The question of how to beat roulette is a loaded question. The answer has several parts and conditions. Firstly, which roulette?
American and European roulette are entirely different games. The appearance of similarity is just that ...only a superficial appearance.
The question of how to beat roulette is actually a question of relativity.
Assuming a random release, American roulette is, in the first instance, relative to the geometric probability of gravity.
With a European regulated release, the game is, in the first instance, relative to the quadratic geometry of the "game" and life's perception of a game.
Each relativity is found through the geometric probability of the original Needle ...but the original Needle is a translating mathematical language with two sides. One side is relative to gravity through its random value of relative 1/4 pi, relative to gravity's straight line pull on an object's (wheel's) pi-angle. The other side is meaninglessly relative to the quadratic value of 1/4 C, meaninglessly relative to the circle of the "game."
American roulette (with a dealer's random release) is relative to the three poles of gravity's pi-angle or "diameter."
European roulette (with a dealer's regulated release) is relative to the four quadratic poles of the game's "circle."
A geometric player using "action at a distance" will find a flat bet advantage at both games but the advantage --and how to geometrically find it-- is different for each.
American roulette with a dealer's random release is the only random table game that is random relative to gravity. All other table games are relative to the "game" in the first instance ...and require a deeper finesse. We will soon be discussing the deeper finesse. However, it can only be --and must be-- understood relative to the only true randomness of gaming. That is: American roulette with a dealer's random release of the ball.
It appears that different wheels may be fundamentally oriented at different poles of a pi-angle at different times. This appears to occur from an overriding geometric sequence that is so large that at any given time, one wheel is averagely oriented at a pi-angle pole while another is averagely oriented at the Center of Rotation. Therefore, the practical approach appears to be: short sessions at several different wheels.
At American roulette (eternal caveat: with a dealer's random release) a geometric player would want to either quit after the first win or be prepared to play many more, perhaps even hundreds of spins. The Pi-odds Roulette Study and Roulette Statistics both suggest that 1,728 (one thousand seven hundred twenty eight) or a number roughly approximate thereto, is the necessary number of spins required for the averages to theoretically mathematically flesh out.
That is: the three poles of a pi-angle multiplied by the four poles of a circle, multiplied by itself three times (once for each of the pi-angle's three poles).
While a flat bet advantage my occur quickly, these are long term averages. While the Center of Rotation (that is: the middle pole of a pi-angle) is finessed through and not counted ...it still must be allowed to occur.
European roulette appears to deliver a flat bet advantage quicker. Indeed, all other table games are wrapped around the deeper finesse and modified geometry as exemplified by European roulette, but we will first be exploring the more fundamental underlying relativity of gravity. That is: American roulette with a dealer's random release of the ball. See Cracking Roulette in Exploring Randomness.