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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 1️⃣ table" – 1910

illustration to George Eliot's Daniel Deronda

Roulette (named after the French word

meaning "little wheel") is a casino 1️⃣ game which was likely developed from the Italian

game Biribi. In the game, a player may choose to place a 1️⃣ bet on a single number,

various groupings of numbers, the color red or black, whether the number is odd or

1️⃣ even, or if the numbers are high (19–36) or low (1–18).

To determine the winning

number, a croupier spins a wheel 1️⃣ in one direction, then spins a ball in the opposite

direction around a tilted circular track running around the outer 1️⃣ edge of the wheel.

The ball eventually loses momentum, passes through an area of deflectors, and falls

onto the wheel 1️⃣ 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, 1️⃣ "Sands Roulette")[1] colored and numbered pockets on the wheel. The

winnings are then paid to anyone who has placed a 1️⃣ successful bet.

History [ edit

]

18th-century E.O. wheel with gamblers

The first form of roulette was devised in

18th-century France. Many historians 1️⃣ believe Blaise Pascal introduced a primitive form

of roulette in the 17th century in his search for a perpetual motion 1️⃣ machine. [2] The

roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game

Biribi.[3] 1️⃣ A primitive form of roulette, known as 'EO' (Even/Odd), was played in

England in the late 18th century using a 1️⃣ gaming wheel similar to that used in

roulette.[4]

The game has been played in its present form since as early as 1️⃣ 1796 in

Paris. An early description of the roulette game in its current form is found in a

French novel 1️⃣ La Roulette, ou le Jour by Jaques Lablee, which describes a roulette wheel

in the Palais Royal in Paris in 1️⃣ 1796. The description included the house pockets:

"There are exactly two slots reserved for the bank, whence it derives its 1️⃣ sole

mathematical advantage." It then goes on to describe the layout with "two betting

spaces containing the bank's two numbers, 1️⃣ zero and double zero". The book was published

in 1801. An even earlier reference to a game of this name 1️⃣ was published in regulations

for New France (Québec) in 1758, which banned the games of "dice, hoca, faro, and

roulette".[5]

The 1️⃣ roulette wheels used in the casinos of Paris in the late 1790s had

red for the single zero and black 1️⃣ for the double zero. To avoid confusion, the color

green was selected for the zeros in roulette wheels starting in 1️⃣ the 1800s.

In 1843, in

the German spa casino town of Bad Homburg, fellow Frenchmen François and Louis Blanc

introduced the 1️⃣ single 0 style roulette wheel in order to compete against other casinos

offering the traditional wheel with single and double 1️⃣ zero house pockets.[6]

In some

forms of early American roulette wheels, there were numbers 1 to 28, plus a single

zero, 1️⃣ a double zero, and an American Eagle. The Eagle slot, which was a symbol of

American liberty, was a house 1️⃣ slot that brought the casino an extra edge. Soon, the

tradition vanished and since then the wheel features only numbered 1️⃣ slots. According to

Hoyle "the single 0, the double 0, and the eagle are never bars; but when the ball

1️⃣ falls into either of them, the banker sweeps every thing upon the table, except what

may happen to be bet 1️⃣ on either one of them, when he pays twenty-seven for one, which is

the amount paid for all sums bet 1️⃣ upon any single figure".[7]

1800s engraving of the

French roulette

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

1️⃣ becoming one of the most famous and most popular casino games. When the German

government abolished gambling in the 1860s, 1️⃣ the Blanc family moved to the last legal

remaining casino operation in Europe at Monte Carlo, where they established a 1️⃣ gambling

mecca for the elite of Europe. It was here that the single zero roulette wheel became

the premier game, 1️⃣ and over the years was exported around the world, except in the

United States where the double zero wheel remained 1️⃣ dominant.

Early American West

makeshift game

In the United States, the French double zero wheel made its way up the

Mississippi from 1️⃣ New Orleans, and then westward. It was here, because of rampant

cheating by both operators and gamblers, that the wheel 1️⃣ was eventually placed on top of

the table to prevent devices from being hidden in the table or wheel, and 1️⃣ the betting

layout was simplified. This eventually evolved into the American-style roulette game.

The American game was developed in the 1️⃣ gambling dens across the new territories where

makeshift games had been set up, whereas the French game evolved with style 1️⃣ and leisure

in Monte Carlo.

During the first part of the 20th century, the only casino towns of

note were Monte 1️⃣ Carlo with the traditional single zero French wheel, and Las Vegas with

the American double zero wheel. In the 1970s, 1️⃣ casinos began to flourish around the

world. In 1996 the first online casino, generally believed to be InterCasino, made it

1️⃣ possible to play roulette online.[8] By 2008, there were several hundred casinos

worldwide offering roulette games. The double zero wheel 1️⃣ is found in the U.S., Canada,

South America, and the Caribbean, while the single zero wheel is predominant

elsewhere.

The sum 1️⃣ of all the numbers on the roulette wheel (from 0 to 36) is 666,

which is the "Number of the 1️⃣ Beast".[9]

Rules of play against a casino [ edit ]

Roulette

with red 12 as the winner

Roulette players have a variety of 1️⃣ betting options. "Inside"

bets involve selecting either the exact number on which the ball will land, or a small

group 1️⃣ of numbers adjacent to each other on the layout. "Outside" bets, by contrast,

allow players to select a larger group 1️⃣ of numbers based on properties such as their

color or parity (odd/even). The payout odds for each type of bet 1️⃣ are based on its

probability.

