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Casino game of chance

This article is about the casino game. For other uses, see Roulette (disambiguation)

Roulette ball

"Gwendolen at the roulette 💸 table" – 1910 illustration to George Eliot's Daniel Deronda

Roulette (named after the French word meaning "little wheel") is a casino 💸 game which was likely developed from the Italian game Biribi. In the game, a player may choose to place a 💸 bet on a single number, various groupings of numbers, the color red or black, whether the number is odd or 💸 even, or if the numbers are high (19–36) or low (1–18).

To determine the winning number, a croupier spins a wheel 💸 in one direction, then spins a ball in the opposite direction around a tilted circular track running around the outer 💸 edge of the wheel. The ball eventually loses momentum, passes through an area of deflectors, and falls onto the wheel 💸 and into one of thirty-seven (single-zero, French or European style roulette) or thirty-eight (double-zero, American style roulette) or thirty-nine (triple-zero, 💸 "Sands Roulette")[1] colored and numbered pockets on the wheel. The winnings are then paid to anyone who has placed a 💸 successful bet.

History [ edit ]

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.

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]

Rules of play against a casino [ edit ]

Roulette with red 12 as the winner

Roulette players have a variety of 💸 betting options. "Inside" bets involve selecting either the exact number on which the ball will land, or a small group 💸 of numbers adjacent to each other on the layout. "Outside" bets, by contrast, allow players to select a larger group 💸 of numbers based on properties such as their color or parity (odd/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 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 losing bets either by hand or by rake, and determine the payouts for the remaining inside 💸 and outside winning bets. When the dealer is finished making payouts, the dolly is removed from the board and players 💸 may collect their winnings and make new bets. Winning chips remain on the board until picked up by a player.

California 💸 Roulette [ edit ]

In 2004, California legalized a form of roulette known as California Roulette.[10] By law, the game must 💸 use cards and not slots on the roulette wheel to pick the winning number.

Roulette wheel number sequence [ edit ]

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:[citation needed]

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

Roulette table layout [ edit ]

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.

Types of bets [ edit ]

In roulette, bets can be either inside or outside.[12]

Inside bets [ 💸 edit ]

Name Description Chip placement Straight/Single Bet on a single number Entirely within the square for the chosen number Split 💸 Bet on two vertically/horizontally adjacent numbers (e.g. 14-17 or 8–9) On the edge shared by the numbers Street Bet on 💸 three consecutive numbers in a horizontal line (e.g. 7-8-9) On the outer edge of the number at either end of 💸 the line Corner/Square Bet on four numbers that meet at one corner (e.g. 10-11-13-14) On the common corner Six Line/Double 💸 Street Bet on six consecutive numbers that form two horizontal lines (e.g. 31-32-33-34-35-36) On the outer corner shared by the 💸 two leftmost or the two rightmost numbers Trio/Basket A three-number bet that involves at least one zero: 0-1-2 (either layout); 💸 0-2-3 (single-zero only); 0-00-2 and 00-2-3 (double-zero only) On the corner shared by the three chosen numbers First Four Bet 💸 on 0-1-2-3 (Single-zero layout only) On the outer corner shared by 0-1 or 0-3 Top Line Bet on 0-00-1-2-3 (Double-zero 💸 layout only) On the outer corner shared by 0-1 or 00-3

Outside bets [ edit ]

Outside bets typically have smaller payouts 💸 with better odds at winning. Except as noted, all of these bets lose if a zero comes up.

