Casino game of chance
This article is about the casino game. For other uses, see
Roulette (disambiguation)
Roulette ball
"Gwendolen at the roulette 0️⃣ table" – 1910
illustration to George Eliot's Daniel Deronda
Roulette (named after the French word
meaning "little wheel") is a casino 0️⃣ game which was likely developed from the Italian
game Biribi. In the game, a player may choose to place a 0️⃣ bet on a single number,
various groupings of numbers, the color red or black, whether the number is odd or
0️⃣ even, or if the numbers are high (19–36) or low (1–18).
To determine the winning
number, a croupier spins a wheel 0️⃣ in one direction, then spins a ball in the opposite
direction around a tilted circular track running around the outer 0️⃣ edge of the wheel.
The ball eventually loses momentum, passes through an area of deflectors, and falls
onto the wheel 0️⃣ 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, 0️⃣ "Sands Roulette")[1] colored and numbered pockets on the wheel. The
winnings are then paid to anyone who has placed a 0️⃣ successful bet.
History [ edit
]
18th-century E.O. wheel with gamblers
The first form of roulette was devised in
18th-century France. Many historians 0️⃣ believe Blaise Pascal introduced a primitive form
of roulette in the 17th century in his search for a perpetual motion 0️⃣ machine. [2] The
roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game
Biribi.[3] 0️⃣ A primitive form of roulette, known as 'EO' (Even/Odd), was played in
England in the late 18th century using a 0️⃣ gaming wheel similar to that used in
roulette.[4]
The game has been played in its present form since as early as 0️⃣ 1796 in
Paris. An early description of the roulette game in its current form is found in a
French novel 0️⃣ La Roulette, ou le Jour by Jaques Lablee, which describes a roulette wheel
in the Palais Royal in Paris in 0️⃣ 1796. The description included the house pockets:
"There are exactly two slots reserved for the bank, whence it derives its 0️⃣ sole
mathematical advantage." It then goes on to describe the layout with "two betting
spaces containing the bank's two numbers, 0️⃣ zero and double zero". The book was published
in 1801. An even earlier reference to a game of this name 0️⃣ was published in regulations
for New France (Québec) in 1758, which banned the games of "dice, hoca, faro, and
roulette".[5]
The 0️⃣ roulette wheels used in the casinos of Paris in the late 1790s had
red for the single zero and black 0️⃣ for the double zero. To avoid confusion, the color
green was selected for the zeros in roulette wheels starting in 0️⃣ the 1800s.
In 1843, in
the German spa casino town of Bad Homburg, fellow Frenchmen François and Louis Blanc
introduced the 0️⃣ single 0 style roulette wheel in order to compete against other casinos
offering the traditional wheel with single and double 0️⃣ zero house pockets.[6]
In some
forms of early American roulette wheels, there were numbers 1 to 28, plus a single
zero, 0️⃣ a double zero, and an American Eagle. The Eagle slot, which was a symbol of
American liberty, was a house 0️⃣ slot that brought the casino an extra edge. Soon, the
tradition vanished and since then the wheel features only numbered 0️⃣ slots. According to
Hoyle "the single 0, the double 0, and the eagle are never bars; but when the ball
0️⃣ falls into either of them, the banker sweeps every thing upon the table, except what
may happen to be bet 0️⃣ on either one of them, when he pays twenty-seven for one, which is
the amount paid for all sums bet 0️⃣ upon any single figure".[7]
1800s engraving of the
French roulette
In the 19th century, roulette spread all over Europe and the US,
0️⃣ becoming one of the most famous and most popular casino games. When the German
government abolished gambling in the 1860s, 0️⃣ the Blanc family moved to the last legal
remaining casino operation in Europe at Monte Carlo, where they established a 0️⃣ gambling
mecca for the elite of Europe. It was here that the single zero roulette wheel became
the premier game, 0️⃣ and over the years was exported around the world, except in the
United States where the double zero wheel remained 0️⃣ dominant.
Early American West
makeshift game
In the United States, the French double zero wheel made its way up the
Mississippi from 0️⃣ New Orleans, and then westward. It was here, because of rampant
cheating by both operators and gamblers, that the wheel 0️⃣ was eventually placed on top of
the table to prevent devices from being hidden in the table or wheel, and 0️⃣ the betting
layout was simplified. This eventually evolved into the American-style roulette game.
The American game was developed in the 0️⃣ gambling dens across the new territories where
makeshift games had been set up, whereas the French game evolved with style 0️⃣ and leisure
in Monte Carlo.
During the first part of the 20th century, the only casino towns of
note were Monte 0️⃣ Carlo with the traditional single zero French wheel, and Las Vegas with
the American double zero wheel. In the 1970s, 0️⃣ casinos began to flourish around the
world. In 1996 the first online casino, generally believed to be InterCasino, made it
0️⃣ possible to play roulette online.[8] By 2008, there were several hundred casinos
worldwide offering roulette games. The double zero wheel 0️⃣ is found in the U.S., Canada,
South America, and the Caribbean, while the single zero wheel is predominant
elsewhere.
The sum 0️⃣ of all the numbers on the roulette wheel (from 0 to 36) is 666,
which is the "Number of the 0️⃣ Beast".[9]
Rules of play against a casino [ edit ]
Roulette
with red 12 as the winner
Roulette players have a variety of 0️⃣ betting options. "Inside"
bets involve selecting either the exact number on which the ball will land, or a small
group 0️⃣ of numbers adjacent to each other on the layout. "Outside" bets, by contrast,
allow players to select a larger group 0️⃣ of numbers based on properties such as their
color or parity (odd/even). The payout odds for each type of bet 0️⃣ are based on its
probability.
