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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]

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