1 to 18 💸 (Low or Manque), or 19 to 36 (High or Passe) A bet that the number will be in the chosen 💸 range. Red or black (Rouge ou Noir) A bet that the number will be the chosen color. Even or odd 💸 (Pair ou Impair) A bet that the number will be of the chosen type. Dozen bet A bet that the 💸 number will be in the chosen dozen: first (1-12, Première douzaine or P12), second (13-24, Moyenne douzaine or M12), or 💸 third (25-36, Dernière douzaine or D12). Column bet A bet that the number will be in the chosen vertical column 💸 of 12 numbers, such as 1-4-7-10 on down to 34. The chip is placed on the space below the final 💸 number in this sequence. Snake Bet A special bet that covers the numbers 1, 5, 9, 12, 14, 16, 19, 💸 23, 27, 30, 32, and 34. It has the same payout as the dozen bet and takes its name from 💸 the zigzagging, snakelike pattern traced out by these numbers. The snake bet is not available in all casinos; when it 💸 is allowed, the chip is placed on the lower corner of the 34 square that borders the 19-36 betting box. 💸 Some layouts mark the bet with a two-headed snake that winds from 1 to 34, and the bet can be 💸 placed on the head at either end of the body.

In the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) 💸 result in the player losing only half of their bet if a zero comes up.

Bet odds table [ edit ]

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

e x p e c t e d v a l u e = 1 n ( 36 💸 − n ) = 36 n − 1 , {\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.

Bet name Winning spaces Payout Odds 💸 against winning (French) Expected value

(on aR$1 bet) (French) Odds against winning (American) Expected value

(on aR$1 bet) (American) 0 0 35 💸 to 1 36 to 1 −$0.027 37 to 1 −$0.053 00 00 35 to 1 37 to 1 −$0.053 Straight 💸 up Any single number 35 to 1 36 to 1 −$0.027 37 to 1 −$0.053 Row 0, 00 17 to 💸 1 18 to 1 −$0.053 Split any two adjoining numbers vertical or horizontal 17 to 1 17 + 1 ⁄ 💸 2 to 1 −$0.027 18 to 1 −$0.053 Street any three numbers horizontal (1, 2, 3 or 4, 5, 6, 💸 etc.) 11 to 1 11 + 1 ⁄ 3 to 1 −$0.027 11 + 2 ⁄ 3 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 + 1 ⁄ 4 to 1 −$0.027 8 + 1 ⁄ 2 to 1 −$0.053 Top line (US) 💸 0, 00, 1, 2, 3 6 to 1 6 + 3 ⁄ 5 to 1 −$0.079 Top line (European) 0, 💸 1, 2, 3 8 to 1 8 + 1 ⁄ 4 to 1 −$0.027 Double Street 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 + 1 ⁄ 6 to 1 −$0.027 5 + 1 ⁄ 3 to 1 −$0.053 1st column 1, 4, 💸 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 2 to 1 2 + 1 ⁄ 12 to 1 💸 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 2nd column 2, 5, 8, 11, 14, 17, 20, 23, 26, 💸 29, 32, 35 2 to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 💸 1 −$0.053 3rd column 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36 2 to 1 2 💸 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 1st dozen 1 through 12 💸 2 to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 2nd 💸 dozen 13 through 24 2 to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 💸 to 1 −$0.053 3rd dozen 25 through 36 2 to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 💸 + 1 ⁄ 6 to 1 −$0.053 Odd 1, 3, 5, ..., 35 1 to 1 1 + 1 ⁄ 💸 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Even 2, 4, 6, ..., 36 1 to 💸 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Red 32, 19, 💸 21, 25, 34, 27, 36, 30, 23, 5, 16, 1, 14, 9, 18, 7, 12, 3 1 to 1 1 💸 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Black 15, 4, 2, 17, 💸 6, 13, 11, 8, 10, 24, 33, 20, 31, 22, 29, 28, 35, 26 1 to 1 1 + 1 💸 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 1 to 18 1, 2, 3, ..., 💸 18 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 💸 19 to 36 19, 20, 21, ..., 36 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 💸 + 1 ⁄ 9 to 1 −$0.053

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.

House edge [ edit ]

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)

Mathematical model [ edit ]

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 ( Ω , 2 Ω , P ) {\displaystyle (\Omega ,2^{\Omega },\mathbb 💸 {P} )} , where Ω = { 0 , … , 36 } {\displaystyle \Omega =\{0,\ldots ,36\}} , P ( 💸 A ) = | A | 37 {\displaystyle \mathbb {P} (A)={\frac {|A|}{37}}} for all A ∈ 2 Ω {\displaystyle A\in 💸 2^{\Omega }} .

