Until you understand how it works, you guys talking about the odds always being against the gambler need to keep your mouths shut. There is nothing wrong with this approach and for gaining small sums it is perfectly feasible and safe. It is not, however, a way to make a large sum. In fact, it's sort of an inverse lottery ticket.
Bet some amount on slightly less than 50% chance and double the amount you bid each round that you lose. When you do eventually win and walk away, you will have made a gain equal to the original amount. If you start with a small amount, you will be able to cover the doubled bet more times, doubling your odds of coming out ahead for each time that you can do so.
Given a 53% chance to lose each round, the odds that you will lose 10 rounds in a row are .17% or slightly less than 2/1000. Losing twenty in a row is .0003% or 3 in a million. Now, the feasibility of covering those bets... less promising.
With a $100 initial bet, you would need over 100,000 dollars to get those first odds and well over a million to get the latter. But the odds of getting that far are astronomically small.
So, if you happen to have 100,000 dollars lying around, you could go out to a casino now and make 100 with 99.8% certainty. But, obviously, it's probably not worth it.
What I toyed with was the possibility of playing a game where you could bet on odds well over 50% at increasingly reduced gains. In such a scenario, the exponential decay is extremely rapid, so you can start off with much larger initial bets while needing a smaller bankroll to get those same odds. Unfortunately roulette does not work that way.
For the detractors... of COURSE roulette has a negative expected value. Hell, it probably has the worst expected value in a casino. That does not mean that the above will "eventually fail to work". It absolutely works; it just is not particularly feasible.