. The only exceptions 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 (French Roulette) where the house edge is halved because only half the stake is lost when a zero comes up. This is commonly called the "la partage" rule, and it is considered the main difference between European and French roulette. There is also a modification of this rule, which is called the "en prison" rule. These rules cut the house edge into half (1.35%) in French roulette, when playing even-money bets, as half of the even-money bets are given back to the player if the zero is drawn in the wheel.

The house edge should not be confused with the "hold". The hold is the average percentage of the money originally brought to the table that the player loses before he leaves—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% to 30%, significantly more than the 5.26% house edge. This reflects the fact that the player is churning the same money over and over again. A 23.6% hold, for example, would imply that, on average, the player bets the total he brought to the table five times, as 23.6% is approximately equal to 100% − (100% − 5.26%)⁵. For example, a player with $100 making $10 bets on red (which has a near 50/50 chance of winning) is highly unlikely to lose all his money after only 10 bets, and will most likely continue to bet until he has lost all of his money or decides to leave. A player making $10 bets on a single number (with only 1/38 chance of success) with a $100 bankroll is far more likely to lose all of his money after only 10 bets.

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.

As an example, we can examine the European roulette model, that is, roulette with only one zero. Since this roulette has 37 cells with equal odds of hitting, this is a final model of field probability ${\displaystyle (\Omega ,2^{\Omega },\mathbb {P} )}$, where ${\displaystyle \Omega =\{0,\ldots ,36\}}$, ${\displaystyle \mathbb {P} (A)={\frac {|A|}{37}}}$ for all ${\displaystyle A\in 2^{\Omega }}$.

Call the bet ${\displaystyle S}$ a triple ${\displaystyle (A,r,\xi )}$, where ${\displaystyle A}$ is the set of chosen numbers, ${\displaystyle r\in \mathbb {R} _{+}}$ is the size of the bet, and ${\displaystyle \xi$ :\Omega \to \mathbb {R} } determines the return of the bet.

The rules of European roulette have 10 types of bets. First we can examine the 'Straight Up' bet. In this case, ${\displaystyle S=(\{\omega _{0}\},r,\xi )}$, for some ${\displaystyle \omega _{0}\in \Omega }$, and ${\displaystyle \xi }$ is determined by

${\displaystyle \xi (\omega )={\begin{cases}-r,&\omega \neq \omega _{0}\\35\cdot r,&\omega =\omega _{0}\end{cases}}.}$

The bet's expected net return, or profitability, is equal to

${\displaystyle M[\xi ]={\frac {1}{37}}\sum _{\omega \in \Omega }\xi (\omega )={\frac {1}{37}}\left(\xi (\omega ^{\prime })+\sum _{\omega \neq \omega ^{\prime }}\xi (\omega )\right)={\frac {1}{37}}\left(35\cdot r-36\cdot r\right)=-{\frac {r}{37}}\approx -0.027r.}$

Without details, for a bet, black (or red), the rule is determined as

${\displaystyle \xi (\omega )={\begin{cases}-r,&\omega {\text{ is red}}\\-r,&\omega =0\\r,&\omega {\text{ is black}}\end{cases}},}$

and the profitability

${\displaystyle M[\xi ]={\frac {1}{37}}(18\cdot r-18\cdot r-r)=-{\frac {r}{37}}}$.

For similar reasons it is simple to see that the profitability is also equal for all remaining types of bets. ${\displaystyle -{\frac {r}{37}}}$.[9]

In reality this means that, the more bets a player makes, the more he is going to lose independent of the strategies (combinations of bet types or size of bets) that he employs:

${\displaystyle \sum _{n=1}^{\infty }M[\xi _{n}]=-{\frac {1}{37}}\sum _{n=1}^{\infty }r_{n}\to -\infty .}$

Here, the profit margin for the roulette owner is equal to approximately 2.7%. Nevertheless, several roulette strategy systems have been developed despite the losing odds. These systems can not change the odds of the game in favor of the player.

