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 ]