The roulette table usually imposes minimum and maximum bets, and these
rules usually apply separately for 0️⃣ all of a player's inside and outside bets for each
spin. For inside bets at roulette tables, some casinos may 0️⃣ use separate roulette table
chips of various colors to distinguish players at the table. Players can continue to
place bets 0️⃣ as the ball spins around the wheel until the dealer announces "no more bets"
or "rien ne va plus".
Croupier's rake 0️⃣ pushing chips across a roulette layout
When a
winning number and color is determined by the roulette wheel, the dealer will 0️⃣ place a
marker, also known as a dolly, on that number on the roulette table layout. When the
dolly is 0️⃣ on the table, no players may place bets, collect bets or remove any bets from
the table. The dealer will 0️⃣ then sweep away all losing bets either by hand or by rake,
and determine the payouts for the remaining inside 0️⃣ and outside winning bets. When the
dealer is finished making payouts, the dolly is removed from the board and players 0️⃣ may
collect their winnings and make new bets. Winning chips remain on the board until
picked up by a player.
California 0️⃣ Roulette [ edit ]
In 2004, California legalized a
form of roulette known as California Roulette.[10] By law, the game must 0️⃣ use cards and
not slots on the roulette wheel to pick the winning number.
Roulette wheel number
sequence [ edit ]
The 0️⃣ pockets of the roulette wheel are numbered from 0 to 36.
In
number ranges from 1 to 10 and 19 to 0️⃣ 28, odd numbers are red and even are black. In
ranges from 11 to 18 and 29 to 36, odd 0️⃣ numbers are black and even are red.
There is a
green pocket numbered 0 (zero). In American roulette, there is a 0️⃣ second green pocket
marked 00. Pocket number order on the roulette wheel adheres to the following clockwise
sequence in most 0️⃣ 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 0️⃣ 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 0️⃣ European-style layout has a single
zero, and the American style layout is usually a double-zero. The American-style
roulette table with 0️⃣ a wheel at one end is now used in most casinos because it has a
higher house edge compared to 0️⃣ a European layout.[11]
The French style table with a
wheel in the centre and a layout on either side is rarely 0️⃣ found outside of Monte
Carlo.
Types of bets [ edit ]
In roulette, bets can be either inside or
outside.[12]
Inside bets [ 0️⃣ edit ]
Name Description Chip placement Straight/Single Bet
on a single number Entirely within the square for the chosen number Split 0️⃣ Bet on two
vertically/horizontally adjacent numbers (e.g. 14-17 or 8–9) On the edge shared by the
numbers Street Bet on 0️⃣ three consecutive numbers in a horizontal line (e.g. 7-8-9) On
the outer edge of the number at either end of 0️⃣ 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
0️⃣ 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 0️⃣ two leftmost or the two rightmost
numbers Trio/Basket A three-number bet that involves at least one zero: 0-1-2 (either
layout); 0️⃣ 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 0️⃣ 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 0️⃣ layout
only) On the outer corner shared by 0-1 or 00-3
Outside bets [ edit ]
Outside bets
typically have smaller payouts 0️⃣ with better odds at winning. Except as noted, all of
these bets lose if a zero comes up.
1 to 18 0️⃣ (Low or Manque), or 19 to 36 (High or
Passe) A bet that the number will be in the chosen 0️⃣ range. Red or black (Rouge ou Noir)
A bet that the number will be the chosen color. Even or odd 0️⃣ (Pair ou Impair) A bet that
the number will be of the chosen type. Dozen bet A bet that the 0️⃣ number will be in the
chosen dozen: first (1-12, Première douzaine or P12), second (13-24, Moyenne douzaine
or M12), or 0️⃣ third (25-36, Dernière douzaine or D12). Column bet A bet that the number
will be in the chosen vertical column 0️⃣ of 12 numbers, such as 1-4-7-10 on down to 34.
The chip is placed on the space below the final 0️⃣ number in this sequence. Snake Bet A
special bet that covers the numbers 1, 5, 9, 12, 14, 16, 19, 0️⃣ 23, 27, 30, 32, and 34. It
has the same payout as the dozen bet and takes its name from 0️⃣ the zigzagging, snakelike
pattern traced out by these numbers. The snake bet is not available in all casinos;
when it 0️⃣ is allowed, the chip is placed on the lower corner of the 34 square that
borders the 19-36 betting box. 0️⃣ Some layouts mark the bet with a two-headed snake that
winds from 1 to 34, and the bet can be 0️⃣ placed on the head at either end of the body.
In
the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) 0️⃣ result in
the player losing only half of their bet if a zero comes up.
Bet odds table [ edit
]
The 0️⃣ expected value of aR$1 bet (except for the special case of Top line bets), for
American and European roulette, can 0️⃣ be calculated as
e x p e c t e d v a l u e = 1 n (
36 0️⃣ − n ) = 36 n − 1 , {\displaystyle \mathrm {expectedvalue} ={\frac
{1}{n}}(36-n)={\frac {36}{n}}-1,}
where n is the number of 0️⃣ pockets in the wheel.
The
initial bet is returned in addition to the mentioned payout: it can be easily
demonstrated that 0️⃣ this payout formula would lead to a zero expected value of profit if
there were only 36 numbers (that is, 0️⃣ the casino would break even). Having 37 or more
numbers gives the casino its edge.
