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Answer: There are "double zero" or American and "single zero" or European wheels. Both have 18 black and 18 red numbers -- a total of 36.
With 0 and 00, wheels have 38 total grooves. Chances of hitting any number (35-to-1 payoff) are 1/38, of hitting any row of three numbers (11-to-1 payoff) are 3/38, and so forth. With 0 but not 00, wheels have 37 grooves. This increases chances of winning -- for instance 1/37 (35-to-1 payoff) for numbers and 3/37 (11-to-1 payoff) for rows. Odds of winning are therefore somewhat better in single zero games. The real bonus comes because the house edge is cut in half when payouts for comparable bets are equal.
There's an exception. In single zero games, "outside" or "even money" bets -- red, black, odd, even, high, and low -- lose on 0. In most double zero games, outside bets lose only half on 0 or 00. Odds of winning remain 18/37 and 18/38 in single and double zero games, respectively. But owing to the loss of only half a bet in the latter, the edge is the same on these wagers.
Most roulette in this country is double zero. Some casinos have single zero tables, usually in high-limit areas, where they offer more favorable conditions to players willing to make larger bets.