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- Pagamento na Roulette Europeia: 36 x aposta original = retorno de 35+1 = total 36
- Em algumas casas, representações na mesa podem variar, como 0 para representar o "zero"
- Por exemplo, um apostador aposta 10 Créditos roulette scrigno roulette scrigno um número único, então o total retorno de ganhando será 360 Créditos (incluindo roulette scrigno aposta)
- 18 casas possíveis × 17 casas possíveis = 306 número de seções possíveis = 17 : 306 = 0,0555 (igual a 1:18 ou ~ 5.56%) Casa Simples, Pair ou Impair
- 00 e 0 (as casas de zero único, que fornecem: 2 casas possíveis × 36 números = 72 = 36 : 72 = 0,5 (vem a ser igual a 18:36 ou 1:2) Full Number
- Em comparação à aposta de uma casa só, neste caso o / (slash) representará um "split" na vizinhança de dois números vizinhos, representados pelo layout, roulette scrigno roulette scrigno jogos populares como a roulette European
- Por exemplo, um apostador pode recolher uma probabilidade de 17:1 no "split" na versão Americana quando uma bola cai roulette scrigno roulette scrigno trinta
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Na semana passada, ele anunciou que a Grã-Bretanha suspenderia 30 licenças de exportação para armas roulette scrigno Israel provocou uma tempestade 2️⃣ previsível. Críticos da guerra israelense na Gaza acusam o governo do Reino Unido por ser criminalmente suave com relação à 2️⃣ nação israelita e pelo outro lado seu rabino chefe ficou indignado ao anunciarroulette scrignosaída das exportações dos armamento perante 2️⃣ os EUA: O primeiro ministro Benjamin Netanyahu clivou no tema dizendo estar lutando contra Irã ou Hamas; quem regularmente compara 2️⃣ aos nazistas –e também foi um aliado próximo dele - Ministro britânico Ronald Dermer
Outros, compreensivelmente criticaram o governo do Reino 2️⃣ Unido por um tempo profundamente insensível. O anúncio chegou mesmo quando Israel estava convulsionado roulette scrigno angústia depois que seis reféns 2️⃣ foram executados pelo Hamas e sobreviveram no cativeiro durante quase 11 meses antes de serem baleado na cabeça enquanto as 2️⃣ forças israelenses se aproximavam ”.
Mas, além deroulette scrignocrítica ao mau momento do anúncio da política perante o governo Netanyahu 2️⃣ no Reino Unido não protegerá Israel das sanções internacionais aceleradas se suas políticas atuais continuarem.
A alegação de que Israel sozinho 2️⃣ está lutando contra o Irã roulette scrigno nome do Ocidente não nota, no entanto a Grã-Bretanha também anunciou sanções para membros 2️⃣ específicos da força Quds e uma unidade IRGC por fornecer armas aos proxies iranianos incluindo Hezbollah. Isso enfraquece bastante as 2️⃣ alegações sobre como é indiferente ao Reino Unido à ameaça iraniana ”.
A violação acelerada do direito internacional por Israel é 2️⃣ extrema demais para ser ignorada.
A decisão da Grã-Bretanha não foi sobre a luta de Israel contra o Irã, masroulette scrigno2️⃣ política roulette scrigno Gaza. O exame legal das licenças para exportação armas endereçou três possíveis violações do direito internacional humanitário: falha 2️⃣ israelense na obtenção ajuda humanitária aos civis; os maus tratos dos prisioneiros palestinos e seu comportamento nas hostilidadees que ocorreram 2️⃣ no território palestino - ou seja "a revisão" destinavase à proteção mínima padrões humanos durante as guerras (em tempos difíceis). 2️⃣ Os britânicos identificaram prováveis transgressões nos dois primeiros casos...
Mas Gaza é parte integrante do conflito israelo-palestino mais amplo, na Cisjordânia 2️⃣ e roulette scrigno Jerusalém também. Neste quadro maior a quebra acelerada de Israel da lei internacional está sendo muito extremada para 2️⃣ ser ignorada
Ao longo de seis décadas, os esforços roulette scrigno uma paz negociada afundaram e a ocupação israelense passou parecer um 2️⃣ peso pesado. Uma comunidade internacional cansada continuou publicando declarações condenam assentamentos como obstáculo à Paz; mas as palavras se tornaram 2️⃣ rotineiras o público global poderia facilmente esquecer que acordos não são simplesmente manifestações desagradáveis do roubo da terra ou 2️⃣ deslocamentos religiosos para fins fundamentalista-de violência religiosa - sob perspectiva legal: colonato civil na Cisjordânia representa precisamente anexação permanente das 2️⃣ terras pela guerra conquistada por parte dos povos árabes ocidentais (ver).
Bem antes da guerra atual, o governo que Netanyahu estabeleceu 2️⃣ roulette scrigno dezembro de 2024 rasgou a cortina dos esforços antigos e duradouros do Estado na anexação; seus acordos públicos especificaram 2️⃣ os direitos exclusivos à auto-determinações para judeus no país – incluindo "Judeia and Samaria". Uma posição ministerial especial foi criada 2️⃣ com vista ao envio das autoridades governamentais dum corpo militar supostamente temporário até um braço civil estatal.
Desde outubro de 2024, 2️⃣ a situação material dos palestinos na Cisjordânia atingiu um novo patamar. Israel cancelou imediatamente as autorizações para cerca 160 mil 2️⃣ trabalhadores da West Bank que trabalham roulette scrigno Jerusalém ou nos assentamentos – reduzindo os rendimentos e impulsionando o desemprego até 2️⃣ aproximadamente 1/3; também reteve receitas fiscais coletadas pela Autoridade Palestina como resultado disso A AP cortou salários do setor 2️⃣ público ao meio - toda infraestrutura sofreu mesmo com uma crise no nível das cidades palestinas: Gaza (alguns países), além 2️⃣ desta região onde estão localizados).
medida que a autoridade da Autoridade Palestina desmoronou, grupos milicianos fracionários surgiram e cometeram violência contra 2️⃣ israelenses ao lado – tudo antes do dia 7.
Depois de outubro 2024, parecia apenas uma questão roulette scrigno tempo até Israel 2️⃣ ver a necessidade da força esmagadora para acabar com essa ameaça. Finalmente no mês passado um palestino na Cisjordânia parece 2️⃣ ter acidentalmente explodido enquanto preparava o atentado suicida destinado à morte civis e terroristas que estavam mortos por volta do 2️⃣ dia 28 agosto as forças israelenses se mudaram contra várias cidades palestinas ou campos refugiados ao norte das margens ocidentais 2️⃣ (o exército chamou-a "Operação Acampamento dos Verões") sendo esta campanha mais extensa nos últimos vinte anos!
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após a 2️⃣ promoção da newsletter;
Cada novo impulso avança o objetivo que Netanyahu nunca escondeu: soberania permanente sobre toda a Cisjordânia.
