What's the best roulette strategy?
I'm waiting on an email from a client so I'll give a better answer that will actually show you how to make money from online roulette, but you have to understand some basic math.
American roulette has two green zeroes (0 and 00), and European roulette has only one zero. The end result is that the house edge on European roulette is much smaller on all bets. Here's an example for betting on red to show the difference in the house advantage in the two games, but it's also an example of calculating the house edge.
American Roulette: There are 38 numbers (1-36, 0, 00). The chance of landing on red is 18/38, and the chance of not landing on red is 20/38. If you bet $100, then your expected profit is (18/38)(100) + (20/38)(-100) = -$5.26. So the house edge is 5.26% if you bet on red since you will lose $5.26 for every $100 you bet.
European Roulette: There are 37 numbers (1-36, 0). The chance of landing on red in this game is 18/37, and the chance of not landing on red in this game is 19/37. Again, if you bet $100, your expected profit is (18/37)(100) + (19/37)(-100) = -$2.70. In this game, the house edge for a bet on red is 2.70%.
Using bonuses, you can sometimes make money on roulette depending on the terms of the bonus. So let's say you have a 100% deposit bonus on $200 that requires a 30x play-through requirement. This means you'll have to wager a total of $200 * 30 = $6000 before you get your $200 bonus. If you bet no red in European roulette, then by wagering a total of $6000, you expect to lose 2.70% of $6000, which is (6000)(0.027) = $162.
Your average profit in this example would be $38, giving you an effective advantage over the casino of about 0.63% over the $6000 you wagered, while producing a (38/200) = 19% return on your initial investment. This sounds like it's tedious, but it can be sped up a lot of the time because many casinos allow you to automatically play X number of spins. By keeping your bet size low and using the automatic spins feature, your variance stays low and you have much less of a chance of accidentally going bust before clearing the bonus.
The lower the play-through requirements and the higher the size of the bonus, the more profit you'll get. You can easily set up a chart to show what ROI you can get from different play-through requirements, but anything under 30x is generally considered juicy.
Side note: some people might have the bright idea to put bets on both red and black at the same time to make the bonus clear faster. This is a good idea, but very few online casinos will allow you to clear bonuses in this way.
I decided to look for a non-hypothetical example how bonus terms can be worded in a way to trick you. After about 30 seconds, I found the endless 10% match bonus on Bodog that has a 15x play-through requirement. That sounds good if you skim over it, but in reality, it's a 15x play-through requirement on your deposit plus the bonus, not just the amount of the bonus.
For another example of what not to do, "Win Palace" has a small bonus with attractive terms, but doesn't allow you to clear the bonus using roulette. Read the terms closely!
If you're interested in this kind of stuff, Wizard of Odds is a good website with a lot of theory and strategy discussion for a lot of games, including some obscure games.