Bet name Winning spaces Payout Odds 0️⃣ against winning
(French) Expected value
(on aR$1 bet) (French) Odds against winning (American) Expected
value
(on aR$1 bet) (American) 0 0 35 0️⃣ to 1 36 to 1 −$0.027 37 to 1 −$0.053 00 00 35 to
1 37 to 1 −$0.053 Straight 0️⃣ up Any single number 35 to 1 36 to 1 −$0.027 37 to 1 −$0.053
Row 0, 00 17 to 0️⃣ 1 18 to 1 −$0.053 Split any two adjoining numbers vertical or
horizontal 17 to 1 17 + 1 ⁄ 0️⃣ 2 to 1 −$0.027 18 to 1 −$0.053 Street any three numbers
horizontal (1, 2, 3 or 4, 5, 6, 0️⃣ etc.) 11 to 1 11 + 1 ⁄ 3 to 1 −$0.027 11 + 2 ⁄ 3 to 1
−$0.053 0️⃣ Corner any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21,
etc.) 8 to 0️⃣ 1 8 + 1 ⁄ 4 to 1 −$0.027 8 + 1 ⁄ 2 to 1 −$0.053 Top line (US) 0️⃣ 0, 00, 1, 2, 3
6 to 1 6 + 3 ⁄ 5 to 1 −$0.079 Top line (European) 0, 0️⃣ 1, 2, 3 8 to 1 8 + 1 ⁄ 4 to 1
−$0.027 Double Street any six numbers from 0️⃣ two horizontal rows (1, 2, 3, 4, 5, 6 or 28,
29, 30, 31, 32, 33 etc.) 5 to 1 0️⃣ 5 + 1 ⁄ 6 to 1 −$0.027 5 + 1 ⁄ 3 to 1 −$0.053 1st
column 1, 4, 0️⃣ 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 2 to 1 2 + 1 ⁄ 12 to 1 0️⃣ −$0.027 2 + 1
⁄ 6 to 1 −$0.053 2nd column 2, 5, 8, 11, 14, 17, 20, 23, 26, 0️⃣ 29, 32, 35 2 to 1 2 + 1 ⁄
12 to 1 −$0.027 2 + 1 ⁄ 6 to 0️⃣ 1 −$0.053 3rd column 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,
33, 36 2 to 1 2 0️⃣ + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 1st dozen 1 through 12 0️⃣ 2
to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 2nd 0️⃣ dozen 13 through 24 2 to 1 2 +
1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 0️⃣ to 1 −$0.053 3rd dozen 25 through 36 2 to 1 2 + 1 ⁄ 12 to
1 −$0.027 2 0️⃣ + 1 ⁄ 6 to 1 −$0.053 Odd 1, 3, 5, ..., 35 1 to 1 1 + 1 ⁄ 0️⃣ 18 to 1 −$0.027 1
+ 1 ⁄ 9 to 1 −$0.053 Even 2, 4, 6, ..., 36 1 to 0️⃣ 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to
1 −$0.053 Red 32, 19, 0️⃣ 21, 25, 34, 27, 36, 30, 23, 5, 16, 1, 14, 9, 18, 7, 12, 3 1 to 1
1 0️⃣ + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Black 15, 4, 2, 17, 0️⃣ 6, 13, 11, 8, 10,
24, 33, 20, 31, 22, 29, 28, 35, 26 1 to 1 1 + 1 0️⃣ ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1
−$0.053 1 to 18 1, 2, 3, ..., 0️⃣ 18 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053
0️⃣ 19 to 36 19, 20, 21, ..., 36 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 0️⃣ + 1 ⁄ 9 to 1 −$0.053
Top
line (0, 00, 1, 2, 3) has a different expected value because of 0️⃣ 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 0️⃣ or even, or high or low.
En prison rules, when used, reduce the house
advantage.
House edge [ edit ]
The house average 0️⃣ or house edge or house advantage (also
called the expected value) is the amount the player loses relative to any 0️⃣ bet made, on
average. If a player bets on a single number in the American game there is a
probability 0️⃣ of 1⁄38 that the player wins 35 times the bet, and a 37⁄38 chance that the
player loses their bet. 0️⃣ The expected value is:
−1 × 37 ⁄ 38 + 35 × 1 ⁄ 38 = −0.0526
(5.26% house edge)
For European 0️⃣ roulette, a single number wins 1⁄37 and loses 36⁄37:
−1
× 36 ⁄ 37 + 35 × 1 ⁄ 37 = 0️⃣ −0.0270 (2.70% house edge)
For triple-zero wheels, a single
number wins 1⁄39 and loses 38⁄39:
−1 × 38 ⁄ 39 + 35 0️⃣ × 1 ⁄ 39 = −0.0769 (7.69% house
edge)
Mathematical model [ edit ]
As an example, the European roulette model, that 0️⃣ is,
roulette with only one zero, can be examined. Since this roulette has 37 cells with
equal odds of hitting, 0️⃣ this is a final model of field probability ( Ω , 2 Ω , P )
{\displaystyle (\Omega ,2^{\Omega },\mathbb 0️⃣ {P} )} , where Ω = { 0 , … , 36 }
{\displaystyle \Omega =\{0,\ldots ,36\}} , P ( 0️⃣ A ) = | A | 37 {\displaystyle \mathbb
{P} (A)={\frac {|A|}{37}}} for all A ∈ 2 Ω {\displaystyle A\in 0️⃣ 2^{\Omega }} .