Call the bet S {\displaystyle S} a triple ( A , r , ξ ) {\displaystyle (A,r,\xi )} 💸 , where A {\displaystyle A} is the set of chosen numbers, r ∈ R + {\displaystyle r\in \mathbb {R} _{+}} 💸 is the size of the bet, and ξ : Ω → R {\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, S = ( { ω 0 } , r , ξ ) {\displaystyle S=(\{\omega _{0}\},r,\xi 💸 )} , for some ω 0 ∈ Ω {\displaystyle \omega _{0}\in \Omega } , and ξ {\displaystyle \xi } is 💸 determined by

ξ ( ω ) = { − r , ω ≠ ω 0 35 ⋅ r , ω = 💸 ω 0 . {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega

eq \omega _{0}\\35\cdot r,&\omega =\omega _{0}\end{cases}}.}

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

M [ ξ ] = 1 37 ∑ ω ∈ Ω ξ ( ω ) = 1 37 ( ξ 💸 ( ω 0 ) + ∑ ω ≠ ω 0 ξ ( ω ) ) = 1 37 ( 35 💸 ⋅ r − 36 ⋅ r ) = − r 37 ≈ − 0.027 r . {\displaystyle M[\xi ]={\frac {1}{37}}\sum 💸 _{\omega \in \Omega }\xi (\omega )={\frac {1}{37}}\left(\xi (\omega _{0})+\sum _{\omega

eq \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

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

and the profitability

M [ ξ ] = 1 37 ( 18 ⋅ r − 18 ⋅ 💸 r − r ) = − r 37 {\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. − r 37 {\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:

∑ n = 1 ∞ M [ ξ 💸 n ] = − 1 37 ∑ n = 1 ∞ r n → − ∞ . {\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 − 3 38 r ≈ − 0.0789 r {\displaystyle -{\frac {3}{38}}r\approx -0.0789r} 💸 , and never better than − r 19 ≈ − 0.0526 r {\displaystyle -{\frac {r}{19}}\approx -0.0526r} .

Simplified mathematical model [ 💸 edit ]

For a roulette wheel with n {\displaystyle n} green numbers and 36 other unique numbers, the chance of the 💸 ball landing on a given number is 1 ( 36 + n ) {\displaystyle {\frac {1}{(36+n)}}} . For a betting 💸 option with p {\displaystyle p} numbers defining a win, the chance of winning a bet is p ( 36 + 💸 n ) {\displaystyle {\frac {p}{(36+n)}}}

For example, if a player bets on red, there are 18 red numbers, p = 18 💸 {\displaystyle p=18} , so the chance of winning is 18 ( 36 + n ) {\displaystyle {\frac {18}{(36+n)}}} .

The payout 💸 given by the casino for a win is based on the roulette wheel having 36 outcomes, and the payout for 💸 a bet is given by 36 p {\displaystyle {\frac {36}{p}}} .

For example, betting on 1-12 there are 12 numbers that 💸 define a win, p = 12 {\displaystyle p=12} , the payout is 36 12 = 3 {\displaystyle {\frac {36}{12}}=3} , 💸 so the bettor wins 3 times their bet.

The average return on a player's bet is given by p ( 36 💸 + n ) × 36 p = 36 ( 36 + n ) {\displaystyle {\frac {p}{(36+n)}}\times {\frac {36}{p}}={\frac {36}{(36+n)}}}

For n 💸 > 0 {\displaystyle n>0} , the average return is always lower than 1, so on average a player will lose 💸 money.

With 1 green number, n = 1 {\displaystyle n=1} , the average return is 36 37 {\displaystyle {\frac {36}{37}}} , 💸 that is, after a bet the player will on average have 36 37 {\displaystyle {\frac {36}{37}}} of their original bet 💸 returned to them. With 2 green numbers, n = 2 {\displaystyle n=2} , the average return is 36 38 {\displaystyle 💸 {\frac {36}{38}}} . With 3 green numbers, n = 3 {\displaystyle n=3} , the average return is 36 39 {\displaystyle 💸 {\frac {36}{39}}} .