The roulette table usually imposes minimum and maximum bets, and these

rules usually apply separately for 1️⃣ all of a player's inside and outside bets for each

spin. For inside bets at roulette tables, some casinos may 1️⃣ use separate roulette table

chips of various colors to distinguish players at the table. Players can continue to

place bets 1️⃣ as the ball spins around the wheel until the dealer announces "no more bets"

or "rien ne va plus".

Croupier's rake 1️⃣ pushing chips across a roulette layout

When a

winning number and color is determined by the roulette wheel, the dealer will 1️⃣ place a

marker, also known as a dolly, on that number on the roulette table layout. When the

dolly is 1️⃣ on the table, no players may place bets, collect bets or remove any bets from

the table. The dealer will 1️⃣ then sweep away all losing bets either by hand or by rake,

and determine the payouts for the remaining inside 1️⃣ and outside winning bets. When the

dealer is finished making payouts, the dolly is removed from the board and players 1️⃣ may

collect their winnings and make new bets. Winning chips remain on the board until

picked up by a player.

California 1️⃣ Roulette [ edit ]

In 2004, California legalized a

form of roulette known as California Roulette.[10] By law, the game must 1️⃣ use cards and

not slots on the roulette wheel to pick the winning number.

Roulette wheel number

sequence [ edit ]

The 1️⃣ pockets of the roulette wheel are numbered from 0 to 36.

In

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

ranges from 11 to 18 and 29 to 36, odd 1️⃣ numbers are black and even are red.

There is a

green pocket numbered 0 (zero). In American roulette, there is a 1️⃣ second green pocket

marked 00. Pocket number order on the roulette wheel adheres to the following clockwise

sequence in most 1️⃣ 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

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

8-29-7-28-12-35-3-26

Roulette table layout [ edit ]

French style layout, French single

zero 1️⃣ 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 1️⃣ European-style layout has a single

zero, and the American style layout is usually a double-zero. The American-style

roulette table with 1️⃣ a wheel at one end is now used in most casinos because it has a

higher house edge compared to 1️⃣ a European layout.[11]

The French style table with a

wheel in the centre and a layout on either side is rarely 1️⃣ found outside of Monte

Carlo.

Types of bets [ edit ]

In roulette, bets can be either inside or

outside.[12]

Inside bets [ 1️⃣ edit ]

Name Description Chip placement Straight/Single Bet

on a single number Entirely within the square for the chosen number Split 1️⃣ Bet on two

vertically/horizontally adjacent numbers (e.g. 14-17 or 8–9) On the edge shared by the

numbers Street Bet on 1️⃣ three consecutive numbers in a horizontal line (e.g. 7-8-9) On

the outer edge of the number at either end of 1️⃣ 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

1️⃣ 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 1️⃣ two leftmost or the two rightmost

numbers Trio/Basket A three-number bet that involves at least one zero: 0-1-2 (either

layout); 1️⃣ 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 1️⃣ 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 1️⃣ layout

only) On the outer corner shared by 0-1 or 00-3

Outside bets [ edit ]

Outside bets

typically have smaller payouts 1️⃣ with better odds at winning. Except as noted, all of

these bets lose if a zero comes up.

1 to 18 1️⃣ (Low or Manque), or 19 to 36 (High or

Passe) A bet that the number will be in the chosen 1️⃣ range. Red or black (Rouge ou Noir)

A bet that the number will be the chosen color. Even or odd 1️⃣ (Pair ou Impair) A bet that

the number will be of the chosen type. Dozen bet A bet that the 1️⃣ number will be in the

chosen dozen: first (1-12, Première douzaine or P12), second (13-24, Moyenne douzaine

or M12), or 1️⃣ third (25-36, Dernière douzaine or D12). Column bet A bet that the number

will be in the chosen vertical column 1️⃣ of 12 numbers, such as 1-4-7-10 on down to 34.

The chip is placed on the space below the final 1️⃣ number in this sequence. Snake Bet A

special bet that covers the numbers 1, 5, 9, 12, 14, 16, 19, 1️⃣ 23, 27, 30, 32, and 34. It

has the same payout as the dozen bet and takes its name from 1️⃣ the zigzagging, snakelike

pattern traced out by these numbers. The snake bet is not available in all casinos;

when it 1️⃣ is allowed, the chip is placed on the lower corner of the 34 square that

borders the 19-36 betting box. 1️⃣ Some layouts mark the bet with a two-headed snake that

winds from 1 to 34, and the bet can be 1️⃣ placed on the head at either end of the body.

In

the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) 1️⃣ result in

the player losing only half of their bet if a zero comes up.

Bet odds table [ edit

]

The 1️⃣ expected value of aR$1 bet (except for the special case of Top line bets), for

American and European roulette, can 1️⃣ be calculated as

e x p e c t e d v a l u e = 1 n (

36 1️⃣ − n ) = 36 n − 1 , {\displaystyle \mathrm {expectedvalue} ={\frac

{1}{n}}(36-n)={\frac {36}{n}}-1,}

where n is the number of 1️⃣ pockets in the wheel.

