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. [2] The roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game Biribi.[3] A primitive form of roulette, known as 'EO' (Even/Odd), was played in England in the late 18th century using a gaming wheel similar to that used in roulette.[4]

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".[5]

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.

A caricature by James Gillray, 1822

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.[6]

In some forms of early American roulette wheels, there were numbers 1 to 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 an 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 the 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".[7]

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 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 from 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, generally believed to be InterCasino, made it possible to play roulette online.[8] 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".[9]

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 by 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 because it has a higher house edge compared to a European layout.[11]

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 be either inside or outside.[12]

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 (that is, the casino would break even). 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 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)

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)

As an example, the European roulette model, that is, roulette with only one zero, can be examined. 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.[13]

The rules of European roulette have 10 types of bets. First the 'Straight Up' bet can be imagined. 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

${\displaystyle M[\xi ]={\frac {1}{37}}\sum _{\omega \in \Omega }\xi (\omega )={\frac {1}{37}}\left(\xi (\omega _{0})+\sum _{\omega \neq \omega _{0}}\xi (\omega )\right)={\frac {1}{37}}\left(35\cdot r-36\cdot r\right)=-{\frac {r}{37}}\approx -0.027r.}$

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. ${\displaystyle -{\frac {r}{37}}}$.[14]

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

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

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 ${\displaystyle -{\frac {r}{19}}\approx -0.0526r}$.

All roulette tables deal with only four elements:

• 1. The roulette wheel.
• 2. The roulette table (aka layout).
• 3. The ball. These days the ball is most likely high impact plastic, but originally it was made of ivory. Modern casinos maintain the integrity of their roulette balls with regular magnetic and x-ray exams.
• 4. The chips. Some casinos allow the player to use generic casino chips at the roulette tables, but most require the player to buy in at the table. The croupier has stacks of various colored chips. Usually each player gets a different color to help avoid confusion of bets, and the player can designate the value of the chip. The chips are typically valued at either $1 or the table minimum; if the player wishes, the chips may be worth $0.25 so long as the "total" wager meets the table minimums for their respective sectors, for example by placing four $0.25 bets to meet a $1 table minimum.

All roulette tables operated by a casino have the same basic mechanics:

• There is a balanced mechanical wheel with colored pockets separated by identical vanes and the wheel which spins freely on a supporting post.
• The wheel is held within a wooden frame which contains a track around the upper outer edge and blocks of a variety of designs placed approximately halfway down the face of the frame.
• A plastic or ivory ball is spun in the track in the frame that holds the wheel. As the ball loses momentum the centrifugal force is no longer sufficient to hold the ball in the groove and it falls down the face of the frame. As the ball hits a block its trajectory is randomly altered on all 3 planes (X, Y, and Z) causing the ball to bounce and skip.
• The ball falls onto the spinning wheel and eventually lands into one of the pockets.
• The number of the pocket the ball falls into determines how the bets placed on the layout table are treated.

After this the specifics of individual tables can vary greatly.[15]

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 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 they immediately place 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.[16] 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 they run out of money.

The American mathematician Patrick Billingsley said[17] 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.

Types of betting system

Betting systems in roulette can be divided in to two main categories:

Negative progression system (e.g. Martingale)

Negative progression systems involve increasing the size of one's bet when they lose. This is the most common type of betting system. The goal of this system is to recoup losses faster so that one can return to a winning position more quickly after a losing streak. The typical shape of these systems is small but consistent wins followed by occasional catastrophic losses. Examples of negative progression systems include the Martingale system, the Fibonacci system, the Labouchère system, and the d'Alembert system.

Positive progression system (e.g. Paroli)

Positive progression systems involve increasing the size of one's bet when one wins. The goal of these systems is to either exacerbate the effects of winning streaks (e.g. the Paroli system) or to take advantage of changes in luck to recover more quickly from previous losses (e.g. Oscar's grind). The shape of these systems is typically small but consistent losses followed by occasional big wins. However, over the long run these wins do not compensate for the losses incurred in between.[23]

• 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.[24]
• In 1963 Sean Connery, filming From Russia with Love in Italy, attended the casino in Saint-Vincent and won three consecutive times on the number 17, his winnings riding on the second and third spins.[25]
• 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.[26]

• Bauernroulette
• Boule
• Eudaemons
• Monte Carlo Paradox
• Russian roulette
• Straperlo
• The Gambler, a novel written by Fyodor Dostoevsky inspired by his addiction to roulette
• Le multicolore; a game similar to roulette