I won't spell it out here because the fun is in working out these problems, at least it is for me. I'll shove you in the right direction though.
Betting on a single number is foolish. The mathematical probability of hitting any single number is only 2.7%. In other words, the house absolutely loves you.
Dozens and Columns are better, 32.4%. Still, the house advantage is huge.
Even/Odd or Red/Black get you up to 48.6%. Hey, that's a deal, right?
Well, no. The problem with all of these calculations you'll find around the internet is that they are equivalent to picking a random number (or 12 or whatever) out of 38. The problem is that this is NOT how the roulette works.
The roulette has a spinning wheel with numbers separated by fences. The ball spins as well. Along the path of the ball there are also little bumpers that can alter the path of the ball.
Yes, in the long term it is just like picking random numbers. However, if you look at what makes you win or loose at the "micro" level it is a little simpler.
If you bet on a single number the ball only has to move one slot for you to loose. As it lands on the number field the ball has a bunch of excess energy. The surfaces are hard and it bounces around with great efficiency. It can go over one or more number fences very easily.
In fact, if you study every single common bet, single numbers, rows, columns, dozens, color, even/odd, etc. they all share one trait: If the ball jumps over just ONE fence you loose.
If you've played roulette enough you'll eventually run into this stereotype: Big guy. Smells and looks like money. Shows up with piles of cash, gold watch and gold chain around his neck. And starts to place piles of cash on numbers he is pulling out of his anal orifice. Most of the time these guys loose a ton of money. Why? The "one fence" problem.
OK, I think that sets it up. Actually, it is probably beyond obvious at this point. Take a look at a roulette wheel and think about how you should bet to solve the problem that makes every single common bet nearly worthless.
The genius of the roulette is in the wheel.