Call the
bet S {\displaystyle S} a triple ( A , r , ξ ) {\displaystyle (A,r,\xi )} 0️⃣ , where A
{\displaystyle A} is the set of chosen numbers, r ∈ R + {\displaystyle r\in \mathbb {R}
_{+}} 0️⃣ is the size of the bet, and ξ : Ω → R {\displaystyle \xi :\Omega \to \mathbb {R}
} determines 0️⃣ the return of the bet.[13]
The rules of European roulette have 10 types of
bets. First the 'Straight Up' bet can 0️⃣ be imagined. In this case, S = ( { ω 0 } , r , ξ
) {\displaystyle S=(\{\omega _{0}\},r,\xi 0️⃣ )} , for some ω 0 ∈ Ω {\displaystyle \omega
_{0}\in \Omega } , and ξ {\displaystyle \xi } is 0️⃣ determined by
ξ ( ω ) = { − r , ω ≠ ω
0 35 ⋅ r , ω = 0️⃣ 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 0️⃣ to
M [ ξ ] = 1 37 ∑ ω ∈ Ω ξ ( ω ) = 1 37 ( ξ 0️⃣ ( ω 0 ) + ∑ ω ≠ ω
0 ξ ( ω ) ) = 1 37 ( 35 0️⃣ ⋅ r − 36 ⋅ r ) = − r 37 ≈ − 0.027 r . {\displaystyle M[\xi
]={\frac {1}{37}}\sum 0️⃣ _{\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, 0️⃣ for a bet, black (or red), the rule is determined as
ξ ( ω ) = { − r , ω 0️⃣ is
red − r , ω = 0 r , ω is black , {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega
{\text{ is 0️⃣ red}}\\-r,&\omega =0\\r,&\omega {\text{ is black}}\end{cases}},}
and the
profitability
M [ ξ ] = 1 37 ( 18 ⋅ r − 18 ⋅ 0️⃣ 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 0️⃣ to see that the profitability is also equal for all remaining types of bets. − r
37 {\displaystyle -{\frac {r}{37}}} 0️⃣ .[14]
In reality this means that, the more bets a
player makes, the more they are going to lose independent of 0️⃣ the strategies
(combinations of bet types or size of bets) that they employ:
∑ n = 1 ∞ M [ ξ 0️⃣ n ] = − 1
37 ∑ n = 1 ∞ r n → − ∞ . {\displaystyle \sum _{n=1}^{\infty 0️⃣ }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, 0️⃣ several roulette strategy
systems have been developed despite the losing odds. These systems can not change the
odds of the 0️⃣ game in favor of the player.
It is worth noting that the odds for the
player in American roulette are even 0️⃣ worse, as the bet profitability is at worst − 3 38
r ≈ − 0.0789 r {\displaystyle -{\frac {3}{38}}r\approx -0.0789r} 0️⃣ , and never better
than − r 19 ≈ − 0.0526 r {\displaystyle -{\frac {r}{19}}\approx -0.0526r} .
Simplified
mathematical model [ 0️⃣ edit ]
For a roulette wheel with n {\displaystyle n} green numbers
and 36 other unique numbers, the chance of the 0️⃣ ball landing on a given number is 1 ( 36
+ n ) {\displaystyle {\frac {1}{(36+n)}}} . For a betting 0️⃣ option with p {\displaystyle
p} numbers defining a win, the chance of winning a bet is p ( 36 + 0️⃣ n ) {\displaystyle
{\frac {p}{(36+n)}}}
For example, if a player bets on red, there are 18 red numbers, p
= 18 0️⃣ {\displaystyle p=18} , so the chance of winning is 18 ( 36 + n ) {\displaystyle
{\frac {18}{(36+n)}}} .
The payout 0️⃣ given by the casino for a win is based on the
roulette wheel having 36 outcomes, and the payout for 0️⃣ a bet is given by 36 p
{\displaystyle {\frac {36}{p}}} .
For example, betting on 1-12 there are 12 numbers
that 0️⃣ define a win, p = 12 {\displaystyle p=12} , the payout is 36 12 = 3 {\displaystyle
{\frac {36}{12}}=3} , 0️⃣ so the bettor wins 3 times their bet.
The average return on a
player's bet is given by p ( 36 0️⃣ + n ) × 36 p = 36 ( 36 + n ) {\displaystyle {\frac
{p}{(36+n)}}\times {\frac {36}{p}}={\frac {36}{(36+n)}}}
For n 0️⃣ > 0 {\displaystyle n>0}
, the average return is always lower than 1, so on average a player will lose
0️⃣ money.
With 1 green number, n = 1 {\displaystyle n=1} , the average return is 36 37
{\displaystyle {\frac {36}{37}}} , 0️⃣ that is, after a bet the player will on average have
36 37 {\displaystyle {\frac {36}{37}}} of their original bet 0️⃣ returned to them. With 2
green numbers, n = 2 {\displaystyle n=2} , the average return is 36 38 {\displaystyle
0️⃣ {\frac {36}{38}}} . With 3 green numbers, n = 3 {\displaystyle n=3} , the average
return is 36 39 {\displaystyle 0️⃣ {\frac {36}{39}}} .
This shows that the expected return
is independent of the choice of bet.