This shows that the expected return is independent of the choice of bet.

Mechanics [ edit ]

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 eitherR$1 or the table minimum; if the player wishes, 💸 the chips may be worthR$0.25 so long as the "total" wager meets the table minimums for their respective sectors, for 💸 example by placing fourR$0.25 bets to meet aR$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]

Called (or call) bets or announced bets [ edit ]

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.

Voisins du zéro (neighbors of zero) [ edit ]

This 💸 is a name, more accurately "grands voisins du zéro", for the 17 numbers that lie between 22 and 25 on 💸 the wheel, including 22 and 25 themselves. The series is 22-18-29-7-28-12-35-3-26-0-32-15-19-4-21-2-25 (on a single-zero wheel).

Nine chips or multiples thereof are 💸 bet. Two chips are placed on the 0-2-3 trio; one on the 4–7 split; one on 12–15; one on 18–21; 💸 one on 19–22; two on the 25-26-28-29 corner; and one on 32–35.

Jeu zéro (zero game) [ edit ]

Zero game, also 💸 known as zero spiel (Spiel is German for game or play), is the name for the numbers closest to zero. 💸 All numbers in the zero game are included in the voisins, but are placed differently. The numbers bet on are 💸 12-35-3-26-0-32-15.

The bet consists of four chips or multiples thereof. Three chips are bet on splits and one chip straight-up: one 💸 chip on 0–3 split, one on 12–15 split, one on 32–35 split and one straight-up on number 26.

This type of 💸 bet is popular in Germany and many European casinos. It is also offered as a 5-chip bet in many Eastern 💸 European casinos. As a 5-chip bet, it is known as "zero spiel naca" and includes, in addition to the chips 💸 placed as noted above, a straight-up on number 19.

Le tiers du cylindre (third of the wheel) [ edit ]

This is 💸 the name for the 12 numbers that lie on the opposite side of the wheel between 27 and 33, including 💸 27 and 33 themselves. On a single-zero wheel, the series is 27-13-36-11-30-8-23-10-5-24-16-33. The full name (although very rarely used, most 💸 players refer to it as "tiers") for this bet is "le tiers du cylindre" (translated from French into English meaning 💸 one third of the wheel) because it covers 12 numbers (placed as 6 splits), which is as close to 1⁄3 💸 of the wheel as one can get.

Very popular in British casinos, tiers bets outnumber voisins and orphelins bets by a 💸 massive margin.

Six chips or multiples thereof are bet. One chip is placed on each of the following splits: 5–8, 10–11, 💸 13–16, 23–24, 27–30, and 33–36.

The tiers bet is also called the "small series" and in some casinos (most notably in 💸 South Africa) "series 5-8".

A variant known as "tiers 5-8-10-11" has an additional chip placed straight up on 5, 8, 10, 💸 and 11m and so is a 10-piece bet. In some places the variant is called "gioco Ferrari" with a straight 💸 up on 8, 11, 23 and 30, the bet is marked with a red G on the racetrack.

Orphelins (orphans) [ 💸 edit ]

These numbers make up the two slices of the wheel outside the tiers and voisins. They contain a total 💸 of 8 numbers, comprising 17-34-6 and 1-20-14-31-9.

Five chips or multiples thereof are bet on four splits and a straight-up: one 💸 chip is placed straight-up on 1 and one chip on each of the splits: 6–9, 14–17, 17–20, and 31–34.

... and 💸 the neighbors [ edit ]

A number may be backed along with the two numbers on the either side of it 💸 in a 5-chip bet. For example, "0 and the neighbors" is a 5-chip bet with one piece straight-up on 3, 💸 26, 0, 32, and 15. Neighbors bets are often put on in combinations, for example "1, 9, 14, and the 💸 neighbors" is a 15-chip bet covering 18, 22, 33, 16 with one chip, 9, 31, 20, 1 with two chips 💸 and 14 with three chips.