Na sexta-feira, as 2️⃣ Forças de Defesa Israel (IDF) supostamente deixaram Jenin após nove dias do que alguns descreveram como um cerco. Mas não 2️⃣ há nenhuma indicação se e quando a operação vai realmente acabar nominalmente sob ameaças A Operação C está firmemente 2️⃣ enveredada roulette scrigno deixar o intenso combate peter fora da Cisjordânia enquanto mantém uma forte aderência militar – às vezes por 2️⃣ anos - assim comroulette scrignoocupação original 18 ano sul Líbano depois das invasões 1982; para os futuros possíveis Gaza: 2️⃣ na Margem Ocidental já estava controle israelense
Israel não vai parar por aí. Ministros-chaves apreciam a perspectiva de dominar Gaza também! 2️⃣ Itamar Ben Gvir, ministro da segurança nacional e pediu o reestabelecimento dos assentamentos judeus roulette scrigno janeiro que tinham sido feitos 2️⃣ pelos israelenses na Faixa De Jerusalém para esse fim; Um Knesset caucus foi estabelecido pela extrema direita legisladores no sentido 2️⃣ do avançoroulette scrignochamada: ativistas estão criando uma nova distribuição perto das finanças militares desde as cercadas pelo governo israelense 2️⃣ - esperando até ao dia seguinte (em inglês).
Críticos de esquerda provavelmente estão correto que a suspensão do pequeno número das 2️⃣ licenças britânicas para exportação não será suficiente, o bastante pra impedir uma agenda mais ampla. Sanções muito severas falharam roulette scrigno 2️⃣ conter as ações dos regimes como Irã ou Rússia
Por outro lado, aqueles que atacam o Reino Unido por tomar medidas 2️⃣ para restringir as decisões mais perigosas de Israel devem desafiar eles mesmos ao governo Netanyahu a abandonarroulette scrignoestratégia fatídica.
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Embora roulette scrigno origem exata seja desconhecida, a roleta era popular 🫰 na Itália como um jogo de azar simples no século XVII.
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No final dos anos 1790, as roletas utilizadas nos cassinos de Paris possuíam vermelho para o único zero e preto 🏧 para o duplo zero. Para evitar confusões, o verde foi selecionado para os zeros nas roleta, a partir do século 🏧 18.
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Casino game of chance
This article is about the casino game. For other uses, see
Roulette (disambiguation)
Roulette ball
"Gwendolen at the roulette 🍏 table" – 1910
illustration to George Eliot's Daniel Deronda
Roulette (named after the French word
meaning "little wheel") is a casino 🍏 game which was likely developed from the Italian
game Biribi. In the game, a player may choose to place a 🍏 bet on a single number,
various groupings of numbers, the color red or black, whether the number is odd or
🍏 even, or if the numbers are high (19–36) or low (1–18).
To determine the winning
number, a croupier spins a wheel 🍏 in one direction, then spins a ball in the opposite
direction around a tilted circular track running around the outer 🍏 edge of the wheel.
The ball eventually loses momentum, passes through an area of deflectors, and falls
onto the wheel 🍏 and into one of thirty-seven (single-zero, French or European style
roulette) or thirty-eight (double-zero, American style roulette) or thirty-nine
(triple-zero, 🍏 "Sands Roulette")[1] colored and numbered pockets on the wheel. The
winnings are then paid to anyone who has placed a 🍏 successful bet.
History [ edit
]
18th-century E.O. wheel with gamblers
The first form of roulette was devised in
18th-century France. Many historians 🍏 believe Blaise Pascal introduced a primitive form
of roulette in the 17th century in his search for a perpetual motion 🍏 machine. [2] The
roulette mechanism is a hybrid of a gaming wheel invented in 1720 and the Italian game
Biribi.[3] 🍏 A primitive form of roulette, known as 'EO' (Even/Odd), was played in
England in the late 18th century using a 🍏 gaming wheel similar to that used in
roulette.[4]
The game has been played in its present form since as early as 🍏 1796 in
Paris. An early description of the roulette game in its current form is found in a
French novel 🍏 La Roulette, ou le Jour by Jaques Lablee, which describes a roulette wheel
in the Palais Royal in Paris in 🍏 1796. The description included the house pockets:
"There are exactly two slots reserved for the bank, whence it derives its 🍏 sole
mathematical advantage." It then goes on to describe the layout with "two betting
spaces containing the bank's two numbers, 🍏 zero and double zero". The book was published
in 1801. An even earlier reference to a game of this name 🍏 was published in regulations
for New France (Québec) in 1758, which banned the games of "dice, hoca, faro, and
roulette".[5]
The 🍏 roulette wheels used in the casinos of Paris in the late 1790s had
red for the single zero and black 🍏 for the double zero. To avoid confusion, the color
green was selected for the zeros in roulette wheels starting in 🍏 the 1800s.
In 1843, in
the German spa casino town of Bad Homburg, fellow Frenchmen François and Louis Blanc
introduced the 🍏 single 0 style roulette wheel in order to compete against other casinos
offering the traditional wheel with single and double 🍏 zero house pockets.[6]
In some
forms of early American roulette wheels, there were numbers 1 to 28, plus a single
zero, 🍏 a double zero, and an American Eagle. The Eagle slot, which was a symbol of
American liberty, was a house 🍏 slot that brought the casino an extra edge. Soon, the
tradition vanished and since then the wheel features only numbered 🍏 slots. According to
Hoyle "the single 0, the double 0, and the eagle are never bars; but when the ball
🍏 falls into either of them, the banker sweeps every thing upon the table, except what
may happen to be bet 🍏 on either one of them, when he pays twenty-seven for one, which is
the amount paid for all sums bet 🍏 upon any single figure".[7]
1800s engraving of the
French roulette
In the 19th century, roulette spread all over Europe and the US,
🍏 becoming one of the most famous and most popular casino games. When the German
government abolished gambling in the 1860s, 🍏 the Blanc family moved to the last legal
remaining casino operation in Europe at Monte Carlo, where they established a 🍏 gambling
mecca for the elite of Europe. It was here that the single zero roulette wheel became
the premier game, 🍏 and over the years was exported around the world, except in the
United States where the double zero wheel remained 🍏 dominant.
Early American West
makeshift game
In the United States, the French double zero wheel made its way up the
Mississippi from 🍏 New Orleans, and then westward. It was here, because of rampant
cheating by both operators and gamblers, that the wheel 🍏 was eventually placed on top of
the table to prevent devices from being hidden in the table or wheel, and 🍏 the betting
layout was simplified. This eventually evolved into the American-style roulette game.
The American game was developed in the 🍏 gambling dens across the new territories where
makeshift games had been set up, whereas the French game evolved with style 🍏 and leisure
in Monte Carlo.
During the first part of the 20th century, the only casino towns of
note were Monte 🍏 Carlo with the traditional single zero French wheel, and Las Vegas with
the American double zero wheel. In the 1970s, 🍏 casinos began to flourish around the
world. In 1996 the first online casino, generally believed to be InterCasino, made it
🍏 possible to play roulette online.[8] By 2008, there were several hundred casinos
worldwide offering roulette games. The double zero wheel 🍏 is found in the U.S., Canada,
South America, and the Caribbean, while the single zero wheel is predominant
elsewhere.
