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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

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

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

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]

See also [ edit ]

I refer to all the days as "Bonus Days." Now that I am in my golden years I refer to them as "Double Bonus Days!"