In roulette a croupier spins a wheel in one direction, and then spins a ball in the opposite direction around the perimeter of the wheel. The ball drops onto the wheel and eventually lands in one of 36 (in European roulette) or 37 (in American roulette) coloured and numbered pockets on the wheel. The pockets are numbered 0-36, with a single 0 green pocket in European roulette, and 0 and 00 green pockets in American roulette.
You can place a variety of bets, all based on which pocket they believe the ball will land on the wheel. You can make "inside" bets (picking the exact number of the pocket the ball will land in) as well as "outside" bets (picking various groupings of pockets, pocket colours, or whether it will land in an odd or even numbered pocket). Payouts are based on specific posted odds at the table, as far as which bets pay off what amount.
While you have lots of options when it comes to betting at the roulette table, the odds of most of them are exactly the same. Overall, the house advantage for American roulette is about 5.25%, and is about 2.7% for European roulette.
The odds for individual bets are much what you’d expect them to be, as far as the odds of picking a single number correctly being 37 to 1, the odds of picking red or black correctly being 1.111 to 1, and so on, based solely on the math and the numbers available on the table to bet on.
Remember, it's the presence of the 0 (and the 00 in American roulette) that skews the odds in favour of the house, as the ball dropping into a 0 or 00 causes many common bets on the table to lose, such as red/black or even/odd.
The first form of roulette was created in France in the 17th century, reportedly by mathematician Blaise Pascal. The game has been played in its current form since the early 1800s, and was very popular in Paris. Interestingly enough, it was only in 1842 that the "0" number was added to the roulette wheel, which has become largely responsible for the house advantage that the casino has in roulette for many bets.
Roulette spread to the US in the early 1800s, where casinos and gambling house operators weren't content with the existing house advantage, so they added a second zero (the 00) to increase the casino’s edge even more. In the 1800s roulette spread all over both Europe and the US, becoming one of the most famous and most popular casino games.
Perhaps because of its European roots and prominence in areas such as Monte Carlo, roulette has always been viewed as a slightly classier, more glamorous casino game than some of its counterparts.
Like many casino games, there's simply no guaranteed winning strategy for roulette. Because it has a higher house advantage than games such as craps or blackjack, one could argue that the best roulette strategy is to simply stay away from the table, as the odds are stacked against you from the very beginning. If you love roulette, though, by all means feel free to play and enjoy the game.