It is worth noting that the odds for the player in American roulette are even worse, as the bet profitability is at worst ${\displaystyle -{\frac {3}{38}}r\approx -0.0789r}$, and never better than ${\displaystyle -{\frac {r}{19}}\approx -0.0526r}$.

Traditional roulette wheel sectors

Although most often named "call bets" technically these bets are more accurately referred to as "announced bets". The legal distinction between a "call bet" and an "announced bet" is that a "call bet" is a bet called by the player without him placing any money on the table to cover the cost of the bet. In many jurisdictions (most notably the United Kingdom) this is considered gambling on credit and is illegal. An "announced bet" is a bet called by the player for which he immediately places enough money to cover the amount of the bet on the table, prior to the outcome of the spin or hand in progress being known.

There are different number series in roulette that have special names attached to them. Most commonly these bets are known as "the French bets" and each covers a section of the wheel. For the sake of accuracy, zero spiel, although explained below, is not a French bet, it is more accurately "the German bet". 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.

Over the years, many people have tried to beat the casino, and turn roulette—a game designed to turn a profit for the house—into one on which the player expects to win. Most of the time this comes down to the use of betting systems, strategies which say that the house edge can be beaten by simply employing a special pattern of bets, often relying on the "Gambler's fallacy", the idea that past results are any guide to the future (for example, if a roulette wheel has come up 10 times in a row on red, that red on the next spin is any more or less likely than if the last spin was black).

All betting systems that rely on patterns, when employed on casino edge games will result, on average, in the player losing money.[10] In practice, players employing betting systems may win, and may indeed win very large sums of money, but the losses (which, depending on the design of the betting system, may occur quite rarely) will outweigh the wins. Certain systems, such as the Martingale, described below, are extremely risky, because the worst-case scenario (which is mathematically certain to happen, at some point) may see the player chasing losses with ever-bigger bets until he runs out of money.

The American mathematician Patrick Billingsley said[11] that no betting system can convert a subfair game into a profitable enterprise. 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 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 the 1960s and early 1970s, Richard Jarecki won about $1.2 million at dozens of European casinos. He claimed that he was using a mathematical system designed on a powerful computer. In reality, he simply observed more than 10,000 spins of each roulette wheel to determine flaws in the wheels. Eventually the casinos realized that flaws in the wheels could be exploited, and replaced older wheels. The manufacture of roulette wheels has improved over time.[17]
• In 2004, Ashley Revell of London sold all of his possessions, clothing included, and placed his entire net worth of US$135,300 on red at the Plaza Hotel in Las Vegas. The ball landed on "Red 7" and Revell walked away with $270,600.[18]

• The 1866 novella, titled The Gambler, by the famous Russian writer Fyodor Dostoyevsky has a prime focus of the game as a major theme throughout the story. At the point of his life that he wrote this, gambling was at its peak for him. The novella is insightful about the game itself, and has technical descriptions of how he played the wheel and explains each move the main character does while playing the game.
• In the 1937 comedic short story "All's Well with Bingo", by British writer P. G. Wodehouse, the main character Bingo Little plays roulette at the Monte Carlo casino, betting on black. When his wife Rosie, who does not want him to gamble, comes by the table, Bingo cannot claim his winnings or else Rosie will see he is gambling. He has no choice but to let it all ride. Fortunately, black keeps coming up. Eventually, Rosie leaves, and Bingo is able to take his winnings. The story also references the Martingale betting strategy and the "en prison" rule.