The

initial bet is returned in addition to the mentioned payout: it can be easily

demonstrated that 1️⃣ this payout formula would lead to a zero expected value of profit if

there were only 36 numbers (that is, 1️⃣ the casino would break even). Having 37 or more

numbers gives the casino its edge.

Bet name Winning spaces Payout Odds 1️⃣ against winning

(French) Expected value

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

value

(on aR$1 bet) (American) 0 0 35 1️⃣ to 1 36 to 1 −$0.027 37 to 1 −$0.053 00 00 35 to

1 37 to 1 −$0.053 Straight 1️⃣ up Any single number 35 to 1 36 to 1 −$0.027 37 to 1 −$0.053

Row 0, 00 17 to 1️⃣ 1 18 to 1 −$0.053 Split any two adjoining numbers vertical or

horizontal 17 to 1 17 + 1 ⁄ 1️⃣ 2 to 1 −$0.027 18 to 1 −$0.053 Street any three numbers

horizontal (1, 2, 3 or 4, 5, 6, 1️⃣ etc.) 11 to 1 11 + 1 ⁄ 3 to 1 −$0.027 11 + 2 ⁄ 3 to 1

−$0.053 1️⃣ Corner any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21,

etc.) 8 to 1️⃣ 1 8 + 1 ⁄ 4 to 1 −$0.027 8 + 1 ⁄ 2 to 1 −$0.053 Top line (US) 1️⃣ 0, 00, 1, 2, 3

6 to 1 6 + 3 ⁄ 5 to 1 −$0.079 Top line (European) 0, 1️⃣ 1, 2, 3 8 to 1 8 + 1 ⁄ 4 to 1

−$0.027 Double Street any six numbers from 1️⃣ two horizontal rows (1, 2, 3, 4, 5, 6 or 28,

29, 30, 31, 32, 33 etc.) 5 to 1 1️⃣ 5 + 1 ⁄ 6 to 1 −$0.027 5 + 1 ⁄ 3 to 1 −$0.053 1st

column 1, 4, 1️⃣ 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 2 to 1 2 + 1 ⁄ 12 to 1 1️⃣ −$0.027 2 + 1

⁄ 6 to 1 −$0.053 2nd column 2, 5, 8, 11, 14, 17, 20, 23, 26, 1️⃣ 29, 32, 35 2 to 1 2 + 1 ⁄

12 to 1 −$0.027 2 + 1 ⁄ 6 to 1️⃣ 1 −$0.053 3rd column 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,

33, 36 2 to 1 2 1️⃣ + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 1st dozen 1 through 12 1️⃣ 2

to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 2nd 1️⃣ dozen 13 through 24 2 to 1 2 +

1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 1️⃣ to 1 −$0.053 3rd dozen 25 through 36 2 to 1 2 + 1 ⁄ 12 to

1 −$0.027 2 1️⃣ + 1 ⁄ 6 to 1 −$0.053 Odd 1, 3, 5, ..., 35 1 to 1 1 + 1 ⁄ 1️⃣ 18 to 1 −$0.027 1

+ 1 ⁄ 9 to 1 −$0.053 Even 2, 4, 6, ..., 36 1 to 1️⃣ 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to

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

1 1️⃣ + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Black 15, 4, 2, 17, 1️⃣ 6, 13, 11, 8, 10,

24, 33, 20, 31, 22, 29, 28, 35, 26 1 to 1 1 + 1 1️⃣ ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1

−$0.053 1 to 18 1, 2, 3, ..., 1️⃣ 18 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053

1️⃣ 19 to 36 19, 20, 21, ..., 36 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 1️⃣ + 1 ⁄ 9 to 1 −$0.053

Top

line (0, 00, 1, 2, 3) has a different expected value because of 1️⃣ 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 1️⃣ or even, or high or low.

En prison rules, when used, reduce the house

advantage.

House edge [ edit ]

The house average 1️⃣ or house edge or house advantage (also

called the expected value) is the amount the player loses relative to any 1️⃣ bet made, on

average. If a player bets on a single number in the American game there is a

probability 1️⃣ of 1⁄38 that the player wins 35 times the bet, and a 37⁄38 chance that the

player loses their bet. 1️⃣ The expected value is:

−1 × 37 ⁄ 38 + 35 × 1 ⁄ 38 = −0.0526

(5.26% house edge)

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

−1

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

For triple-zero wheels, a single

number wins 1⁄39 and loses 38⁄39:

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

edge)

Mathematical model [ edit ]

As an example, the European roulette model, that 1️⃣ is,

roulette with only one zero, can be examined. Since this roulette has 37 cells with

equal odds of hitting, 1️⃣ this is a final model of field probability ( Ω , 2 Ω , P )

{\displaystyle (\Omega ,2^{\Omega },\mathbb 1️⃣ {P} )} , where Ω = { 0 , … , 36 }

{\displaystyle \Omega =\{0,\ldots ,36\}} , P ( 1️⃣ A ) = | A | 37 {\displaystyle \mathbb

{P} (A)={\frac {|A|}{37}}} for all A ∈ 2 Ω {\displaystyle A\in 1️⃣ 2^{\Omega }} .