Mechanics [ edit ]
All roulette tables 0️⃣ deal with
only four elements:
1. The roulette wheel.
2. The roulette table (aka layout).
3. The
ball. These days the ball is 0️⃣ most likely high impact plastic, but originally it was
made of ivory. Modern casinos maintain the integrity of their roulette 0️⃣ balls with
regular magnetic and x-ray exams.
4. The chips. Some casinos allow the player to use
generic casino chips at 0️⃣ the roulette tables, but most require the player to buy in at
the table. The croupier has stacks of various 0️⃣ colored chips. Usually each player gets a
different color to help avoid confusion of bets, and the player can designate 0️⃣ the value
of the chip. The chips are typically valued at eitherR$1 or the table minimum; if the
player wishes, 0️⃣ the chips may be worthR$0.25 so long as the "total" wager meets the
table minimums for their respective sectors, for 0️⃣ example by placing fourR$0.25 bets to
meet aR$1 table minimum.
All roulette tables operated by a casino have the same basic
0️⃣ mechanics:
There is a balanced mechanical wheel with colored pockets separated by
identical vanes and the wheel which spins freely on 0️⃣ a supporting post.
The wheel is
held within a wooden frame which contains a track around the upper outer edge and
0️⃣ blocks of a variety of designs placed approximately halfway down the face of the
frame.
A plastic or ivory ball is 0️⃣ spun in the track in the frame that holds the wheel.
As the ball loses momentum the centrifugal force is 0️⃣ no longer sufficient to hold the
ball in the groove and it falls down the face of the frame. As 0️⃣ the ball hits a block
its trajectory is randomly altered on all 3 planes (X, Y, and Z) causing the 0️⃣ ball to
bounce and skip.
The ball falls onto the spinning wheel and eventually lands into one
of the pockets.
The number 0️⃣ of the pocket the ball falls into determines how the bets
placed on the layout table are treated.
After this the 0️⃣ specifics of individual tables
can vary greatly.[15]
Called (or call) bets or announced bets [ edit ]
Traditional
roulette wheel sectors
Although most 0️⃣ often named "call bets" technically these bets are
more accurately referred to as "announced bets". The legal distinction between a 0️⃣ "call
bet" and an "announced bet" is that a "call bet" is a bet called by the player without
placing 0️⃣ any money on the table to cover the cost of the bet. In many jurisdictions
(most notably the United Kingdom) 0️⃣ this is considered gambling on credit and is illegal.
An "announced bet" is a bet called by the player for 0️⃣ which they immediately place
enough money to cover the amount of the bet on the table, prior to the outcome 0️⃣ of the
spin or hand in progress being known.
There are different number series in roulette
that have special names attached 0️⃣ to them. Most commonly these bets are known as "the
French bets" and each covers a section of the wheel. 0️⃣ For the sake of accuracy, zero
spiel, although explained below, is not a French bet, it is more accurately "the 0️⃣ German
bet". Players at a table may bet a set amount per series (or multiples of that amount).
The series 0️⃣ are based on the way certain numbers lie next to each other on the roulette
wheel. Not all casinos offer 0️⃣ these bets, and some may offer additional bets or
variations on these.
Voisins du zéro (neighbors of zero) [ edit ]
This 0️⃣ is a name, more
accurately "grands voisins du zéro", for the 17 numbers that lie between 22 and 25 on
0️⃣ 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 0️⃣ 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; 0️⃣ 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 0️⃣ known as zero spiel (Spiel is
German for game or play), is the name for the numbers closest to zero. 0️⃣ All numbers in
the zero game are included in the voisins, but are placed differently. The numbers bet
on are 0️⃣ 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 0️⃣ 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 0️⃣ bet is popular
in Germany and many European casinos. It is also offered as a 5-chip bet in many
Eastern 0️⃣ European casinos. As a 5-chip bet, it is known as "zero spiel naca" and
includes, in addition to the chips 0️⃣ placed as noted above, a straight-up on number
19.
Le tiers du cylindre (third of the wheel) [ edit ]
This is 0️⃣ the name for the 12
numbers that lie on the opposite side of the wheel between 27 and 33, including 0️⃣ 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 0️⃣ players refer to it as "tiers") for this
bet is "le tiers du cylindre" (translated from French into English meaning 0️⃣ one third of
the wheel) because it covers 12 numbers (placed as 6 splits), which is as close to 1⁄3
0️⃣ of the wheel as one can get.
Very popular in British casinos, tiers bets outnumber
voisins and orphelins bets by a 0️⃣ massive margin.
Six chips or multiples thereof are bet.
One chip is placed on each of the following splits: 5–8, 10–11, 0️⃣ 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 0️⃣ 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, 0️⃣ and 11m and so is a 10-piece bet. In
some places the variant is called "gioco Ferrari" with a straight 0️⃣ up on 8, 11, 23 and
30, the bet is marked with a red G on the racetrack.
Orphelins (orphans) [ 0️⃣ edit ]
These
numbers make up the two slices of the wheel outside the tiers and voisins. They contain
a total 0️⃣ 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 0️⃣ 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 0️⃣ the neighbors
[ edit ]
A number may be backed along with the two numbers on the either side of it 0️⃣ in
a 5-chip bet. For example, "0 and the neighbors" is a 5-chip bet with one piece
straight-up on 3, 0️⃣ 26, 0, 32, and 15. Neighbors bets are often put on in combinations,
for example "1, 9, 14, and the 0️⃣ neighbors" is a 15-chip bet covering 18, 22, 33, 16 with
one chip, 9, 31, 20, 1 with two chips 0️⃣ and 14 with three chips.
