Which sequence should I bet in roulette to maximize my probability of winning?

Answer by A Quora admin:

Mike Caro published the definitive strategy for playing roulette (Mike Caro's Roulette System #1) on rec.gambling many years ago. I don't have the original link, but following these rules will cut the house edge all the way down to zero, which is basically the best you can do on a fair wheel.

Caro’s Roulette System #1
First, never bet simply red or black. Also don’t bet odd or even. These are equally poor, consistently losing wagers.
Second, don’t be suckered into betting zero or double zero, despite what some experts may suggest. This may seem like you’re betting with the house, but for technical reasons you are actually betting against the house — and you are taking the worst of it.
So, in order to negate the house advantage, you MUST stick to straight non-green number bets. All odd red numbers turn out to be bad choices, based on over two trillion computer trials. Don’t bet them.
All even black numbers fair poorly, and cannot be bet, for much the same reason, which I won’t explain here.
Let’s get straight to the money-saving advice. Any bet you decide to make MUST cover only even-red or odd-black numbers. There are no exceptions.
Finally, you need to be very disciplined in excluding the number 30 and the group of consecutive numbers that begins with 11 and continues clockwise through and including 14.