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Roulette

This page is about the game. Mathematics has another concept named roulette.


Roulette is a casino gambling game. A croupier turns a round roulette wheel which has 37 or 38 separately numbered pockets in which a ball must land. The main pockets are numbered from 1 to 36 and change between red and black, with number 1 being red. In addition there is a pocket numbered 0 of green color. In most roulette wheels in the United States but not in Europe, there is a second zero compartment marked 00, also colored green.

If a player bets on a single number and wins, the pay is 35 to 1. This means the bet is multiplied by 35, while also the bet is returned, in total it is multiplied by 36. (In a lottery one would say 'the prize is 36 times the cost of the ticket', because in a lottery the cost of the ticket is not returned additionally.)

There is a common misconception that the green numbers are "house numbers" and that by betting on them one "gains the house edge." In fact, it is true that the house's advantage comes from the existence of the green numbers (a game without them would be statistically fair) however they are no more or less likely to come up than any other number.

A player can bet on numbers, combinations and even colors.

Contents

Board depiction (American Roulette)

0 00
1-
18
1st
12
1 2 3
4 5 6
odd 7 8 9
10 11 12
red 2nd
12
13 14 15
16 17 18
blk 19 20 21
22 23 24
even 3rd
12
25 26 27
28 29 30
19-
36
31 32 33
34 35 36

Bet odds table (American Roulette)

(in addition to the mentioned payout the bet is returned)

Bet name Winning spaces Payout
0 0 35 to 1
00 00 35 to 1
1 1 35 to 1
2 2 35 to 1
.
.
.
.
.
.
36 36 35 to 1
Row 00 0, 00 17 to 1
Row 3 1, 2, 3 11 to 1
Row 6 4, 5, 6 11 to 1
Row 9 7, 8, 9 11 to 1
.
.
.
.
.
.
Row 36 34, 35, 36 11 to 1
Column 1 1, 4, 7, ..., 34 2 to 1
Column 2 2, 5, 8, ..., 35 2 to 1
Column 3 3, 6, 9, ..., 36 2 to 1
First 12 1, 2, 3, ..., 12 2 to 1
Middle 12 13, 14, 15, ..., 24 2 to 1
Last 12 25, 26, 27, ..., 36 2 to 1
Odd 1, 3, 5, ..., 35 1 to 1
Even 2, 4, 6, ..., 36 1 to 1
Red 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 1 to 1
Black 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 1 to 1
1 to 18 1, 2, 3, ..., 18 1 to 1
19 to 36 19, 20, 21, ..., 36 1 to 1
five number bet 0, 00, 1, 2, 3 6 to 1

Note also that 0 and 00 are neither odd nor even in this game.

The house average or house edge is what is lost on average relative to the bet. If a player bets on a single number in the American game there is a probability of 1/38 that the player gets 36 times the bet (including the return), so they end up having on average 36/38=0.9474 times the bet. Thus the house average for American roulette is 1/19 (5.26%); the same applies for the other kinds of bets, except for the five number bet where it is greater than 7%. The house average is approximately halved in the European game.

Number Trivia

Roulette has been known as the devil's wheel since the total of all numbers adds up to 666, the legendary number of the beast.

Betting Strategies and Tactics

Albert Einstein is reputed to have stated, "You cannot beat a roulette table unless you steal money from it."

And yet, 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 gamer 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. As the referenced article on Martingales points out, this betting strategy is fundamentally flawed in practice.

Various attempts have been made by engineers to overcome the house edge through predicting the mechanical performance of the wheel, most notably by Joseph Jaggers, the man who broke the bank at Monte Carlo in 1873. Claude Shannon, a mathematician and computer scientist best known for his contributions to information theory, built arguably the first wearable computer to do so in 1961 [1].

To try to prevent exploits like this, the casinos monitor the performance of their wheels, and rebalance and realign them regularly to try to keep the result of the spins as random as possible.

More recently Thomas Bass , in his book The Newtonian Casino 1991, has claimed to be able to predict wheel performance in real time. He is also the author of The Eudaemonic Pie , which describes the exploits of a group of computer hackers who attempt to use computers in their shoes to win at roulette by predicting where the ball will fall. In 2004, it was reported that a group in London had used mobile cameraphones to predict the path of the ball, a cheating technique called sector targeting . [2] In December 2004 court adjudged that they didn't cheat because their special laser cameraphone and microchip weren't influencing the ball - they kept all 1.3m. [3]

Famous Bets

In 2004, Ashley Revell of London sold all of his possessions, clothing included, and brought US$135,300 to the Plaza Hotel in Las Vegas and put it all on "Red" at the roulette table in a double-or-nothing bet. The ball landed on "Red 7" and Revell walked away with his money doubled to $270,600.

See also

External link

Last updated: 05-13-2005 19:48:13
Last updated: 05-13-2005 07:56:04