• In the 1942 film Casablanca, Rick's Café Américain has a trick roulette wheel. Rick (played by Humphrey Bogart) uncharacteristically takes pity on a young Bulgarian refugee couple. The husband has lost most of his money at roulette, trying to win enough to bribe police Captain Renault. Rick suggests the man bet on 22. After the number comes up, Rick tells him to let it all ride. He does, and wins again. Rick tells him to cash in his winnings and never come back.
• In season 5, episode 25 of American sitcom I Love Lucy, Lucy Goes to Monte Carlo, Lucy finds a chip on the floor of the casino and tries to return it by placing it on the roulette table. The number she places it on hits. She tries to explain to the dealer that she did not want to place the bet, but he does not understand and thinks she wants to let it ride. She continues to win while trying to return the money. She finally gives up and collects her winnings and hides it from Ricky in the Mertz's hotel room. When Ricky finds the money, he thinks that Fred has been embezzling it from Ricky's concert earnings.
• In the 17 February 1965 episode of the classic series, Danger Man, The Ubiquitous Mr. Lovegrove, John Drake (Patrick McGoohan) is injured in a car accident, and hallucinates he's involved with the nefarious manager of a London casino. By placing bets on a roulette wheel - at a predetermined time - with a croupier in on the scheme - money is transferred with information without any outside bettors being aware.
• In the 22 October 1966 episode ("Odds on Evil") of the Mission: Impossible series, the IMF team uses a wearable computer (à la Thorpe and Shannon, above) to predict the outcome of each spin of the roulette wheel at a fictional casino in a European principality. The $200,000 they win at roulette provides the stake they need to challenge the prince to a high-stakes game of Banco, in which they take the Prince for the money he was planning to use to buy arms in order to go to war against a neighbor.[19]
• In the 1971 Western comedy Support Your Local Gunfighter, James Garner's character has a gambling addiction—he cannot stop betting everything he has on a single roulette spin. He loses several times, but finally wins at the very end.
• 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.
• In the third part of the 1998 film Run, Lola, Run, Lola (Franka Potente) 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 a European roulette wheel are exactly 1368-to-1 against.
• On season 1 of ITV1's Red or Black?, a player can win £1,000,000 by guessing either red or black on the roulette wheel.
• In the 2010 Disney Pixar film Toy Story 3, a scene featured a See 'n Say being used as a roulette wheel for gambling.
• In the 2011 film Fast Five, Don Omar and Tego Calderón play roulette and each bet their millions on red or black.
• In the 2012 film Madagascar 3: Europe's Most Wanted, the Penguins let their money ride/bet all of their money on a roulette wheel, selecting black and winning back twice as much.
• In the 2015 Tamil film Vai Raja Vai directed by Aishwarya R. Dhanush, Gautham Karthik is being coerced to use his special power - 'premonition' - to beat the roulette table. He walks away winning against the casino by predicting the outcome in the roulette table.

• Players should not collect their winnings and betting chips until all bets have been paid. This is to avoid confusion and minimize the chance for players to steal other players' chips.
• Players must not touch chips after the dealer gives the hand signal or announces "no more bets." Players are not allowed to remove, change, or add bets beyond this point.
• When the dealer has placed the dolly (the plastic marker used to mark the winning number), it is strictly prohibited to touch any chips on a winning bet.
• Dealers are not allowed to take cash from a player's hand. To purchase chips with cash, place it on the table. This provides a better view of the transaction for casino surveillance.
• The use of electronic equipment at the table, such as mobile phones and cameras, is prohibited in most jurisdictions.
• The only items allowed in front of a player are chips, money, drinks, and cigarettes. Bulky items like wallets, purses, or bags must not be placed on the table.

• Players should place chips on the board rather than tossing them. Tossed chips may displace other bets or roll down to the "chipping machine". If the player cannot reach to place a bet themselves, they should announce the bet to the dealer. This is treated as any other call bet.
• Changes for cash or color chips are supposed to be done in between spins. If the dealer has time, they will make changes during the spin, but they will most likely prioritize call bets before changes.
• All call bets are considered courtesy bets and are only placed if the dealer has time to change and place the bets. The bet is considered taken only if the dealer and the inspector dealer has repeated the bet. If the dealer does not take the bet, they will announce "no bet". To argue with the dealer about which bets have been taken is considered extremely impolite and will most likely render a warning from the inspector dealer or pit boss.
• Most casinos ban food at the table. Drinking rules vary.

• Bauernroulette
• Boule
• Eudaemons
• Monte Carlo Paradox
• Russian roulette
• Straperlo

Wikimedia Commons has media related to Roulette.

• Roulette at Curlie