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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Because your resources are limited (or because the casino has a limit on bet sizes), with that strategy you will have a large chance of a small gain–BUT also a small chance of a large loss.
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