The sum 🍏 of all the numbers on the roulette wheel (from 0 to 36) is 666,
which is the "Number of the 🍏 Beast".[9]
Rules of play against a casino [ edit ]
Roulette
with red 12 as the winner
Roulette players have a variety of 🍏 betting options. "Inside"
bets involve selecting either the exact number on which the ball will land, or a small
group 🍏 of numbers adjacent to each other on the layout. "Outside" bets, by contrast,
allow players to select a larger group 🍏 of numbers based on properties such as their
color or parity (odd/even). The payout odds for each type of bet 🍏 are based on its
probability.
The roulette table usually imposes minimum and maximum bets, and these
rules usually apply separately for 🍏 all of a player's inside and outside bets for each
spin. For inside bets at roulette tables, some casinos may 🍏 use separate roulette table
chips of various colors to distinguish players at the table. Players can continue to
place bets 🍏 as the ball spins around the wheel until the dealer announces "no more bets"
or "rien ne va plus".
Croupier's rake 🍏 pushing chips across a roulette layout
When a
winning number and color is determined by the roulette wheel, the dealer will 🍏 place a
marker, also known as a dolly, on that number on the roulette table layout. When the
dolly is 🍏 on the table, no players may place bets, collect bets or remove any bets from
the table. The dealer will 🍏 then sweep away all losing bets either by hand or by rake,
and determine the payouts for the remaining inside 🍏 and outside winning bets. When the
dealer is finished making payouts, the dolly is removed from the board and players 🍏 may
collect their winnings and make new bets. Winning chips remain on the board until
picked up by a player.
California 🍏 Roulette [ edit ]
In 2004, California legalized a
form of roulette known as California Roulette.[10] By law, the game must 🍏 use cards and
not slots on the roulette wheel to pick the winning number.
Roulette wheel number
sequence [ edit ]
The 🍏 pockets of the roulette wheel are numbered from 0 to 36.
In
number ranges from 1 to 10 and 19 to 🍏 28, odd numbers are red and even are black. In
ranges from 11 to 18 and 29 to 36, odd 🍏 numbers are black and even are red.
There is a
green pocket numbered 0 (zero). In American roulette, there is a 🍏 second green pocket
marked 00. Pocket number order on the roulette wheel adheres to the following clockwise
sequence in most 🍏 casinos:[citation needed]
Single-zero wheel
0-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-18-29-7-
28-12-35-3-26 Double-zero wheel
0-28-9-26-30-11-7-20-32-17-5-22-34-15-3-24-36-13-1-00-27-10-25-29-12-8-19-31-18-6-21-33
-16-4-23-35-14-2 Triple-zero wheel
0-000-00-32-15-19-4-21-2-25-17-34-6-27-13-36-11-30-8-23-10-5-24-16-33-1-20-14-31-9-22-1
8-29-7-28-12-35-3-26
Roulette table layout [ edit ]
French style layout, French single
zero 🍏 wheel
The cloth-covered betting area on a roulette table is known as the layout.
The layout is either single-zero or double-zero.
The 🍏 European-style layout has a single
zero, and the American style layout is usually a double-zero. The American-style
roulette table with 🍏 a wheel at one end is now used in most casinos because it has a
higher house edge compared to 🍏 a European layout.[11]
The French style table with a
wheel in the centre and a layout on either side is rarely 🍏 found outside of Monte
Carlo.
Types of bets [ edit ]
In roulette, bets can be either inside or
outside.[12]
Inside bets [ 🍏 edit ]
Name Description Chip placement Straight/Single Bet
on a single number Entirely within the square for the chosen number Split 🍏 Bet on two
vertically/horizontally adjacent numbers (e.g. 14-17 or 8–9) On the edge shared by the
numbers Street Bet on 🍏 three consecutive numbers in a horizontal line (e.g. 7-8-9) On
the outer edge of the number at either end of 🍏 the line Corner/Square Bet on four
numbers that meet at one corner (e.g. 10-11-13-14) On the common corner Six Line/Double
🍏 Street Bet on six consecutive numbers that form two horizontal lines (e.g.
31-32-33-34-35-36) On the outer corner shared by the 🍏 two leftmost or the two rightmost
numbers Trio/Basket A three-number bet that involves at least one zero: 0-1-2 (either
layout); 🍏 0-2-3 (single-zero only); 0-00-2 and 00-2-3 (double-zero only) On the corner
shared by the three chosen numbers First Four Bet 🍏 on 0-1-2-3 (Single-zero layout only)
On the outer corner shared by 0-1 or 0-3 Top Line Bet on 0-00-1-2-3 (Double-zero 🍏 layout
only) On the outer corner shared by 0-1 or 00-3
Outside bets [ edit ]
Outside bets
typically have smaller payouts 🍏 with better odds at winning. Except as noted, all of
these bets lose if a zero comes up.
1 to 18 🍏 (Low or Manque), or 19 to 36 (High or
Passe) A bet that the number will be in the chosen 🍏 range. Red or black (Rouge ou Noir)
A bet that the number will be the chosen color. Even or odd 🍏 (Pair ou Impair) A bet that
the number will be of the chosen type. Dozen bet A bet that the 🍏 number will be in the
chosen dozen: first (1-12, Première douzaine or P12), second (13-24, Moyenne douzaine
or M12), or 🍏 third (25-36, Dernière douzaine or D12). Column bet A bet that the number
will be in the chosen vertical column 🍏 of 12 numbers, such as 1-4-7-10 on down to 34.
The chip is placed on the space below the final 🍏 number in this sequence. Snake Bet A
special bet that covers the numbers 1, 5, 9, 12, 14, 16, 19, 🍏 23, 27, 30, 32, and 34. It
has the same payout as the dozen bet and takes its name from 🍏 the zigzagging, snakelike
pattern traced out by these numbers. The snake bet is not available in all casinos;
when it 🍏 is allowed, the chip is placed on the lower corner of the 34 square that
borders the 19-36 betting box. 🍏 Some layouts mark the bet with a two-headed snake that
winds from 1 to 34, and the bet can be 🍏 placed on the head at either end of the body.
In
the United Kingdom, the farthest outside bets (low/high, red/black, even/odd) 🍏 result in
the player losing only half of their bet if a zero comes up.
Bet odds table [ edit
]
The 🍏 expected value of aR$1 bet (except for the special case of Top line bets), for
American and European roulette, can 🍏 be calculated as
e x p e c t e d v a l u e = 1 n (
36 🍏 − n ) = 36 n − 1 , {\displaystyle \mathrm {expectedvalue} ={\frac
{1}{n}}(36-n)={\frac {36}{n}}-1,}
where n is the number of 🍏 pockets in the wheel.
The
initial bet is returned in addition to the mentioned payout: it can be easily
demonstrated that 🍏 this payout formula would lead to a zero expected value of profit if
there were only 36 numbers (that is, 🍏 the casino would break even). Having 37 or more
numbers gives the casino its edge.
