If you bet $100, your odds of winning are around 50% and if you lose, bet $200, and so on and so forth until you win, and then cash out with a guaranteed profit. Assuming odds of black are 47.37% as per American roulette, your odds of not winning a single one after 6 tries are 0.02125 (I think) and decrease exponentially after each subsequent try.
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To expand on /u/EastNine ‘s point — the expected (average) profit from multiple bets is the sum of the expected profits of the individual bets. The expected profit making a bet on roulette is always negative — unless you possess some physics hack that boosts your winning probability, which famously has happened on rare occasions, but the main consequence is tricking suckers into losing money trying to replicate the achievement.
No matter what complicated formula you use to decide how much to wager, you cannot obtain a positive average return through a series of bets whose individual expected returns are all negative, which is the case for every bet at a fair roulette wheel. If you understand this more general rule, you will also avoid falling for a thousand other broken betting strategies that try to turn a series of bad bets into a good outcome. Complicated betting schemes to turn profit on a series of bad bets are just like perpetual motion machines that try to create new mass-energy or predictably reduce entropy. The most reliable way to evaluate such a system isn’t to bog yourself down in the details and very possibly miscalculate (“Wow, it works!”) Your best shot is understanding that the claim being made is fundamentally impossible, and refusing to get roped in.
You might make a profit on a series of mostly money-losing bets, so long as at least a few of the bets are actually good bets, and you bet more when the odds are good. Betting big when there are many face cards in a blackjack deck famously can be a legitimately profitable strategy, which is why you have little chance of finding a casino that will let you pull it off.
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