Any of the above bets may be combined, e.g. "orphelins by 1 and zero and the 💸 neighbors by 1". The "...and the neighbors" is often assumed by the croupier.

Final bets [ edit ]

Another bet offered on 💸 the single-zero game is "final", "finale" or "finals".

Final 4, for example, is a 4-chip bet and consists of one chip 💸 placed on each of the numbers ending in 4, that is 4, 14, 24, and 34. Final 7 is a 💸 3-chip bet, one chip each on 7, 17, and 27. Final bets from final 0 (zero) to final 6 cost 💸 four chips. Final bets 7, 8 and 9 cost three chips.

Some casinos also offer split-final bets, for example final 5-8 💸 would be a 4-chip bet, one chip each on the splits 5–8, 15–18, 25–28, and one on 35.

Full completes/maximums [ 💸 edit ]

A complete bet places all of the inside bets on a certain number. Full complete bets are most often 💸 bet by high rollers as maximum bets.

The maximum amount allowed to be wagered on a single bet in European roulette 💸 is based on a progressive betting model. If the casino allows a maximum bet ofR$1,000 on a 35-to-1 straight-up, then 💸 on each 17-to-1 split connected to that straight-up,R$2,000 may be wagered. Each 8-to-1 corner that covers four numbers) may haveR$4,000 💸 wagered on it. Each 11-to-1 street that covers three numbers may haveR$3,000 wagered on it. Each 5-to-1 six-line may haveR$6,000 💸 wagered on it. EachR$1,000 incremental bet would be represented by a marker that is used to specifically identify the player 💸 and the amount bet.

For instance, if a patron wished to place a full complete bet on 17, the player would 💸 call "17 to the maximum". This bet would require a total of 40 chips, orR$40,000. To manually place the same 💸 wager, the player would need to bet:

17 to the maximum Bet type Number(s) bet on Chips Amount waged Straight-up 17 💸 1R$1,000 Split 14-17 2R$2,000 Split 16-17 2R$2,000 Split 17-18 2R$2,000 Split 17-20 2R$2,000 Street 16-17-18 3R$3,000 Corner 13-14-16-17 4R$4,000 Corner 💸 14-15-17-18 4R$4,000 Corner 16-17-19-20 4R$4,000 Corner 17-18-20-21 4R$4,000 Six line 13-14-15-16-17-18 6R$6,000 Six line 16-17-18-19-20-21 6R$6,000 Total 40R$40,000

The player calls 💸 their bet to the croupier (most often after the ball has been spun) and places enough chips to cover the 💸 bet on the table within reach of the croupier. The croupier will immediately announce the bet (repeat what the player 💸 has just said), ensure that the correct monetary amount has been given while simultaneously placing a matching marker on the 💸 number on the table and the amount wagered.

The payout for this bet if the chosen number wins is 392 chips, 💸 in the case of aR$1000 straight-up maximum,R$40,000 bet, a payout ofR$392,000. The player's wagered 40 chips, as with all winning 💸 bets in roulette, are still their property and in the absence of a request to the contrary are left up 💸 to possibly win again on the next spin.

Based on the location of the numbers on the layout, the number of 💸 chips required to "complete" a number can be determined.

Zero costs 17 chips to complete and pays 235 chips.

Number 1 and 💸 number 3 each cost 27 chips and pay 297 chips.

Number 2 is a 36-chip bet and pays 396 chips.

1st column 💸 numbers 4 to 31 and 3rd column numbers 6 to 33, cost 30 chips each to complete. The payout for 💸 a win on these 30-chip bets is 294 chips.

2nd column numbers 5 to 32 cost 40 chips each to complete. 💸 The payout for a win on these numbers is 392 chips.

Numbers 34 and 36 each cost 18 chips and pay 💸 198 chips.

Number 35 is a 24-chip bet which pays 264 chips.