Bet name Winning spaces Payout Odds 🍏 against winning
(French) Expected value
(on aR$1 bet) (French) Odds against winning (American) Expected
value
(on aR$1 bet) (American) 0 0 35 🍏 to 1 36 to 1 −$0.027 37 to 1 −$0.053 00 00 35 to
1 37 to 1 −$0.053 Straight 🍏 up Any single number 35 to 1 36 to 1 −$0.027 37 to 1 −$0.053
Row 0, 00 17 to 🍏 1 18 to 1 −$0.053 Split any two adjoining numbers vertical or
horizontal 17 to 1 17 + 1 ⁄ 🍏 2 to 1 −$0.027 18 to 1 −$0.053 Street any three numbers
horizontal (1, 2, 3 or 4, 5, 6, 🍏 etc.) 11 to 1 11 + 1 ⁄ 3 to 1 −$0.027 11 + 2 ⁄ 3 to 1
−$0.053 🍏 Corner any four adjoining numbers in a block (1, 2, 4, 5 or 17, 18, 20, 21,
etc.) 8 to 🍏 1 8 + 1 ⁄ 4 to 1 −$0.027 8 + 1 ⁄ 2 to 1 −$0.053 Top line (US) 🍏 0, 00, 1, 2, 3
6 to 1 6 + 3 ⁄ 5 to 1 −$0.079 Top line (European) 0, 🍏 1, 2, 3 8 to 1 8 + 1 ⁄ 4 to 1
−$0.027 Double Street any six numbers from 🍏 two horizontal rows (1, 2, 3, 4, 5, 6 or 28,
29, 30, 31, 32, 33 etc.) 5 to 1 🍏 5 + 1 ⁄ 6 to 1 −$0.027 5 + 1 ⁄ 3 to 1 −$0.053 1st
column 1, 4, 🍏 7, 10, 13, 16, 19, 22, 25, 28, 31, 34 2 to 1 2 + 1 ⁄ 12 to 1 🍏 −$0.027 2 + 1
⁄ 6 to 1 −$0.053 2nd column 2, 5, 8, 11, 14, 17, 20, 23, 26, 🍏 29, 32, 35 2 to 1 2 + 1 ⁄
12 to 1 −$0.027 2 + 1 ⁄ 6 to 🍏 1 −$0.053 3rd column 3, 6, 9, 12, 15, 18, 21, 24, 27, 30,
33, 36 2 to 1 2 🍏 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 1st dozen 1 through 12 🍏 2
to 1 2 + 1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 to 1 −$0.053 2nd 🍏 dozen 13 through 24 2 to 1 2 +
1 ⁄ 12 to 1 −$0.027 2 + 1 ⁄ 6 🍏 to 1 −$0.053 3rd dozen 25 through 36 2 to 1 2 + 1 ⁄ 12 to
1 −$0.027 2 🍏 + 1 ⁄ 6 to 1 −$0.053 Odd 1, 3, 5, ..., 35 1 to 1 1 + 1 ⁄ 🍏 18 to 1 −$0.027 1
+ 1 ⁄ 9 to 1 −$0.053 Even 2, 4, 6, ..., 36 1 to 🍏 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to
1 −$0.053 Red 32, 19, 🍏 21, 25, 34, 27, 36, 30, 23, 5, 16, 1, 14, 9, 18, 7, 12, 3 1 to 1
1 🍏 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053 Black 15, 4, 2, 17, 🍏 6, 13, 11, 8, 10,
24, 33, 20, 31, 22, 29, 28, 35, 26 1 to 1 1 + 1 🍏 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1
−$0.053 1 to 18 1, 2, 3, ..., 🍏 18 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 + 1 ⁄ 9 to 1 −$0.053
🍏 19 to 36 19, 20, 21, ..., 36 1 to 1 1 + 1 ⁄ 18 to 1 −$0.027 1 🍏 + 1 ⁄ 9 to 1 −$0.053
Top
line (0, 00, 1, 2, 3) has a different expected value because of 🍏 approximation of the
correct 6+1⁄5-to-1 payout obtained by the formula to 6-to-1. The values 0 and 00 are
not odd 🍏 or even, or high or low.
En prison rules, when used, reduce the house
advantage.
House edge [ edit ]
The house average 🍏 or house edge or house advantage (also
called the expected value) is the amount the player loses relative to any 🍏 bet made, on
average. If a player bets on a single number in the American game there is a
probability 🍏 of 1⁄38 that the player wins 35 times the bet, and a 37⁄38 chance that the
player loses their bet. 🍏 The expected value is:
−1 × 37 ⁄ 38 + 35 × 1 ⁄ 38 = −0.0526
(5.26% house edge)
For European 🍏 roulette, a single number wins 1⁄37 and loses 36⁄37:
−1
× 36 ⁄ 37 + 35 × 1 ⁄ 37 = 🍏 −0.0270 (2.70% house edge)
For triple-zero wheels, a single
number wins 1⁄39 and loses 38⁄39:
−1 × 38 ⁄ 39 + 35 🍏 × 1 ⁄ 39 = −0.0769 (7.69% house
edge)
Mathematical model [ edit ]
As an example, the European roulette model, that 🍏 is,
roulette with only one zero, can be examined. Since this roulette has 37 cells with
equal odds of hitting, 🍏 this is a final model of field probability ( Ω , 2 Ω , P )
{\displaystyle (\Omega ,2^{\Omega },\mathbb 🍏 {P} )} , where Ω = { 0 , … , 36 }
{\displaystyle \Omega =\{0,\ldots ,36\}} , P ( 🍏 A ) = | A | 37 {\displaystyle \mathbb
{P} (A)={\frac {|A|}{37}}} for all A ∈ 2 Ω {\displaystyle A\in 🍏 2^{\Omega }} .
Call the
bet S {\displaystyle S} a triple ( A , r , ξ ) {\displaystyle (A,r,\xi )} 🍏 , where A
{\displaystyle A} is the set of chosen numbers, r ∈ R + {\displaystyle r\in \mathbb {R}
_{+}} 🍏 is the size of the bet, and ξ : Ω → R {\displaystyle \xi :\Omega \to \mathbb {R}
} determines 🍏 the return of the bet.[13]
The rules of European roulette have 10 types of
bets. First the 'Straight Up' bet can 🍏 be imagined. In this case, S = ( { ω 0 } , r , ξ
) {\displaystyle S=(\{\omega _{0}\},r,\xi 🍏 )} , for some ω 0 ∈ Ω {\displaystyle \omega
_{0}\in \Omega } , and ξ {\displaystyle \xi } is 🍏 determined by
ξ ( ω ) = { − r , ω ≠ ω
0 35 ⋅ r , ω = 🍏 ω 0 . {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega
eq \omega
_{0}\\35\cdot r,&\omega =\omega _{0}\end{cases}}.}
The bet's expected net return, or
profitability, is equal 🍏 to
M [ ξ ] = 1 37 ∑ ω ∈ Ω ξ ( ω ) = 1 37 ( ξ 🍏 ( ω 0 ) + ∑ ω ≠ ω
0 ξ ( ω ) ) = 1 37 ( 35 🍏 ⋅ r − 36 ⋅ r ) = − r 37 ≈ − 0.027 r . {\displaystyle M[\xi
]={\frac {1}{37}}\sum 🍏 _{\omega \in \Omega }\xi (\omega )={\frac {1}{37}}\left(\xi
(\omega _{0})+\sum _{\omega
eq \omega _{0}}\xi (\omega )\right)={\frac
{1}{37}}\left(35\cdot r-36\cdot r\right)=-{\frac {r}{37}}\approx -0.027r.}
Without
details, 🍏 for a bet, black (or red), the rule is determined as
ξ ( ω ) = { − r , ω 🍏 is
red − r , ω = 0 r , ω is black , {\displaystyle \xi (\omega )={\begin{cases}-r,&\omega
{\text{ is 🍏 red}}\\-r,&\omega =0\\r,&\omega {\text{ is black}}\end{cases}},}
and the
profitability
M [ ξ ] = 1 37 ( 18 ⋅ r − 18 ⋅ 🍏 r − r ) = − r 37 {\displaystyle M[\xi
]={\frac {1}{37}}(18\cdot r-18\cdot r-r)=-{\frac {r}{37}}}
For similar reasons it is
simple 🍏 to see that the profitability is also equal for all remaining types of bets. − r
37 {\displaystyle -{\frac {r}{37}}} 🍏 .[14]
In reality this means that, the more bets a
player makes, the more they are going to lose independent of 🍏 the strategies
(combinations of bet types or size of bets) that they employ:
∑ n = 1 ∞ M [ ξ 🍏 n ] = − 1
37 ∑ n = 1 ∞ r n → − ∞ . {\displaystyle \sum _{n=1}^{\infty 🍏 }M[\xi _{n}]=-{\frac
{1}{37}}\sum _{n=1}^{\infty }r_{n}\to -\infty .}
Here, the profit margin for the
roulette owner is equal to approximately 2.7%. Nevertheless, 🍏 several roulette strategy
systems have been developed despite the losing odds. These systems can not change the
odds of the 🍏 game in favor of the player.
