Roulette Rules:
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 "for 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%.
Single Zero Rules
Most high-end casinos in the United States have single-zero wheels. This includes Las Vegas, Atlantic City, the Grand in Tunica, and Foxwoods in Connecticut. 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%.
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.