Aces Guide to Gambling

Roulette Strategy & Rules :

Zeros determine the odds in roulette

About The Author

Michael Shackleford is known as "The Wizard of Odds", due to his mathematical analysis of many games of chance.

If you are willing to learn and want to maximize your odds, then visit his website at

The Wizard of Odds

Roulette is one of the easiest games to play and understand in the casino. As usual, however, the easier a game is to understand the greater the house edge, and roulette is no exception. If you must play roulette you would be well advised to seek out a single-zero game. If you must play double-zero roulette just stay away from the 0,00,1,2,3 five-number combination which has the highest house edge.

There are a host of different bets you can make, most of which have the same house edge. If there were no zeros on the wheel all of the bets would pay fair odds, (for example, 35 to one for a bet on a single number). It could be said that it is the zeros that give the house its edge and are often thought of as the "dealer's numbers", despite the fact that the player can bet on them.

The following table shows all the various bets, their payoff, probability of winning, and house edge for a double-zero wheel. In the case of single-zero games the payoffs are the same but the house edge is always 2.70%.

Double-zero roulette
Bet Pays Probability House edge
Red 1:1 47.37% 5.26%
Black 1:1 47.37% 5.26%
Odd 1:1 47.37% 5.26%
Even 1:1 47.37% 5.26%
1 to 18 1:1 47.37% 5.26%
19 to 36 1:1 47.37% 5.26%
1 to 12 2:1 31.58% 5.26%
13 to 24 2:1 31.58% 5.26%
25 to 36 2:1 31.58% 5.26%
Any one number 35:1 2.63% 5.26%
Two number combination 17:1 5.26% 5.26%
Three number combination 11:1 7.89% 5.26%
Four number combination 8:1 10.53% 5.26%
Six number combination 5:1 15.79% 5.26%
0,00,1,2,3 combination 6:1 13.16% 7.89%


The numbers on the wheel

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. In particular the numbers are usually organized in pairs, with one number in between, and whose sum is either 37 or 39. This is true of all of the following pairs: (10,29), (25,12), (29,8), (12,19), (8,31), (19,18), (31,6), (18,21), (6,33), (21,16), (33,4), (16,23), (4,35), (23,14), (35,2), (9,30), (26,11), (30,7), (7,32), (20,17), (32,5), (17,22), (5,34), (22,15), (34,3), (15,24), (3,36), (24,13), (36,1). The only numbers that fall outside this pattern are 27,14,2,28,11,13, and 1.

Locations of single-zero games

At a few places in the United States, and many in Europe, you can find single-zero roulette. This is a much better gamble than double-zero roulette, with a house advantage of 1/37 =~ 2.70%. Many of the single-zero wheels in the U.S. have high minimums. I know of or have heard about single-zero roulette at:
  • The Tropicana (Las Vegas)
  • The Frontier (Las Vegas)
  • The Monte Carlo (Las Vegas)
  • The Stratosphere (Las Vegas)
  • Mandalay Bay (Las Vegas), $25 minimum
  • Grand Casino (Tunica)

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