Call the

bet S {\displaystyle S} a triple ( A , r , ξ ) {\displaystyle (A,r,\xi )} 1️⃣ , where A

{\displaystyle A} is the set of chosen numbers, r ∈ R + {\displaystyle r\in \mathbb {R}

_{+}} 1️⃣ is the size of the bet, and ξ : Ω → R {\displaystyle \xi :\Omega \to \mathbb {R}

} determines 1️⃣ the return of the bet.[13]

The rules of European roulette have 10 types of

bets. First the 'Straight Up' bet can 1️⃣ be imagined. In this case, S = ( { ω 0 } , r , ξ

) {\displaystyle S=(\{\omega _{0}\},r,\xi 1️⃣ )} , for some ω 0 ∈ Ω {\displaystyle \omega

_{0}\in \Omega } , and ξ {\displaystyle \xi } is 1️⃣ determined by

ξ ( ω ) = { − r , ω ≠ ω

0 35 ⋅ r , ω = 1️⃣ 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 1️⃣ to

M [ ξ ] = 1 37 ∑ ω ∈ Ω ξ ( ω ) = 1 37 ( ξ 1️⃣ ( ω 0 ) + ∑ ω ≠ ω

0 ξ ( ω ) ) = 1 37 ( 35 1️⃣ ⋅ r − 36 ⋅ r ) = − r 37 ≈ − 0.027 r . {\displaystyle M[\xi

]={\frac {1}{37}}\sum 1️⃣ _{\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, 1️⃣ for a bet, black (or red), the rule is determined as

ξ ( ω ) = { − r , ω 1️⃣ is

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

{\text{ is 1️⃣ red}}\\-r,&\omega =0\\r,&\omega {\text{ is black}}\end{cases}},}

and the

profitability

M [ ξ ] = 1 37 ( 18 ⋅ r − 18 ⋅ 1️⃣ 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 1️⃣ to see that the profitability is also equal for all remaining types of bets. − r

37 {\displaystyle -{\frac {r}{37}}} 1️⃣ .[14]

In reality this means that, the more bets a

player makes, the more they are going to lose independent of 1️⃣ the strategies

(combinations of bet types or size of bets) that they employ:

∑ n = 1 ∞ M [ ξ 1️⃣ n ] = − 1

37 ∑ n = 1 ∞ r n → − ∞ . {\displaystyle \sum _{n=1}^{\infty 1️⃣ }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, 1️⃣ several roulette strategy

systems have been developed despite the losing odds. These systems can not change the

odds of the 1️⃣ game in favor of the player.

It is worth noting that the odds for the

player in American roulette are even 1️⃣ worse, as the bet profitability is at worst − 3 38

r ≈ − 0.0789 r {\displaystyle -{\frac {3}{38}}r\approx -0.0789r} 1️⃣ , and never better

than − r 19 ≈ − 0.0526 r {\displaystyle -{\frac {r}{19}}\approx -0.0526r} .

Simplified

mathematical model [ 1️⃣ edit ]

For a roulette wheel with n {\displaystyle n} green numbers

and 36 other unique numbers, the chance of the 1️⃣ ball landing on a given number is 1 ( 36

+ n ) {\displaystyle {\frac {1}{(36+n)}}} . For a betting 1️⃣ option with p {\displaystyle

p} numbers defining a win, the chance of winning a bet is p ( 36 + 1️⃣ n ) {\displaystyle

{\frac {p}{(36+n)}}}

For example, if a player bets on red, there are 18 red numbers, p

= 18 1️⃣ {\displaystyle p=18} , so the chance of winning is 18 ( 36 + n ) {\displaystyle

{\frac {18}{(36+n)}}} .

The payout 1️⃣ given by the casino for a win is based on the

roulette wheel having 36 outcomes, and the payout for 1️⃣ a bet is given by 36 p

{\displaystyle {\frac {36}{p}}} .

For example, betting on 1-12 there are 12 numbers

that 1️⃣ define a win, p = 12 {\displaystyle p=12} , the payout is 36 12 = 3 {\displaystyle

{\frac {36}{12}}=3} , 1️⃣ so the bettor wins 3 times their bet.

The average return on a

player's bet is given by p ( 36 1️⃣ + n ) × 36 p = 36 ( 36 + n ) {\displaystyle {\frac

{p}{(36+n)}}\times {\frac {36}{p}}={\frac {36}{(36+n)}}}

For n 1️⃣ > 0 {\displaystyle n>0}

, the average return is always lower than 1, so on average a player will lose

1️⃣ money.

With 1 green number, n = 1 {\displaystyle n=1} , the average return is 36 37

{\displaystyle {\frac {36}{37}}} , 1️⃣ that is, after a bet the player will on average have

36 37 {\displaystyle {\frac {36}{37}}} of their original bet 1️⃣ returned to them. With 2

green numbers, n = 2 {\displaystyle n=2} , the average return is 36 38 {\displaystyle

1️⃣ {\frac {36}{38}}} . With 3 green numbers, n = 3 {\displaystyle n=3} , the average

return is 36 39 {\displaystyle 1️⃣ {\frac {36}{39}}} .

This shows that the expected return

is independent of the choice of bet.

Mechanics [ edit ]

All roulette tables 1️⃣ deal with

only four elements:

1. The roulette wheel.

2. The roulette table (aka layout).

3. The

ball. These days the ball is 1️⃣ most likely high impact plastic, but originally it was

made of ivory. Modern casinos maintain the integrity of their roulette 1️⃣ balls with

regular magnetic and x-ray exams.