Any of the above bets
may be combined, e.g. "orphelins by 1 and zero and the 0️⃣ neighbors by 1". The "...and the
neighbors" is often assumed by the croupier.
Final bets [ edit ]
Another bet offered on
0️⃣ the single-zero game is "final", "finale" or "finals".
Final 4, for example, is a
4-chip bet and consists of one chip 0️⃣ placed on each of the numbers ending in 4, that is
4, 14, 24, and 34. Final 7 is a 0️⃣ 3-chip bet, one chip each on 7, 17, and 27. Final bets
from final 0 (zero) to final 6 cost 0️⃣ four chips. Final bets 7, 8 and 9 cost three
chips.
Some casinos also offer split-final bets, for example final 5-8 0️⃣ 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 [ 0️⃣ edit ]
A complete bet places all of the inside bets on a certain
number. Full complete bets are most often 0️⃣ bet by high rollers as maximum bets.
The
maximum amount allowed to be wagered on a single bet in European roulette 0️⃣ 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 0️⃣ 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 0️⃣ 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 0️⃣ wagered on it. EachR$1,000 incremental bet would be
represented by a marker that is used to specifically identify the player 0️⃣ and the amount
bet.
For instance, if a patron wished to place a full complete bet on 17, the player
would 0️⃣ call "17 to the maximum". This bet would require a total of 40 chips, orR$40,000.
To manually place the same 0️⃣ wager, the player would need to bet:
17 to the maximum Bet
type Number(s) bet on Chips Amount waged Straight-up 17 0️⃣ 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 0️⃣ 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 0️⃣ their bet to the croupier
(most often after the ball has been spun) and places enough chips to cover the 0️⃣ bet on
the table within reach of the croupier. The croupier will immediately announce the bet
(repeat what the player 0️⃣ has just said), ensure that the correct monetary amount has
been given while simultaneously placing a matching marker on the 0️⃣ number on the table
and the amount wagered.
The payout for this bet if the chosen number wins is 392 chips,
0️⃣ 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 0️⃣ bets in roulette, are still their
property and in the absence of a request to the contrary are left up 0️⃣ to possibly win
again on the next spin.
Based on the location of the numbers on the layout, the number
of 0️⃣ chips required to "complete" a number can be determined.
Zero costs 17 chips to
complete and pays 235 chips.
Number 1 and 0️⃣ number 3 each cost 27 chips and pay 297
chips.
Number 2 is a 36-chip bet and pays 396 chips.
1st column 0️⃣ numbers 4 to 31 and 3rd
column numbers 6 to 33, cost 30 chips each to complete. The payout for 0️⃣ a win on these
30-chip bets is 294 chips.
2nd column numbers 5 to 32 cost 40 chips each to complete.
0️⃣ The payout for a win on these numbers is 392 chips.
Numbers 34 and 36 each cost 18
chips and pay 0️⃣ 198 chips.
Number 35 is a 24-chip bet which pays 264 chips.
Most
typically (Mayfair casinos in London and other top-class European 0️⃣ casinos) with these
maximum or full complete bets, nothing (except the aforementioned maximum button) is
ever placed on the layout 0️⃣ even in the case of a win. Experienced gaming staff, and the
type of customers playing such bets, are fully 0️⃣ aware of the payouts and so the croupier
simply makes up the correct payout, announces its value to the table 0️⃣ inspector (floor
person in the U.S.) and the customer, and then passes it to the customer, but only
after a 0️⃣ verbal authorization from the inspector has been received.
Also typically at
this level of play (house rules allowing) the experienced croupier 0️⃣ caters to the needs
of the customer and will most often add the customer's winning bet to the payout, as
0️⃣ the type of player playing these bets very rarely bets the same number two spins in
succession. For example, the 0️⃣ 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 0️⃣ 432 chips
/R$432,000, that is 392 + 40, with the announcement that the payout "is with your bet
down".
There are 0️⃣ also several methods to determine the payout when a number adjacent to
a chosen number is the winner, for example, 0️⃣ player bets 40 chips on "23 to the maximum"
and number 26 is the winning number. The most notable method 0️⃣ is known as the "station"
system or method. When paying in stations, the dealer counts the number of ways or
0️⃣ stations that the winning number hits the complete bet. In the example above, 26 hits 4
stations - 2 different 0️⃣ corners, 1 split and 1 six-line. The dealer takes the number 4,
multiplies it by 30 and adds the remaining 0️⃣ 8 to the payout: 4 × 30 = 120, 120 + 8 =
128. If calculated as stations, they would 0️⃣ just multiply 4 by 36, making 144 with the
players bet down.
In some casinos, a player may bet full complete 0️⃣ for less than the
table straight-up maximum, for example, "number 17 full complete byR$25" would
costR$1000, that is 40 chips 0️⃣ each atR$25 value.
Betting strategies and tactics [ edit
]
Over the years, many people have tried to beat the casino, and 0️⃣ turn roulette—a game
designed to turn a profit for the house—into one on which the player expects to win.
Most 0️⃣ of the time this comes down to the use of betting systems, strategies which say
that the house edge can 0️⃣ be beaten by simply employing a special pattern of bets, often
relying on the "Gambler's fallacy", the idea that past 0️⃣ results are any guide to the
future (for example, if a roulette wheel has come up 10 times in a 0️⃣ row on red, that red
on the next spin is any more or less likely than if the last spin 0️⃣ was black).