It is worth noting that the odds for the
player in American roulette are even 🍏 worse, as the bet profitability is at worst − 3 38
r ≈ − 0.0789 r {\displaystyle -{\frac {3}{38}}r\approx -0.0789r} 🍏 , and never better
than − r 19 ≈ − 0.0526 r {\displaystyle -{\frac {r}{19}}\approx -0.0526r} .
Simplified
mathematical model [ 🍏 edit ]
For a roulette wheel with n {\displaystyle n} green numbers
and 36 other unique numbers, the chance of the 🍏 ball landing on a given number is 1 ( 36
+ n ) {\displaystyle {\frac {1}{(36+n)}}} . For a betting 🍏 option with p {\displaystyle
p} numbers defining a win, the chance of winning a bet is p ( 36 + 🍏 n ) {\displaystyle
{\frac {p}{(36+n)}}}
For example, if a player bets on red, there are 18 red numbers, p
= 18 🍏 {\displaystyle p=18} , so the chance of winning is 18 ( 36 + n ) {\displaystyle
{\frac {18}{(36+n)}}} .
The payout 🍏 given by the casino for a win is based on the
roulette wheel having 36 outcomes, and the payout for 🍏 a bet is given by 36 p
{\displaystyle {\frac {36}{p}}} .
For example, betting on 1-12 there are 12 numbers
that 🍏 define a win, p = 12 {\displaystyle p=12} , the payout is 36 12 = 3 {\displaystyle
{\frac {36}{12}}=3} , 🍏 so the bettor wins 3 times their bet.
The average return on a
player's bet is given by p ( 36 🍏 + n ) × 36 p = 36 ( 36 + n ) {\displaystyle {\frac
{p}{(36+n)}}\times {\frac {36}{p}}={\frac {36}{(36+n)}}}
For n 🍏 > 0 {\displaystyle n>0}
, the average return is always lower than 1, so on average a player will lose
🍏 money.
With 1 green number, n = 1 {\displaystyle n=1} , the average return is 36 37
{\displaystyle {\frac {36}{37}}} , 🍏 that is, after a bet the player will on average have
36 37 {\displaystyle {\frac {36}{37}}} of their original bet 🍏 returned to them. With 2
green numbers, n = 2 {\displaystyle n=2} , the average return is 36 38 {\displaystyle
🍏 {\frac {36}{38}}} . With 3 green numbers, n = 3 {\displaystyle n=3} , the average
return is 36 39 {\displaystyle 🍏 {\frac {36}{39}}} .
This shows that the expected return
is independent of the choice of bet.
Mechanics [ edit ]
All roulette tables 🍏 deal with
only four elements:
1. The roulette wheel.
2. The roulette table (aka layout).
3. The
ball. These days the ball is 🍏 most likely high impact plastic, but originally it was
made of ivory. Modern casinos maintain the integrity of their roulette 🍏 balls with
regular magnetic and x-ray exams.
4. The chips. Some casinos allow the player to use
generic casino chips at 🍏 the roulette tables, but most require the player to buy in at
the table. The croupier has stacks of various 🍏 colored chips. Usually each player gets a
different color to help avoid confusion of bets, and the player can designate 🍏 the value
of the chip. The chips are typically valued at eitherR$1 or the table minimum; if the
player wishes, 🍏 the chips may be worthR$0.25 so long as the "total" wager meets the
table minimums for their respective sectors, for 🍏 example by placing fourR$0.25 bets to
meet aR$1 table minimum.
All roulette tables operated by a casino have the same basic
🍏 mechanics:
There is a balanced mechanical wheel with colored pockets separated by
identical vanes and the wheel which spins freely on 🍏 a supporting post.
The wheel is
held within a wooden frame which contains a track around the upper outer edge and
🍏 blocks of a variety of designs placed approximately halfway down the face of the
frame.
A plastic or ivory ball is 🍏 spun in the track in the frame that holds the wheel.
As the ball loses momentum the centrifugal force is 🍏 no longer sufficient to hold the
ball in the groove and it falls down the face of the frame. As 🍏 the ball hits a block
its trajectory is randomly altered on all 3 planes (X, Y, and Z) causing the 🍏 ball to
bounce and skip.
The ball falls onto the spinning wheel and eventually lands into one
of the pockets.
The number 🍏 of the pocket the ball falls into determines how the bets
placed on the layout table are treated.
After this the 🍏 specifics of individual tables
can vary greatly.[15]
Called (or call) bets or announced bets [ edit ]
Traditional
roulette wheel sectors
Although most 🍏 often named "call bets" technically these bets are
more accurately referred to as "announced bets". The legal distinction between a 🍏 "call
bet" and an "announced bet" is that a "call bet" is a bet called by the player without
placing 🍏 any money on the table to cover the cost of the bet. In many jurisdictions
(most notably the United Kingdom) 🍏 this is considered gambling on credit and is illegal.
An "announced bet" is a bet called by the player for 🍏 which they immediately place
enough money to cover the amount of the bet on the table, prior to the outcome 🍏 of the
spin or hand in progress being known.
There are different number series in roulette
that have special names attached 🍏 to them. Most commonly these bets are known as "the
French bets" and each covers a section of the wheel. 🍏 For the sake of accuracy, zero
spiel, although explained below, is not a French bet, it is more accurately "the 🍏 German
bet". Players at a table may bet a set amount per series (or multiples of that amount).
The series 🍏 are based on the way certain numbers lie next to each other on the roulette
wheel. Not all casinos offer 🍏 these bets, and some may offer additional bets or
variations on these.
