Roulette

Last Update: Feb. 11, 2012

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Introduction

Roulette is one of the easiest games to play and understand in the casino. As usual the easier a game is to understand the greater the house edge, and roulette is no exception. If you are looking for a easy to understand and slow paced table game, and are willing to sacrifice on the house edge, then you may like roulette. If you want something more stimulating or with a decent return I would suggest looking at other games.

One difference between roulette and all other table games is that roulette chips have no value denomination printed on them. This actually is the true definition of a chip, one which indicates its value is technically called a check. The roulette table comes with six to eight sets of different colored chips, each set consisting of 300 chips. When a player buys-in they get their own color and the value would be the buy-in divided by the number of chips received. The dealer will place a token on top of the dealer's stack of that color of chips to indicate the value.

United States Rules

A U.S. roulette wheel consists of 38 numbered slots:numbers 1 to 36, a zero, and a double zero. The betting layout consists of every individual number as well as a host of "outside" or combinations of numbers. After the players make their bets the dealer spins the wheel and a ball and after several seconds the ball will land in one of the numbered slots.

The following table displays the available bets, the win (on a "to one" basis), and the probability of winning under U.S. rules. All casinos in the U.S. follow these rules except for in Atlantic City. The house edge on all bets is 1/19, or 5.26%, except for one bet. The exception is the 0-00-1-2-3 combination, which carries a house edge of 7.89%.

Double-Zero Roulette
Bet	Pays	Probability Win	House Edge
Red	1	47.37%	5.26%
Black	1	47.37%	5.26%
Odd	1	47.37%	5.26%
Even	1	47.37%	5.26%
1 to 18	1	47.37%	5.26%
19 to 36	1	47.37%	5.26%
1 to 12	2	31.58%	5.26%
13 to 24	2	31.58%	5.26%
25 to 36	2	31.58%	5.26%
Sixline (6 numbers)	5	15.79%	5.26%
First five (5 numbers)	6	13.16%	7.89%
Corner (4 numbers)	8	10.53%	5.26%
Street (3 numbers)	11	7.89%	5.26%
Split (2 numbers)	17	5.26%	5.26%
Any one number	35	2.63%	5.26%

Single Zero Rules

Most high-end casinos in the United States have single-zero wheels. This includes Las Vegas, Atlantic City, and Foxwoods in Connecticut. The Grand in Tunica used to, but I don't know if Harrah's kept it after they took over. The limits on the single zero wheels are usually higher than the double zero wheels. A noteworthy exception is the Nevada Palace in Las Vegas, which has a single zero wheel with a 25-cent minimum. The house edge on an American single-zero wheel is 1/37, or 2.70%.

Atlantic City Rules

In Atlantic City any all even money bets (red, black,odd, even, 1-18, 19-36) follow a variation of the European imprisonment rule (see below). In the event the ball lands in 0 or 00 the player will lose only half of any even money bet. This lowers the house edge to 2.63% on these bets. This rule does not apply on single zero wheels.

European Rules

European roulette is played on a single wheel and also features a favorable "en prison" rule. Under this rule ifthe player makes any even money bet (red, black, odd, even, 1-18, 19-36), and the ball lands in zero, then the player gets half the bet back, known as "la partage" in French. In Europe, the player sometimes may also choose to imprison the bet, rather than lose half. If an imprisoned bet wins on the next spin it is released and the player gets it back, without winnings.

What is subject to casino rules is what happens to an imprisoned bet if the ball lands in zero again on the next spin. At some casinos the bet loses, and at others it would become double imprisoned. If a double-imprisoned bet bet won on the next spin, it would move up a level, and become single-imprisoned again. If it lost, then if would become triple-imprisoned if the casino allowed it, otherwise it would lose.

Another variation, found in France, keeps the bet imprisoned until there is a non-zero outcome. So further zeros would not matter.

The following table shows the probability of a win, push, and loss under every imprisonment variation I'm aware of.

When given the choice to lose half or face imprisonment, the expected value is the same under French rules. Otherwise the expected loss is less losing half.

Bally Gaming Rules

Bally Gaming has an electronic representation of roulette, on a long vertical monitor. Every time I have seen it, a single-zero wheel was pictured. Sometimes the pay-offs are standard. However, be warned that sometimes a single-number win pays 31 to 1 (shown on the game as 32 for 1), and a two-number win pays 15 to 1 (shown as 16 for 1). This increases the house edge on both bets to 15.79%.

Best Roulette in the West

Best in Nevada: The Bellegio, Mandalay Bay, MGM Grand, Mirage, Rio, and Wynn all have European roulette, with a house edge of 1.35%. Usually such wheels are in the high-limit rooms, but the MGM and Mirage also have a European wheel in the main casino at a $25 minimum.

Best in California: It is my understanding that the only single-zero roulette in California is at the Barona casino, with a house edge of 2.78%.

Las Vegas Rules Survey

I am proud to present my Las Vegas roulette survey at my companion site Wizard of Vegas .

Number Placement

To the casual observer, it would appear that the numbers on the wheel are not organized and seem to be distributed randomly. The only obvious patterns are that red and black numbers alternate and that usually two odd numbers alternate with two even numbers. However the distribution of numbers was carefully arranged so that the sum of the numbers for any given section of the wheel would be roughly equal to any other section of equal size. Most numbers are part of a pair, with one number between them. These pairs add to either 37 or 39.

For what it is worth, the sum of all the numbers in roulette is 666 .

Wheel Tracking

Some people and books claim that roulette wheels are biased, with a heavy side and a light side. Gravity causes the numbers in the heavy side to hit more often. This, I believe, used to be true when the quality of the equipment was poor. However, modern roulette wheels are much better and very rigorously tested. Only in a casino using a very dated wheel, may you be able to find a biased one by testing many thousands of spins. Based on stories I have heard, your odds of finding such wheels are probably best in Europe.

Betting Systems

Ugh. If you think you can beat roulette with a betting system please read my section debunking betting systems. If you don't believe what I say there, here is what the Encyclopedia Britannica says under the subject of roulette:

The oldest and most common betting system is the Martingale or "doubling-up" system,in which bets are doubled progressively. This probably dates back to the invention of the Roulette wheel, but every day of the week some gambler somewhere reinvents it, or some variation of it, and believes he has something new. Over the years hundreds of "sure-fire" winning systems have been dreamed up, but regardless of what system is used, in the long run it cannot overcome the house's advantage of the 0, or 0 and 00. This house advantage is the only system that consistently wins in the long run.

"No one can possibly win at roulette unless he steals money from the table while the croupier isn't looking." — Albert Einstein

San Diego County Roulette

Precision Spinning

I get asked a lot about whether I believe dealers can influence the spin to a certain area of the wheel. I flatly disbelieve that any dealer can do this, and still follow the usual casino rules for the force of the spin. Many dealers evidently do believe that they can indeed influence the spin. However, if they could, it would be easy to cause a confederate to win, and other players to lose, all while looking completely legitimate. Yet, somehow, you never hear about this actually happening. Nobody is getting caught or selling out, despite the alleged ease of which this is to do, what are the odds of that?

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Internal Links

• 1,000,000 simulated spins (2.67 MB). These spins were created using a Mersenne Twister random number generator. The results are based on a double-zero wheel. For a single-zero wheel, simply ignore the 26,432 double-zero outcomes.
• Diamond Roulette: roulette variant seen in Atlantic City
• Alphabetic Roulette: roulette variant seen at the Fitzgerald's, Las Vegas

External Links

For a simplified explanation of roulette, please see my companion site Wizard of Vegas .