4. The chips. Some casinos allow the player to use

generic casino chips at 1️⃣ the roulette tables, but most require the player to buy in at

the table. The croupier has stacks of various 1️⃣ colored chips. Usually each player gets a

different color to help avoid confusion of bets, and the player can designate 1️⃣ the value

of the chip. The chips are typically valued at eitherR$1 or the table minimum; if the

player wishes, 1️⃣ the chips may be worthR$0.25 so long as the "total" wager meets the

table minimums for their respective sectors, for 1️⃣ example by placing fourR$0.25 bets to

meet aR$1 table minimum.

All roulette tables operated by a casino have the same basic

1️⃣ mechanics:

There is a balanced mechanical wheel with colored pockets separated by

identical vanes and the wheel which spins freely on 1️⃣ a supporting post.

The wheel is

held within a wooden frame which contains a track around the upper outer edge and

1️⃣ blocks of a variety of designs placed approximately halfway down the face of the

frame.

A plastic or ivory ball is 1️⃣ spun in the track in the frame that holds the wheel.

As the ball loses momentum the centrifugal force is 1️⃣ no longer sufficient to hold the

ball in the groove and it falls down the face of the frame. As 1️⃣ the ball hits a block

its trajectory is randomly altered on all 3 planes (X, Y, and Z) causing the 1️⃣ ball to

bounce and skip.

The ball falls onto the spinning wheel and eventually lands into one

of the pockets.

The number 1️⃣ of the pocket the ball falls into determines how the bets

placed on the layout table are treated.

After this the 1️⃣ specifics of individual tables

can vary greatly.[15]

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

Traditional

roulette wheel sectors

Although most 1️⃣ often named "call bets" technically these bets are

more accurately referred to as "announced bets". The legal distinction between a 1️⃣ "call

bet" and an "announced bet" is that a "call bet" is a bet called by the player without

placing 1️⃣ any money on the table to cover the cost of the bet. In many jurisdictions

(most notably the United Kingdom) 1️⃣ this is considered gambling on credit and is illegal.

An "announced bet" is a bet called by the player for 1️⃣ which they immediately place

enough money to cover the amount of the bet on the table, prior to the outcome 1️⃣ of the

spin or hand in progress being known.

There are different number series in roulette

that have special names attached 1️⃣ to them. Most commonly these bets are known as "the

French bets" and each covers a section of the wheel. 1️⃣ For the sake of accuracy, zero

spiel, although explained below, is not a French bet, it is more accurately "the 1️⃣ German

bet". Players at a table may bet a set amount per series (or multiples of that amount).

The series 1️⃣ are based on the way certain numbers lie next to each other on the roulette

wheel. Not all casinos offer 1️⃣ these bets, and some may offer additional bets or

variations on these.

Voisins du zéro (neighbors of zero) [ edit ]

This 1️⃣ is a name, more

accurately "grands voisins du zéro", for the 17 numbers that lie between 22 and 25 on

1️⃣ 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 1️⃣ 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; 1️⃣ 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 1️⃣ known as zero spiel (Spiel is

German for game or play), is the name for the numbers closest to zero. 1️⃣ All numbers in

the zero game are included in the voisins, but are placed differently. The numbers bet

on are 1️⃣ 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 1️⃣ 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 1️⃣ bet is popular

in Germany and many European casinos. It is also offered as a 5-chip bet in many

Eastern 1️⃣ European casinos. As a 5-chip bet, it is known as "zero spiel naca" and

includes, in addition to the chips 1️⃣ placed as noted above, a straight-up on number

19.

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

This is 1️⃣ the name for the 12

numbers that lie on the opposite side of the wheel between 27 and 33, including 1️⃣ 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 1️⃣ players refer to it as "tiers") for this

bet is "le tiers du cylindre" (translated from French into English meaning 1️⃣ one third of

the wheel) because it covers 12 numbers (placed as 6 splits), which is as close to 1⁄3

1️⃣ of the wheel as one can get.

Very popular in British casinos, tiers bets outnumber

voisins and orphelins bets by a 1️⃣ massive margin.

Six chips or multiples thereof are bet.

One chip is placed on each of the following splits: 5–8, 10–11, 1️⃣ 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 1️⃣ 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, 1️⃣ and 11m and so is a 10-piece bet. In

some places the variant is called "gioco Ferrari" with a straight 1️⃣ up on 8, 11, 23 and

30, the bet is marked with a red G on the racetrack.

Orphelins (orphans) [ 1️⃣ edit ]

These

numbers make up the two slices of the wheel outside the tiers and voisins. They contain

a total 1️⃣ 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 1️⃣ 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 1️⃣ the neighbors

[ edit ]

A number may be backed along with the two numbers on the either side of it 1️⃣ in

a 5-chip bet. For example, "0 and the neighbors" is a 5-chip bet with one piece

straight-up on 3, 1️⃣ 26, 0, 32, and 15. Neighbors bets are often put on in combinations,

for example "1, 9, 14, and the 1️⃣ neighbors" is a 15-chip bet covering 18, 22, 33, 16 with

one chip, 9, 31, 20, 1 with two chips 1️⃣ and 14 with three chips.

Any of the above bets

may be combined, e.g. "orphelins by 1 and zero and the 1️⃣ neighbors by 1". The "...and the

neighbors" is often assumed by the croupier.

Final bets [ edit ]

Another bet offered on

1️⃣ the single-zero game is "final", "finale" or "finals".