Voisins du zéro (neighbors of zero) [ edit ]
This 🍏 is a name, more
accurately "grands voisins du zéro", for the 17 numbers that lie between 22 and 25 on
🍏 the wheel, including 22 and 25 themselves. The series is
22-18-29-7-28-12-35-3-26-0-32-15-19-4-21-2-25 (on a single-zero wheel).
Nine chips or
multiples thereof are 🍏 bet. Two chips are placed on the 0-2-3 trio; one on the 4–7
split; one on 12–15; one on 18–21; 🍏 one on 19–22; two on the 25-26-28-29 corner; and one
on 32–35.
Jeu zéro (zero game) [ edit ]
Zero game, also 🍏 known as zero spiel (Spiel is
German for game or play), is the name for the numbers closest to zero. 🍏 All numbers in
the zero game are included in the voisins, but are placed differently. The numbers bet
on are 🍏 12-35-3-26-0-32-15.
The bet consists of four chips or multiples thereof. Three
chips are bet on splits and one chip straight-up: one 🍏 chip on 0–3 split, one on 12–15
split, one on 32–35 split and one straight-up on number 26.
This type of 🍏 bet is popular
in Germany and many European casinos. It is also offered as a 5-chip bet in many
Eastern 🍏 European casinos. As a 5-chip bet, it is known as "zero spiel naca" and
includes, in addition to the chips 🍏 placed as noted above, a straight-up on number
19.
Le tiers du cylindre (third of the wheel) [ edit ]
This is 🍏 the name for the 12
numbers that lie on the opposite side of the wheel between 27 and 33, including 🍏 27 and
33 themselves. On a single-zero wheel, the series is 27-13-36-11-30-8-23-10-5-24-16-33.
The full name (although very rarely used, most 🍏 players refer to it as "tiers") for this
bet is "le tiers du cylindre" (translated from French into English meaning 🍏 one third of
the wheel) because it covers 12 numbers (placed as 6 splits), which is as close to 1⁄3
🍏 of the wheel as one can get.
Very popular in British casinos, tiers bets outnumber
voisins and orphelins bets by a 🍏 massive margin.
Six chips or multiples thereof are bet.
One chip is placed on each of the following splits: 5–8, 10–11, 🍏 13–16, 23–24, 27–30,
and 33–36.
The tiers bet is also called the "small series" and in some casinos (most
notably in 🍏 South Africa) "series 5-8".
A variant known as "tiers 5-8-10-11" has an
additional chip placed straight up on 5, 8, 10, 🍏 and 11m and so is a 10-piece bet. In
some places the variant is called "gioco Ferrari" with a straight 🍏 up on 8, 11, 23 and
30, the bet is marked with a red G on the racetrack.
Orphelins (orphans) [ 🍏 edit ]
These
numbers make up the two slices of the wheel outside the tiers and voisins. They contain
a total 🍏 of 8 numbers, comprising 17-34-6 and 1-20-14-31-9.
Five chips or multiples
thereof are bet on four splits and a straight-up: one 🍏 chip is placed straight-up on 1
and one chip on each of the splits: 6–9, 14–17, 17–20, and 31–34.
... and 🍏 the neighbors
[ edit ]
A number may be backed along with the two numbers on the either side of it 🍏 in
a 5-chip bet. For example, "0 and the neighbors" is a 5-chip bet with one piece
straight-up on 3, 🍏 26, 0, 32, and 15. Neighbors bets are often put on in combinations,
for example "1, 9, 14, and the 🍏 neighbors" is a 15-chip bet covering 18, 22, 33, 16 with
one chip, 9, 31, 20, 1 with two chips 🍏 and 14 with three chips.
Any of the above bets
may be combined, e.g. "orphelins by 1 and zero and the 🍏 neighbors by 1". The "...and the
neighbors" is often assumed by the croupier.
Final bets [ edit ]
Another bet offered on
🍏 the single-zero game is "final", "finale" or "finals".
Final 4, for example, is a
4-chip bet and consists of one chip 🍏 placed on each of the numbers ending in 4, that is
4, 14, 24, and 34. Final 7 is a 🍏 3-chip bet, one chip each on 7, 17, and 27. Final bets
from final 0 (zero) to final 6 cost 🍏 four chips. Final bets 7, 8 and 9 cost three
chips.
Some casinos also offer split-final bets, for example final 5-8 🍏 would be a
4-chip bet, one chip each on the splits 5–8, 15–18, 25–28, and one on 35.
Full
completes/maximums [ 🍏 edit ]
A complete bet places all of the inside bets on a certain
number. Full complete bets are most often 🍏 bet by high rollers as maximum bets.
The
maximum amount allowed to be wagered on a single bet in European roulette 🍏 is based on a
progressive betting model. If the casino allows a maximum bet ofR$1,000 on a 35-to-1
straight-up, then 🍏 on each 17-to-1 split connected to that straight-up,R$2,000 may be
wagered. Each 8-to-1 corner that covers four numbers) may haveR$4,000 🍏 wagered on it.
Each 11-to-1 street that covers three numbers may haveR$3,000 wagered on it. Each
5-to-1 six-line may haveR$6,000 🍏 wagered on it. EachR$1,000 incremental bet would be
represented by a marker that is used to specifically identify the player 🍏 and the amount
bet.
For instance, if a patron wished to place a full complete bet on 17, the player
would 🍏 call "17 to the maximum". This bet would require a total of 40 chips, orR$40,000.
To manually place the same 🍏 wager, the player would need to bet:
17 to the maximum Bet
type Number(s) bet on Chips Amount waged Straight-up 17 🍏 1R$1,000 Split 14-17 2R$2,000
Split 16-17 2R$2,000 Split 17-18 2R$2,000 Split 17-20 2R$2,000 Street 16-17-18 3R$3,000
Corner 13-14-16-17 4R$4,000 Corner 🍏 14-15-17-18 4R$4,000 Corner 16-17-19-20 4R$4,000
Corner 17-18-20-21 4R$4,000 Six line 13-14-15-16-17-18 6R$6,000 Six line
16-17-18-19-20-21 6R$6,000 Total 40R$40,000
The player calls 🍏 their bet to the croupier
(most often after the ball has been spun) and places enough chips to cover the 🍏 bet on
the table within reach of the croupier. The croupier will immediately announce the bet
(repeat what the player 🍏 has just said), ensure that the correct monetary amount has
been given while simultaneously placing a matching marker on the 🍏 number on the table
and the amount wagered.
The payout for this bet if the chosen number wins is 392 chips,
🍏 in the case of aR$1000 straight-up maximum,R$40,000 bet, a payout ofR$392,000. The
player's wagered 40 chips, as with all winning 🍏 bets in roulette, are still their
property and in the absence of a request to the contrary are left up 🍏 to possibly win
again on the next spin.
Based on the location of the numbers on the layout, the number
of 🍏 chips required to "complete" a number can be determined.
Zero costs 17 chips to
complete and pays 235 chips.
Number 1 and 🍏 number 3 each cost 27 chips and pay 297
chips.
Number 2 is a 36-chip bet and pays 396 chips.
1st column 🍏 numbers 4 to 31 and 3rd
column numbers 6 to 33, cost 30 chips each to complete. The payout for 🍏 a win on these
30-chip bets is 294 chips.
