Last Updated: March 2, 2013

Roulette

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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 purchases chips he gets his own color and the value of each chip is 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" bets on 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 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%
Six line (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. The limits on the single zero wheels are usually higher than the double-zero wheels. The house edge on every bet in American single-zero roulette 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 half-back rule (see below). If the ball lands in 0 or 00, then 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" or half-back rule. Under the "half-back" rule, if the 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. 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.

Imprisonment Odds

Imprisonment Win Push Loss Expected
Value
Single 0.48648649 0.01314828 0.50036523 -0.01387874
Double 0.48648649 0.01332346 0.50019005 -0.01370356
Triple 0.48648649 0.01332583 0.50018768 -0.01370120
Infinite 0.48648649 0.01332586 0.50018765 -0.01370117
French 0.48648649 0.01351351 0.50000000 -0.01351351

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.

Short Pays

I've noticed some electronic roulette games don't pay the full 35 to 1 on single-numbers bets, and/or 17 to 1 on double-number bets. Invariably, any game that short pays the player like this is going to be on a double-zero wheel as well. The following two tables show the house edge on single- and double-number bets, according to the win, assuming a double-zero wheel, and based on "to one" odds. Be careful that on electronic games wins are often given on a "for one" basis, meaning the original wager is not returned on a win. To convert a "for one" odds to "to one" odds, subtract one.

Single-Number Bets

Win House Edge
35 to 1 5.26%
34 to 1 7.89%
33 to 1 10.53%
32 to 1 13.16%
31 to 1 15.79%
30 to 1 18.42%

Double-Number Bets

Win House Edge
Win House Edge
17 to 1 5.26%
16 to 1 10.53%
15 to 1 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 2.70%.

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

The California Constitution prohibits a ball and wheel alone to determine the outcome in roulette. In San Diego County the casinos have thought of some creative ways to offer roulette anyway. Visit my page onSan Diego County roulette to see how they do it, and who offers the best odds.

Ball Steering

I get asked a lot about whether I believe dealers can influence the spin to a certain area of the wheel. My answer is an emphatic "no." Maybe on wheels decades old, but not the modern wheels with obstacles between the rim and the numbers, and where the ball bounces all over the place before it lands in a number.

Not only does ball steering not make sense from a physics standpoint, but a logical one as well. A dealer capable of steering the ball would not have to depend on tips for a living but could have a confederate come in, bet thousands on a section of the wheel, the dealer deliberately sends the ball into his friend's section, and they split up the winnings later. By causing section-betting strangers to lose, the wheel could still show a profit, and nobody would suspect a thing, except maybe the losing stranger. Yet, you never seem to hear of this happening.

Blackjack and poker expert Arnold Snyder has a different point of view on this topic. In the interest of presenting both sides, you may wish to read his articles How to Win at Roulette — Part I and Part II. I have the greatest of respect for Snyder, but on this topic, I have to respectfully disagree with him, much as I have always done with Stanford Wong in dice influence in craps.

Play for Free

Play roulette for free with this Flash game. I finally found a Flash game for my site which downloads quickly.

  • 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

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

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