Final 4, for example, is a

4-chip bet and consists of one chip 1️⃣ placed on each of the numbers ending in 4, that is

4, 14, 24, and 34. Final 7 is a 1️⃣ 3-chip bet, one chip each on 7, 17, and 27. Final bets

from final 0 (zero) to final 6 cost 1️⃣ four chips. Final bets 7, 8 and 9 cost three

chips.

Some casinos also offer split-final bets, for example final 5-8 1️⃣ 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 [ 1️⃣ edit ]

A complete bet places all of the inside bets on a certain

number. Full complete bets are most often 1️⃣ bet by high rollers as maximum bets.

The

maximum amount allowed to be wagered on a single bet in European roulette 1️⃣ 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 1️⃣ 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 1️⃣ 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 1️⃣ wagered on it. EachR$1,000 incremental bet would be

represented by a marker that is used to specifically identify the player 1️⃣ and the amount

bet.

For instance, if a patron wished to place a full complete bet on 17, the player

would 1️⃣ call "17 to the maximum". This bet would require a total of 40 chips, orR$40,000.

To manually place the same 1️⃣ wager, the player would need to bet:

17 to the maximum Bet

type Number(s) bet on Chips Amount waged Straight-up 17 1️⃣ 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 1️⃣ 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 1️⃣ their bet to the croupier

(most often after the ball has been spun) and places enough chips to cover the 1️⃣ bet on

the table within reach of the croupier. The croupier will immediately announce the bet

(repeat what the player 1️⃣ has just said), ensure that the correct monetary amount has

been given while simultaneously placing a matching marker on the 1️⃣ number on the table

and the amount wagered.

The payout for this bet if the chosen number wins is 392 chips,

1️⃣ 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 1️⃣ bets in roulette, are still their

property and in the absence of a request to the contrary are left up 1️⃣ to possibly win

again on the next spin.

Based on the location of the numbers on the layout, the number

of 1️⃣ chips required to "complete" a number can be determined.

Zero costs 17 chips to

complete and pays 235 chips.

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

chips.

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

1st column 1️⃣ numbers 4 to 31 and 3rd

column numbers 6 to 33, cost 30 chips each to complete. The payout for 1️⃣ a win on these

30-chip bets is 294 chips.

2nd column numbers 5 to 32 cost 40 chips each to complete.

1️⃣ The payout for a win on these numbers is 392 chips.

Numbers 34 and 36 each cost 18

chips and pay 1️⃣ 198 chips.

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

Most

typically (Mayfair casinos in London and other top-class European 1️⃣ casinos) with these

maximum or full complete bets, nothing (except the aforementioned maximum button) is

ever placed on the layout 1️⃣ even in the case of a win. Experienced gaming staff, and the

type of customers playing such bets, are fully 1️⃣ aware of the payouts and so the croupier

simply makes up the correct payout, announces its value to the table 1️⃣ inspector (floor

person in the U.S.) and the customer, and then passes it to the customer, but only

after a 1️⃣ verbal authorization from the inspector has been received.

Also typically at

this level of play (house rules allowing) the experienced croupier 1️⃣ caters to the needs

of the customer and will most often add the customer's winning bet to the payout, as

1️⃣ the type of player playing these bets very rarely bets the same number two spins in

succession. For example, the 1️⃣ 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 1️⃣ 432 chips

/R$432,000, that is 392 + 40, with the announcement that the payout "is with your bet

down".

There are 1️⃣ also several methods to determine the payout when a number adjacent to

a chosen number is the winner, for example, 1️⃣ player bets 40 chips on "23 to the maximum"

and number 26 is the winning number. The most notable method 1️⃣ is known as the "station"

system or method. When paying in stations, the dealer counts the number of ways or

1️⃣ stations that the winning number hits the complete bet. In the example above, 26 hits 4

stations - 2 different 1️⃣ corners, 1 split and 1 six-line. The dealer takes the number 4,

multiplies it by 30 and adds the remaining 1️⃣ 8 to the payout: 4 × 30 = 120, 120 + 8 =

128. If calculated as stations, they would 1️⃣ just multiply 4 by 36, making 144 with the

players bet down.

In some casinos, a player may bet full complete 1️⃣ for less than the

table straight-up maximum, for example, "number 17 full complete byR$25" would

costR$1000, that is 40 chips 1️⃣ each atR$25 value.

Betting strategies and tactics [ edit

]

Over the years, many people have tried to beat the casino, and 1️⃣ turn roulette—a game

designed to turn a profit for the house—into one on which the player expects to win.

Most 1️⃣ of the time this comes down to the use of betting systems, strategies which say

that the house edge can 1️⃣ be beaten by simply employing a special pattern of bets, often

relying on the "Gambler's fallacy", the idea that past 1️⃣ results are any guide to the

future (for example, if a roulette wheel has come up 10 times in a 1️⃣ row on red, that red

on the next spin is any more or less likely than if the last spin 1️⃣ was black).

All

betting systems that rely on patterns, when employed on casino edge games will result,

on average, in the 1️⃣ player losing money.[16] In practice, players employing betting

systems may win, and may indeed win very large sums of money, 1️⃣ but the losses (which,

depending on the design of the betting system, may occur quite rarely) will outweigh

the wins. 1️⃣ Certain systems, such as the Martingale, described below, are extremely

risky, because the worst-case scenario (which is mathematically certain to 1️⃣ happen, at

some point) may see the player chasing losses with ever-bigger bets until they run out

of money.

