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With all games, the casino makes their money by paying the player less than their true probability of winning. In Roulette, the house edge is created by the presence of the extra pocket numbered zero. There are two types of roulette wheel, the European or French with a single zero pocket and the American with two zero pockets. Naturally, the American wheel creates a greater house edge with its two zero pockets.

The probabilities of winning on each wheel are as follows:

A spin of the single zero pocket wheel has a total of 37 possible outcomes. Each outcome is totally independent of the previous one.

A single number has 2.7% or 1:37 chance of success and 97.3% or 36:37 chance of failure.
Two numbers have 5.41% (2:37) success, 94.59% (35:37) failure.
Three numbers or a row has 8.11% (3:37) success, 91.89% (34:37) failure.
Four numbers has 10.81% (4:37) success, 89.19% (33:37) failure.
Six numbers or two rows have 16.22% (6:37) success, 83.78% (28:37) failure.
Nine numbers or three rows have 24.32% (9:37) success, 75.68% (28:37) failure.
Twelve numbers or four rows / one column / one third has 32.43% (12:37) success, 67.57% (25:37) failure.
Eighteen numbers or lack/red, odd/even, high/low have 48.65% (18/37) success, 51.35% (19:37) failure.

With a double zero pocket added to the wheel as in American Roulette, the house edge can be seen to have improved as all odds are calculated with 38 possible outcomes as follows:

A single number has 2.63% (1:38) chance of success, 97.37% (36:38) chance of failure.
Two numbers have 5.26% (2:38) success, 94.74% (35:38) failure.
Three numbers or a row has 7.89% (3:38) success, 92.11% (34:38) failure.
Four numbers has 10.53% (4:38) success, 89.47% (33:38) failure.
Six numbers or two rows have 15.79% (6:38) success, 84.21% (28:38) failure.
Nine numbers or three rows have 23.68% (9:38) success, 76.32% (28:38) failure.
Twelve numbers or four rows / one column / one third has 31.58% (12:38) success, 68.42% (25:38) failure.
Eighteen numbers or lack/red, odd/even, high/low have 47.37% (18/38) success, 52.63% (19:38) failure.

The verdict on this evidence is to always play the European or French Roulette wheel for slightly better odds of winning.