2nd column numbers 5 to 32 cost 40 chips each to complete.
🍏 The payout for a win on these numbers is 392 chips.
Numbers 34 and 36 each cost 18
chips and pay 🍏 198 chips.
Number 35 is a 24-chip bet which pays 264 chips.
Most
typically (Mayfair casinos in London and other top-class European 🍏 casinos) with these
maximum or full complete bets, nothing (except the aforementioned maximum button) is
ever placed on the layout 🍏 even in the case of a win. Experienced gaming staff, and the
type of customers playing such bets, are fully 🍏 aware of the payouts and so the croupier
simply makes up the correct payout, announces its value to the table 🍏 inspector (floor
person in the U.S.) and the customer, and then passes it to the customer, but only
after a 🍏 verbal authorization from the inspector has been received.
Also typically at
this level of play (house rules allowing) the experienced croupier 🍏 caters to the needs
of the customer and will most often add the customer's winning bet to the payout, as
🍏 the type of player playing these bets very rarely bets the same number two spins in
succession. For example, the 🍏 winning 40-chip /R$40,000 bet on "17 to the maximum" pays
392 chips /R$392,000. The experienced croupier would pay the player 🍏 432 chips
/R$432,000, that is 392 + 40, with the announcement that the payout "is with your bet
down".
There are 🍏 also several methods to determine the payout when a number adjacent to
a chosen number is the winner, for example, 🍏 player bets 40 chips on "23 to the maximum"
and number 26 is the winning number. The most notable method 🍏 is known as the "station"
system or method. When paying in stations, the dealer counts the number of ways or
🍏 stations that the winning number hits the complete bet. In the example above, 26 hits 4
stations - 2 different 🍏 corners, 1 split and 1 six-line. The dealer takes the number 4,
multiplies it by 30 and adds the remaining 🍏 8 to the payout: 4 × 30 = 120, 120 + 8 =
128. If calculated as stations, they would 🍏 just multiply 4 by 36, making 144 with the
players bet down.
In some casinos, a player may bet full complete 🍏 for less than the
table straight-up maximum, for example, "number 17 full complete byR$25" would
costR$1000, that is 40 chips 🍏 each atR$25 value.
Betting strategies and tactics [ edit
]
Over the years, many people have tried to beat the casino, and 🍏 turn roulette—a game
designed to turn a profit for the house—into one on which the player expects to win.
Most 🍏 of the time this comes down to the use of betting systems, strategies which say
that the house edge can 🍏 be beaten by simply employing a special pattern of bets, often
relying on the "Gambler's fallacy", the idea that past 🍏 results are any guide to the
future (for example, if a roulette wheel has come up 10 times in a 🍏 row on red, that red
on the next spin is any more or less likely than if the last spin 🍏 was black).
All
betting systems that rely on patterns, when employed on casino edge games will result,
on average, in the 🍏 player losing money.[16] In practice, players employing betting
systems may win, and may indeed win very large sums of money, 🍏 but the losses (which,
depending on the design of the betting system, may occur quite rarely) will outweigh
the wins. 🍏 Certain systems, such as the Martingale, described below, are extremely
risky, because the worst-case scenario (which is mathematically certain to 🍏 happen, at
some point) may see the player chasing losses with ever-bigger bets until they run out
of money.
The American 🍏 mathematician Patrick Billingsley said[17][unreliable source?]
that no betting system can convert a subfair game into a profitable enterprise. At
least 🍏 in the 1930s, some professional gamblers were able to consistently gain an edge
in roulette by seeking out rigged wheels 🍏 (not difficult to find at that time) and
betting opposite the largest bets.
Prediction methods [ edit ]
Whereas betting systems
are 🍏 essentially an attempt to beat the fact that a geometric series with initial value
of 0.95 (American roulette) or 0.97 🍏 (European roulette) will inevitably over time tend
to zero, engineers instead attempt to overcome the house edge through predicting the
🍏 mechanical performance of the wheel, most notably by Joseph Jagger at Monte Carlo in
1873. These schemes work by determining 🍏 that the ball is more likely to fall at certain
numbers. If effective, they raise the return of the game 🍏 above 100%, defeating the
betting system problem.
Edward O. Thorp (the developer of card counting and an early
hedge-fund pioneer) and 🍏 Claude Shannon (a mathematician and electronic engineer best
known for his contributions to information theory) built the first wearable computer 🍏 to
predict the landing of the ball in 1961. This system worked by timing the ball and
wheel, and using 🍏 the information obtained to calculate the most likely octant where the
ball would fall. Ironically, this technique works best with 🍏 an unbiased wheel though it
could still be countered quite easily by simply closing the table for betting before
beginning 🍏 the spin.
In 1982, several casinos in Britain began to lose large sums of
money at their roulette tables to teams 🍏 of gamblers from the US. Upon investigation by
the police, it was discovered they were using a legal system of 🍏 biased wheel-section
betting. As a result of this, the British roulette wheel manufacturer John Huxley
manufactured a roulette wheel to 🍏 counteract the problem.
The new wheel, designed by
George Melas, was called "low profile" because the pockets had been drastically reduced
🍏 in depth, and various other design modifications caused the ball to descend in a
gradual approach to the pocket area. 🍏 In 1986, when a professional gambling team headed
by Billy Walters wonR$3.8 million using the system on an old wheel 🍏 at the Golden Nugget
in Atlantic City, every casino in the world took notice, and within one year had
switched 🍏 to the new low-profile wheel.
Thomas Bass, in his book The Eudaemonic Pie
(1985) (published as The Newtonian Casino in Britain), 🍏 has claimed to be able to
predict wheel performance in real time. The book describes the exploits of a group 🍏 of
University of California Santa Cruz students, who called themselves the Eudaemons, who
in the late 1970s used computers in 🍏 their shoes to win at roulette. This is an updated
and improved version of Edward O. Thorp's approach, where Newtonian 🍏 Laws of Motion are
applied to track the roulette ball's deceleration; hence the British title.
In the
early 1990s, Gonzalo Garcia-Pelayo 🍏 believed that casino roulette wheels were not
perfectly random, and that by recording the results and analysing them with a 🍏 computer,
he could gain an edge on the house by predicting that certain numbers were more likely
to occur next 🍏 than the 1-in-36 odds offered by the house suggested. He did this at the
Casino de Madrid in Madrid, Spain, 🍏 winning 600,000 euros in a single day, and one
million euros in total. Legal action against him by the casino 🍏 was unsuccessful, being
ruled that the casino should fix its wheel.[18][19]
To defend against exploits like
these, many casinos use tracking 🍏 software, use wheels with new designs, rotate wheel
heads, and randomly rotate pocket rings.[20]
At the Ritz London casino in March 🍏 2004,
two Serbs and a Hungarian used a laser scanner hidden inside a mobile phone linked to a
computer to 🍏 predict the sector of the wheel where the ball was most likely to drop.