The American 1️⃣ mathematician Patrick Billingsley said[17][unreliable source?]

that no betting system can convert a subfair game into a profitable enterprise. At

least 1️⃣ in the 1930s, some professional gamblers were able to consistently gain an edge

in roulette by seeking out rigged wheels 1️⃣ (not difficult to find at that time) and

betting opposite the largest bets.

Prediction methods [ edit ]

Whereas betting systems

are 1️⃣ essentially an attempt to beat the fact that a geometric series with initial value

of 0.95 (American roulette) or 0.97 1️⃣ (European roulette) will inevitably over time tend

to zero, engineers instead attempt to overcome the house edge through predicting the

1️⃣ mechanical performance of the wheel, most notably by Joseph Jagger at Monte Carlo in

1873. These schemes work by determining 1️⃣ that the ball is more likely to fall at certain

numbers. If effective, they raise the return of the game 1️⃣ above 100%, defeating the

betting system problem.

Edward O. Thorp (the developer of card counting and an early

hedge-fund pioneer) and 1️⃣ Claude Shannon (a mathematician and electronic engineer best

known for his contributions to information theory) built the first wearable computer 1️⃣ to

predict the landing of the ball in 1961. This system worked by timing the ball and

wheel, and using 1️⃣ the information obtained to calculate the most likely octant where the

ball would fall. Ironically, this technique works best with 1️⃣ an unbiased wheel though it

could still be countered quite easily by simply closing the table for betting before

beginning 1️⃣ the spin.

In 1982, several casinos in Britain began to lose large sums of

money at their roulette tables to teams 1️⃣ of gamblers from the US. Upon investigation by

the police, it was discovered they were using a legal system of 1️⃣ biased wheel-section

betting. As a result of this, the British roulette wheel manufacturer John Huxley

manufactured a roulette wheel to 1️⃣ counteract the problem.

The new wheel, designed by

George Melas, was called "low profile" because the pockets had been drastically reduced

1️⃣ in depth, and various other design modifications caused the ball to descend in a

gradual approach to the pocket area. 1️⃣ In 1986, when a professional gambling team headed

by Billy Walters wonR$3.8 million using the system on an old wheel 1️⃣ at the Golden Nugget

in Atlantic City, every casino in the world took notice, and within one year had

switched 1️⃣ to the new low-profile wheel.

Thomas Bass, in his book The Eudaemonic Pie

(1985) (published as The Newtonian Casino in Britain), 1️⃣ has claimed to be able to

predict wheel performance in real time. The book describes the exploits of a group 1️⃣ of

University of California Santa Cruz students, who called themselves the Eudaemons, who

in the late 1970s used computers in 1️⃣ their shoes to win at roulette. This is an updated

and improved version of Edward O. Thorp's approach, where Newtonian 1️⃣ Laws of Motion are

applied to track the roulette ball's deceleration; hence the British title.

In the

early 1990s, Gonzalo Garcia-Pelayo 1️⃣ believed that casino roulette wheels were not

perfectly random, and that by recording the results and analysing them with a 1️⃣ computer,

he could gain an edge on the house by predicting that certain numbers were more likely

to occur next 1️⃣ than the 1-in-36 odds offered by the house suggested. He did this at the

Casino de Madrid in Madrid, Spain, 1️⃣ winning 600,000 euros in a single day, and one

million euros in total. Legal action against him by the casino 1️⃣ was unsuccessful, being

ruled that the casino should fix its wheel.[18][19]

To defend against exploits like

these, many casinos use tracking 1️⃣ software, use wheels with new designs, rotate wheel

heads, and randomly rotate pocket rings.[20]

At the Ritz London casino in March 1️⃣ 2004,

two Serbs and a Hungarian used a laser scanner hidden inside a mobile phone linked to a

computer to 1️⃣ predict the sector of the wheel where the ball was most likely to drop.

They netted £1.3m in two nights.[21] 1️⃣ They were arrested and kept on police bail for

nine months, but eventually released and allowed to keep their winnings 1️⃣ as they had not

interfered with the casino equipment.[22]

Specific betting systems [ edit ]

The

numerous even-money bets in roulette have 1️⃣ inspired many players over the years to

attempt to beat the game by using one or more variations of a 1️⃣ martingale betting

strategy, wherein the gambler doubles the bet after every loss, so that the first win

would recover all 1️⃣ previous losses, plus win a profit equal to the original bet. The

problem with this strategy is that, remembering that 1️⃣ past results do not affect the

future, it is possible for the player to lose so many times in a 1️⃣ row, that the player,

doubling and redoubling their bets, either runs out of money or hits the table limit. A

1️⃣ large financial loss is certain in the long term if the player continued to employ this

strategy. Another strategy is 1️⃣ the Fibonacci system, where bets are calculated according

to the Fibonacci sequence. Regardless of the specific progression, no such strategy 1️⃣ can

statistically overcome the casino's advantage, since the expected value of each allowed

bet is negative.

Types of betting system [ 1️⃣ edit ]

Betting systems in roulette can be

divided in to two main categories:

Negative progression system (e.g.