All
betting systems that rely on patterns, when employed on casino edge games will result,
on average, in the 0️⃣ player losing money.[16] In practice, players employing betting
systems may win, and may indeed win very large sums of money, 0️⃣ but the losses (which,
depending on the design of the betting system, may occur quite rarely) will outweigh
the wins. 0️⃣ Certain systems, such as the Martingale, described below, are extremely
risky, because the worst-case scenario (which is mathematically certain to 0️⃣ happen, at
some point) may see the player chasing losses with ever-bigger bets until they run out
of money.
The American 0️⃣ mathematician Patrick Billingsley said[17][unreliable source?]
that no betting system can convert a subfair game into a profitable enterprise. At
least 0️⃣ in the 1930s, some professional gamblers were able to consistently gain an edge
in roulette by seeking out rigged wheels 0️⃣ (not difficult to find at that time) and
betting opposite the largest bets.
Prediction methods [ edit ]
Whereas betting systems
are 0️⃣ essentially an attempt to beat the fact that a geometric series with initial value
of 0.95 (American roulette) or 0.97 0️⃣ (European roulette) will inevitably over time tend
to zero, engineers instead attempt to overcome the house edge through predicting the
0️⃣ mechanical performance of the wheel, most notably by Joseph Jagger at Monte Carlo in
1873. These schemes work by determining 0️⃣ that the ball is more likely to fall at certain
numbers. If effective, they raise the return of the game 0️⃣ above 100%, defeating the
betting system problem.
Edward O. Thorp (the developer of card counting and an early
hedge-fund pioneer) and 0️⃣ Claude Shannon (a mathematician and electronic engineer best
known for his contributions to information theory) built the first wearable computer 0️⃣ to
predict the landing of the ball in 1961. This system worked by timing the ball and
wheel, and using 0️⃣ the information obtained to calculate the most likely octant where the
ball would fall. Ironically, this technique works best with 0️⃣ an unbiased wheel though it
could still be countered quite easily by simply closing the table for betting before
beginning 0️⃣ the spin.
In 1982, several casinos in Britain began to lose large sums of
money at their roulette tables to teams 0️⃣ of gamblers from the US. Upon investigation by
the police, it was discovered they were using a legal system of 0️⃣ biased wheel-section
betting. As a result of this, the British roulette wheel manufacturer John Huxley
manufactured a roulette wheel to 0️⃣ counteract the problem.
The new wheel, designed by
George Melas, was called "low profile" because the pockets had been drastically reduced
0️⃣ in depth, and various other design modifications caused the ball to descend in a
gradual approach to the pocket area. 0️⃣ In 1986, when a professional gambling team headed
by Billy Walters wonR$3.8 million using the system on an old wheel 0️⃣ at the Golden Nugget
in Atlantic City, every casino in the world took notice, and within one year had
switched 0️⃣ to the new low-profile wheel.
Thomas Bass, in his book The Eudaemonic Pie
(1985) (published as The Newtonian Casino in Britain), 0️⃣ has claimed to be able to
predict wheel performance in real time. The book describes the exploits of a group 0️⃣ of
University of California Santa Cruz students, who called themselves the Eudaemons, who
in the late 1970s used computers in 0️⃣ their shoes to win at roulette. This is an updated
and improved version of Edward O. Thorp's approach, where Newtonian 0️⃣ Laws of Motion are
applied to track the roulette ball's deceleration; hence the British title.
In the
early 1990s, Gonzalo Garcia-Pelayo 0️⃣ believed that casino roulette wheels were not
perfectly random, and that by recording the results and analysing them with a 0️⃣ computer,
he could gain an edge on the house by predicting that certain numbers were more likely
to occur next 0️⃣ than the 1-in-36 odds offered by the house suggested. He did this at the
Casino de Madrid in Madrid, Spain, 0️⃣ winning 600,000 euros in a single day, and one
million euros in total. Legal action against him by the casino 0️⃣ was unsuccessful, being
ruled that the casino should fix its wheel.[18][19]
To defend against exploits like
these, many casinos use tracking 0️⃣ software, use wheels with new designs, rotate wheel
heads, and randomly rotate pocket rings.[20]
At the Ritz London casino in March 0️⃣ 2004,
two Serbs and a Hungarian used a laser scanner hidden inside a mobile phone linked to a
computer to 0️⃣ predict the sector of the wheel where the ball was most likely to drop.
They netted £1.3m in two nights.[21] 0️⃣ They were arrested and kept on police bail for
nine months, but eventually released and allowed to keep their winnings 0️⃣ as they had not
interfered with the casino equipment.[22]
Specific betting systems [ edit ]
The
numerous even-money bets in roulette have 0️⃣ inspired many players over the years to
attempt to beat the game by using one or more variations of a 0️⃣ martingale betting
strategy, wherein the gambler doubles the bet after every loss, so that the first win
would recover all 0️⃣ previous losses, plus win a profit equal to the original bet. The
problem with this strategy is that, remembering that 0️⃣ past results do not affect the
future, it is possible for the player to lose so many times in a 0️⃣ row, that the player,
doubling and redoubling their bets, either runs out of money or hits the table limit. A
0️⃣ large financial loss is certain in the long term if the player continued to employ this
strategy. Another strategy is 0️⃣ the Fibonacci system, where bets are calculated according
to the Fibonacci sequence. Regardless of the specific progression, no such strategy 0️⃣ can
statistically overcome the casino's advantage, since the expected value of each allowed
bet is negative.