Most typically (Mayfair casinos in London and other top-class European 💸 casinos) with these maximum or full complete bets, nothing (except the aforementioned maximum button) is ever placed on the layout 💸 even in the case of a win. Experienced gaming staff, and the type of customers playing such bets, are fully 💸 aware of the payouts and so the croupier simply makes up the correct payout, announces its value to the table 💸 inspector (floor person in the U.S.) and the customer, and then passes it to the customer, but only after a 💸 verbal authorization from the inspector has been received.

Also typically at this level of play (house rules allowing) the experienced croupier 💸 caters to the needs of the customer and will most often add the customer's winning bet to the payout, as 💸 the type of player playing these bets very rarely bets the same number two spins in succession. For example, the 💸 winning 40-chip /R$40,000 bet on "17 to the maximum" pays 392 chips /R$392,000. The experienced croupier would pay the player 💸 432 chips /R$432,000, that is 392 + 40, with the announcement that the payout "is with your bet down".

There are 💸 also several methods to determine the payout when a number adjacent to a chosen number is the winner, for example, 💸 player bets 40 chips on "23 to the maximum" and number 26 is the winning number. The most notable method 💸 is known as the "station" system or method. When paying in stations, the dealer counts the number of ways or 💸 stations that the winning number hits the complete bet. In the example above, 26 hits 4 stations - 2 different 💸 corners, 1 split and 1 six-line. The dealer takes the number 4, multiplies it by 30 and adds the remaining 💸 8 to the payout: 4 × 30 = 120, 120 + 8 = 128. If calculated as stations, they would 💸 just multiply 4 by 36, making 144 with the players bet down.

In some casinos, a player may bet full complete 💸 for less than the table straight-up maximum, for example, "number 17 full complete byR$25" would costR$1000, that is 40 chips 💸 each atR$25 value.

Betting strategies and tactics [ edit ]

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][unreliable source?] 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.

Prediction methods [ edit ]

Whereas betting systems are 💸 essentially an attempt to beat the fact that a geometric series with initial value of 0.95 (American roulette) or 0.97 💸 (European roulette) will inevitably over time tend to zero, engineers instead attempt 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. If effective, they raise the return of the game 💸 above 100%, defeating the betting system problem.

Edward O. Thorp (the developer of card counting and an early hedge-fund pioneer) and 💸 Claude Shannon (a mathematician and electronic engineer best known for his contributions to information theory) built the first wearable computer 💸 to predict the landing of the ball in 1961. This system worked by timing the ball and wheel, and using 💸 the information obtained to calculate the most likely octant where the ball would fall. Ironically, this technique works best with 💸 an unbiased wheel though it could still be countered quite easily by simply closing the table for betting before beginning 💸 the spin.

In 1982, several casinos in Britain began to lose large sums of money at their roulette tables to teams 💸 of gamblers from the US. 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 British roulette wheel manufacturer John Huxley manufactured a roulette wheel to 💸 counteract the problem.

The new wheel, designed by George Melas, was called "low profile" because the pockets had been drastically reduced 💸 in depth, and various other design modifications caused the ball to descend in a gradual approach to the pocket area. 💸 In 1986, when a professional gambling team headed by Billy Walters wonR$3.8 million using the system on an old wheel 💸 at the Golden Nugget in Atlantic City, every casino in the world took notice, and within one year had switched 💸 to the new low-profile wheel.

Thomas Bass, in his book The Eudaemonic Pie (1985) (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 University of California Santa Cruz students, who called themselves the Eudaemons, who in the late 1970s used computers in 💸 their shoes to win at roulette. This is an updated and improved version of Edward O. Thorp's approach, where Newtonian 💸 Laws of Motion are applied to track the roulette ball's deceleration; hence the British title.