Martingale)

Negative progression systems involve 1️⃣ increasing the size of one's bet when

they lose. This is the most common type of betting system. The goal 1️⃣ of this system is

to recoup losses faster so that one can return to a winning position more quickly after

1️⃣ a losing streak. The typical shape of these systems is small but consistent wins

followed by occasional catastrophic losses. Examples 1️⃣ of negative progression systems

include the Martingale system, the Fibonacci system, the Labouchère system, and the

d'Alembert system.

Positive progression system 1️⃣ (e.g. Paroli)

Positive progression

systems involve increasing the size of one's bet when one wins. The goal of these

systems is 1️⃣ to either exacerbate the effects of winning streaks (e.g. the Paroli system)

or to take advantage of changes in luck 1️⃣ to recover more quickly from previous losses

(e.g. Oscar's grind). The shape of these systems is typically small but consistent

1️⃣ losses followed by occasional big wins. However, over the long run these wins do not

compensate for the losses incurred 1️⃣ in between.[23]

Reverse Martingale system [ edit

]

The Reverse Martingale system, also known as the Paroli system, follows the idea of

1️⃣ the martingale betting strategy, but reversed. Instead of doubling a bet after a loss

the gambler doubles the bet after 1️⃣ every win. The system creates a false feeling of

eliminating the risk of betting more when losing, but, in reality, 1️⃣ it has the same

problem as the martingale strategy. By doubling bets after every win, one keeps betting

everything they 1️⃣ have won until they either stop playing, or lose it all.

Labouchère

system [ edit ]

The Labouchère System is a progression 1️⃣ betting strategy like the

martingale but does not require the gambler to risk their stake as quickly with

dramatic double-ups. 1️⃣ The Labouchere System involves using a series of numbers in a line

to determine the bet amount, following a win 1️⃣ or a loss. Typically, the player adds the

numbers at the front and end of the line to determine the 1️⃣ size of the next bet. If the

player wins, they cross out numbers and continue working on the smaller line. 1️⃣ If the

player loses, then they add their previous bet to the end of the line and continue to

work 1️⃣ on the longer line. This is a much more flexible progression betting system and

there is much room for the 1️⃣ player to design their initial line to their own playing

preference.

This system is one that is designed so that when 1️⃣ the player has won over a

third of their bets (less than the expected 18/38), they will win. Whereas the

1️⃣ martingale will cause ruin in the event of a long sequence of successive losses, the

Labouchère system will cause bet 1️⃣ size to grow quickly even where a losing sequence is

broken by wins. This occurs because as the player loses, 1️⃣ the average bet size in the

line increases.

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

1️⃣ negative.

D'Alembert system [ edit ]

The system, also called montant et demontant (from

French, meaning upwards and downwards), is often called 1️⃣ a pyramid system. It is based

on a mathematical equilibrium theory devised by a French mathematician of the same

name. 1️⃣ Like the martingale, this system is mainly applied to the even-money outside

bets, and is favored by players who want 1️⃣ to keep the amount of their bets and losses to

a minimum. The betting progression is very simple: After each 1️⃣ loss, one unit is added

to the next bet, and after each win, one unit is deducted from the next 1️⃣ bet. Starting

with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. 1️⃣ If

this is followed by a win, the next bet would be 1 units.

This betting system relies on

the gambler's 1️⃣ fallacy—that the player is more likely to lose following a win, and more

likely to win following a loss.

Other systems 1️⃣ [ edit ]

There are numerous other betting

systems that rely on this fallacy, or that attempt to follow 'streaks' (looking 1️⃣ for

patterns in randomness), varying bet size accordingly.

Many betting systems are sold

online and purport to enable the player to 1️⃣ 'beat' the odds. One such system was

advertised by Jason Gillon of Rotherham, UK, who claimed one could 'earn £200 1️⃣ daily' by

following his betting system, described as a 'loophole'. As the system was advertised

in the UK press, it 1️⃣ was subject to Advertising Standards Authority regulation, and

following a complaint, it was ruled by the ASA that Mr. Gillon 1️⃣ had failed to support

his claims, and that he had failed to show that there was any loophole.

Notable

winnings [ 1️⃣ edit ]

In the 1960s and early 1970s, Richard Jarecki won aboutR$1.2 million

at dozens of European casinos. He claimed that 1️⃣ he was using a mathematical system

designed on a powerful computer. In reality, he simply observed more than 10,000 spins

1️⃣ of each roulette wheel to determine flaws in the wheels. Eventually the casinos

realized that flaws in the wheels could 1️⃣ be exploited, and replaced older wheels. The

manufacture of roulette wheels has improved over time. [24]

In 1963 Sean Connery,

filming 1️⃣ From Russia with Love in Italy, attended the casino in Saint-Vincent and won

three consecutive times on the number 17, 1️⃣ his winnings riding on the second and third

spins. [25]

in Italy, attended the casino in Saint-Vincent and won three consecutive

1️⃣ times on the number 17, his winnings on the second and third spins. In 2004, Ashley

Revell of London sold 1️⃣ all of his possessions, clothing included, and placed his entire

net worth of US$135,300 on red at the Plaza Hotel 1️⃣ in Las Vegas. The ball landed on "Red

7" and Revell walked away withR$270,600.[26]

See also [ edit ]

2.247 casino spin:Restaure minha festa de bônus acumulada

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por Fan Chengzhu/Xinhua)

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por Shi Yalei/Xinhua)

(

por Shi Yalei/Xinhua)

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por Shi Yalei/Xinhua)

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