They netted £1.3m in two nights.[21] 🍏 They were arrested and kept on police bail for
nine months, but eventually released and allowed to keep their winnings 🍏 as they had not
interfered with the casino equipment.[22]
Specific betting systems [ edit ]
The
numerous even-money bets in roulette have 🍏 inspired many players over the years to
attempt to beat the game by using one or more variations of a 🍏 martingale betting
strategy, wherein the gambler doubles the bet after every loss, so that the first win
would recover all 🍏 previous losses, plus win a profit equal to the original bet. The
problem with this strategy is that, remembering that 🍏 past results do not affect the
future, it is possible for the player to lose so many times in a 🍏 row, that the player,
doubling and redoubling their bets, either runs out of money or hits the table limit. A
🍏 large financial loss is certain in the long term if the player continued to employ this
strategy. Another strategy is 🍏 the Fibonacci system, where bets are calculated according
to the Fibonacci sequence. Regardless of the specific progression, no such strategy 🍏 can
statistically overcome the casino's advantage, since the expected value of each allowed
bet is negative.
Types of betting system [ 🍏 edit ]
Betting systems in roulette can be
divided in to two main categories:
Negative progression system (e.g.
Martingale)
Negative progression systems involve 🍏 increasing the size of one's bet when
they lose. This is the most common type of betting system. The goal 🍏 of this system is
to recoup losses faster so that one can return to a winning position more quickly after
🍏 a losing streak. The typical shape of these systems is small but consistent wins
followed by occasional catastrophic losses. Examples 🍏 of negative progression systems
include the Martingale system, the Fibonacci system, the Labouchère system, and the
d'Alembert system.
Positive progression system 🍏 (e.g. Paroli)
Positive progression
systems involve increasing the size of one's bet when one wins. The goal of these
systems is 🍏 to either exacerbate the effects of winning streaks (e.g. the Paroli system)
or to take advantage of changes in luck 🍏 to recover more quickly from previous losses
(e.g. Oscar's grind). The shape of these systems is typically small but consistent
🍏 losses followed by occasional big wins. However, over the long run these wins do not
compensate for the losses incurred 🍏 in between.[23]
Reverse Martingale system [ edit
]
The Reverse Martingale system, also known as the Paroli system, follows the idea of
🍏 the martingale betting strategy, but reversed. Instead of doubling a bet after a loss
the gambler doubles the bet after 🍏 every win. The system creates a false feeling of
eliminating the risk of betting more when losing, but, in reality, 🍏 it has the same
problem as the martingale strategy. By doubling bets after every win, one keeps betting
everything they 🍏 have won until they either stop playing, or lose it all.
Labouchère
system [ edit ]
The Labouchère System is a progression 🍏 betting strategy like the
martingale but does not require the gambler to risk their stake as quickly with
dramatic double-ups. 🍏 The Labouchere System involves using a series of numbers in a line
to determine the bet amount, following a win 🍏 or a loss. Typically, the player adds the
numbers at the front and end of the line to determine the 🍏 size of the next bet. If the
player wins, they cross out numbers and continue working on the smaller line. 🍏 If the
player loses, then they add their previous bet to the end of the line and continue to
work 🍏 on the longer line. This is a much more flexible progression betting system and
there is much room for the 🍏 player to design their initial line to their own playing
preference.
This system is one that is designed so that when 🍏 the player has won over a
third of their bets (less than the expected 18/38), they will win. Whereas the
🍏 martingale will cause ruin in the event of a long sequence of successive losses, the
Labouchère system will cause bet 🍏 size to grow quickly even where a losing sequence is
broken by wins. This occurs because as the player loses, 🍏 the average bet size in the
line increases.
As with all other betting systems, the average value of this system is
🍏 negative.
D'Alembert system [ edit ]
The system, also called montant et demontant (from
French, meaning upwards and downwards), is often called 🍏 a pyramid system. It is based
on a mathematical equilibrium theory devised by a French mathematician of the same
name. 🍏 Like the martingale, this system is mainly applied to the even-money outside
bets, and is favored by players who want 🍏 to keep the amount of their bets and losses to
a minimum. The betting progression is very simple: After each 🍏 loss, one unit is added
to the next bet, and after each win, one unit is deducted from the next 🍏 bet. Starting
with an initial bet of, say, 1 unit, a loss would raise the next bet to 2 units. 🍏 If
this is followed by a win, the next bet would be 1 units.
This betting system relies on
the gambler's 🍏 fallacy—that the player is more likely to lose following a win, and more
likely to win following a loss.
Other systems 🍏 [ edit ]
There are numerous other betting
systems that rely on this fallacy, or that attempt to follow 'streaks' (looking 🍏 for
patterns in randomness), varying bet size accordingly.
Many betting systems are sold
online and purport to enable the player to 🍏 'beat' the odds. One such system was
advertised by Jason Gillon of Rotherham, UK, who claimed one could 'earn £200 🍏 daily' by
following his betting system, described as a 'loophole'. As the system was advertised
in the UK press, it 🍏 was subject to Advertising Standards Authority regulation, and
following a complaint, it was ruled by the ASA that Mr. Gillon 🍏 had failed to support
his claims, and that he had failed to show that there was any loophole.
Notable
winnings [ 🍏 edit ]
In the 1960s and early 1970s, Richard Jarecki won aboutR$1.2 million
at dozens of European casinos. He claimed that 🍏 he was using a mathematical system
designed on a powerful computer. In reality, he simply observed more than 10,000 spins
🍏 of each roulette wheel to determine flaws in the wheels. Eventually the casinos
realized that flaws in the wheels could 🍏 be exploited, and replaced older wheels. The
manufacture of roulette wheels has improved over time. [24]
In 1963 Sean Connery,
filming 🍏 From Russia with Love in Italy, attended the casino in Saint-Vincent and won
three consecutive times on the number 17, 🍏 his winnings riding on the second and third
spins. [25]
in Italy, attended the casino in Saint-Vincent and won three consecutive
🍏 times on the number 17, his winnings on the second and third spins. In 2004, Ashley
Revell of London sold 🍏 all of his possessions, clothing included, and placed his entire
net worth of US$135,300 on red at the Plaza Hotel 🍏 in Las Vegas. The ball landed on "Red
7" and Revell walked away withR$270,600.[26]
See also [ edit ]
pokerschool
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roulette scrigno
A Roulette é um jogo popular roulette scrigno roulette scrigno todos os cassinos, virtuals ou físicos, e é conhecido pelo seu wheel com casas para números e cores.
Se você tem interesse roulette scrigno roulette scrigno jogar Roulette, talvez se pergunte: "Quanto é pago quando o número 0 sai?" ou "Quais são as probabilidades do número 0?" Neste artigo, vamos responder essas perguntas e te ensinar sobre as probabilidades e pagamentos da Roulette.
Probabilidade e Pagamentos na Roulette
No geral, quanto mais improvável uma aposta for, melhor será o pagamento. Isso significa que quanto mais difícil uma determinada aposta for de acontecer, mais casino pagará caso você essa aposta.
Existem duas versões diferentes da Roulette: a Europeia e a Americana. Em ambas as versões temos o 0 (zero) e, além disso, na versão Americana você encontrará também o 00 (double-zero).
roulette scrigno
Apostando roulette scrigno roulette scrigno Duas Casas (Split)
O Pagamento na Split divide-se igualmente:
Bolas a Duas Casas (em português, um "split")
pokersenhas
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