Types of betting system [ 0️⃣ edit ]
Betting systems in roulette can be
divided in to two main categories:
Negative progression system (e.g.
Martingale)
Negative progression systems involve 0️⃣ increasing the size of one's bet when
they lose. This is the most common type of betting system. The goal 0️⃣ of this system is
to recoup losses faster so that one can return to a winning position more quickly after
0️⃣ a losing streak. The typical shape of these systems is small but consistent wins
followed by occasional catastrophic losses. Examples 0️⃣ of negative progression systems
include the Martingale system, the Fibonacci system, the Labouchère system, and the
d'Alembert system.
Positive progression system 0️⃣ (e.g. Paroli)
Positive progression
systems involve increasing the size of one's bet when one wins. The goal of these
systems is 0️⃣ to either exacerbate the effects of winning streaks (e.g. the Paroli system)
or to take advantage of changes in luck 0️⃣ to recover more quickly from previous losses
(e.g. Oscar's grind). The shape of these systems is typically small but consistent
0️⃣ losses followed by occasional big wins. However, over the long run these wins do not
compensate for the losses incurred 0️⃣ in between.[23]
Reverse Martingale system [ edit
]
The Reverse Martingale system, also known as the Paroli system, follows the idea of
0️⃣ the martingale betting strategy, but reversed. Instead of doubling a bet after a loss
the gambler doubles the bet after 0️⃣ every win. The system creates a false feeling of
eliminating the risk of betting more when losing, but, in reality, 0️⃣ it has the same
problem as the martingale strategy. By doubling bets after every win, one keeps betting
everything they 0️⃣ have won until they either stop playing, or lose it all.
Labouchère
system [ edit ]
The Labouchère System is a progression 0️⃣ betting strategy like the
martingale but does not require the gambler to risk their stake as quickly with
dramatic double-ups. 0️⃣ The Labouchere System involves using a series of numbers in a line
to determine the bet amount, following a win 0️⃣ or a loss. Typically, the player adds the
numbers at the front and end of the line to determine the 0️⃣ size of the next bet. If the
player wins, they cross out numbers and continue working on the smaller line. 0️⃣ If the
player loses, then they add their previous bet to the end of the line and continue to
work 0️⃣ on the longer line. This is a much more flexible progression betting system and
there is much room for the 0️⃣ player to design their initial line to their own playing
preference.
This system is one that is designed so that when 0️⃣ the player has won over a
third of their bets (less than the expected 18/38), they will win. Whereas the
0️⃣ martingale will cause ruin in the event of a long sequence of successive losses, the
Labouchère system will cause bet 0️⃣ size to grow quickly even where a losing sequence is
broken by wins. This occurs because as the player loses, 0️⃣ the average bet size in the
line increases.
As with all other betting systems, the average value of this system is
0️⃣ negative.
D'Alembert system [ edit ]
The system, also called montant et demontant (from
French, meaning upwards and downwards), is often called 0️⃣ a pyramid system. It is based
on a mathematical equilibrium theory devised by a French mathematician of the same
name. 0️⃣ Like the martingale, this system is mainly applied to the even-money outside
bets, and is favored by players who want 0️⃣ to keep the amount of their bets and losses to
a minimum. The betting progression is very simple: After each 0️⃣ loss, one unit is added
to the next bet, and after each win, one unit is deducted from the next 0️⃣ bet. Starting
with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. 0️⃣ If
this is followed by a win, the next bet would be 1 units.
This betting system relies on
the gambler's 0️⃣ fallacy—that the player is more likely to lose following a win, and more
likely to win following a loss.
Other systems 0️⃣ [ edit ]
There are numerous other betting
systems that rely on this fallacy, or that attempt to follow 'streaks' (looking 0️⃣ for
patterns in randomness), varying bet size accordingly.
Many betting systems are sold
online and purport to enable the player to 0️⃣ 'beat' the odds. One such system was
advertised by Jason Gillon of Rotherham, UK, who claimed one could 'earn £200 0️⃣ daily' by
following his betting system, described as a 'loophole'. As the system was advertised
in the UK press, it 0️⃣ was subject to Advertising Standards Authority regulation, and
following a complaint, it was ruled by the ASA that Mr. Gillon 0️⃣ had failed to support
his claims, and that he had failed to show that there was any loophole.
Notable
winnings [ 0️⃣ edit ]
In the 1960s and early 1970s, Richard Jarecki won aboutR$1.2 million
at dozens of European casinos. He claimed that 0️⃣ he was using a mathematical system
designed on a powerful computer. In reality, he simply observed more than 10,000 spins
0️⃣ of each roulette wheel to determine flaws in the wheels. Eventually the casinos
realized that flaws in the wheels could 0️⃣ be exploited, and replaced older wheels. The
manufacture of roulette wheels has improved over time. [24]
In 1963 Sean Connery,
filming 0️⃣ From Russia with Love in Italy, attended the casino in Saint-Vincent and won
three consecutive times on the number 17, 0️⃣ his winnings riding on the second and third
spins. [25]
in Italy, attended the casino in Saint-Vincent and won three consecutive
0️⃣ times on the number 17, his winnings on the second and third spins. In 2004, Ashley
Revell of London sold 0️⃣ all of his possessions, clothing included, and placed his entire
net worth of US$135,300 on red at the Plaza Hotel 0️⃣ in Las Vegas. The ball landed on "Red
7" and Revell walked away withR$270,600.[26]
See also [ edit ]