In the early 1990s, Gonzalo Garcia-Pelayo 💸 believed that casino roulette wheels were not perfectly random, and that by recording the results and analysing them with a 💸 computer, he could gain an edge on the house by predicting that certain numbers were more likely to occur next 💸 than the 1-in-36 odds offered by the house suggested. He did this at the Casino de Madrid in Madrid, Spain, 💸 winning 600,000 euros in a single day, and one million euros in total. Legal action against him by the casino 💸 was unsuccessful, being ruled that the casino should fix its wheel.[18][19]

To defend against exploits like these, many casinos use tracking 💸 software, use wheels with new designs, rotate wheel heads, and randomly rotate pocket rings.[20]

At the Ritz London casino in March 💸 2004, two Serbs and a Hungarian 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 netted £1.3m in two nights.[21] 💸 They were arrested and kept on police bail for nine months, but eventually released and allowed to keep their winnings 💸 as they had not interfered with the casino equipment.[22]

Specific betting systems [ edit ]

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 gambler 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. The problem with this strategy is that, remembering that 💸 past results do not affect the future, it is possible for the player to lose so many times in a 💸 row, that the player, doubling and redoubling their bets, either runs out of money or hits the table limit. A 💸 large financial loss is certain in the long term if the player continued to employ this strategy. 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, since the expected value of each allowed bet is negative.

Types of betting system [ 💸 edit ]

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]

Reverse Martingale system [ edit ]

The Reverse Martingale system, also known as the Paroli system, follows the idea of 💸 the martingale betting strategy, but reversed. Instead of doubling a bet after a loss the gambler doubles the bet after 💸 every win. The system creates a false feeling of eliminating the risk of betting more when losing, but, in reality, 💸 it has the same problem as the martingale strategy. By doubling bets after every win, one keeps betting everything they 💸 have won until they either stop playing, or lose it all.

Labouchère system [ edit ]

The Labouchère System is a progression 💸 betting strategy like the martingale but does not require the gambler to risk their stake as quickly with dramatic double-ups. 💸 The Labouchere System involves using a series of numbers in a line to determine the bet amount, following a win 💸 or a loss. Typically, the player adds the numbers at the front and end of the line to determine the 💸 size of the next bet. If the player wins, they cross out numbers and continue working on the smaller line. 💸 If the player loses, then they add their previous bet to the end of the line and continue to work 💸 on the longer line. This is a much more flexible progression betting system and there is much room for the 💸 player to design their initial line to their own playing preference.

This system is one that is designed so that when 💸 the player has won over a third of their bets (less than the expected 18/38), they will win. Whereas the 💸 martingale will cause ruin in the event of a long sequence of successive losses, the Labouchère system will cause bet 💸 size to grow quickly even where a losing sequence is broken by wins. This occurs because as the player loses, 💸 the average bet size in the line increases.

As with all other betting systems, the average value of this system is 💸 negative.

D'Alembert system [ edit ]

The system, also called montant et demontant (from French, meaning upwards and downwards), is often called 💸 a pyramid system. It is based on a mathematical equilibrium theory devised by a French mathematician of the same name. 💸 Like the martingale, this system is mainly applied to the even-money outside bets, and is favored by players who want 💸 to keep the amount of their bets and losses to a minimum. The betting progression is very simple: After each 💸 loss, one unit is added to the next bet, and after each win, one unit is deducted from the next 💸 bet. Starting with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. 💸 If this is followed by a win, the next bet would be 1 units.

This betting system relies on the gambler's 💸 fallacy—that the player is more likely to lose following a win, and more likely to win following a loss.

Other systems 💸 [ edit ]

There are numerous other betting systems that rely on this fallacy, or that attempt to follow 'streaks' (looking 💸 for patterns in randomness), varying bet size accordingly.

Many betting systems are sold online and purport to enable the player to 💸 'beat' the odds. One such system was advertised by Jason Gillon of Rotherham, UK, who claimed one could 'earn £200 💸 daily' by following his betting system, described as a 'loophole'. As the system was advertised in the UK press, it 💸 was subject to Advertising Standards Authority regulation, and following a complaint, it was ruled by the ASA that Mr. Gillon 💸 had failed to support his claims, and that he had failed to show that there was any loophole.

Notable winnings [ 💸 edit ]

In the 1960s and early 1970s, Richard Jarecki won aboutR$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 Italy, attended the casino in Saint-Vincent and won three consecutive 💸 times on the number 17, his winnings on the second and third spins. 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 withR$270,600.[26]