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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This strategy loses in the long run. If you only try it once, you might eventually get your money back, plus your initial bet. Not great winnings. But if you then keep playing to try to win more–winning just $100 at a time–eventually you will have a bad streak that will overrun your ability to continue the strategy.
This seems counterintuitive, I guess, at least it did to me when I was younger and coded a simulation in Commodore 64 to test exactly this strategy. And it was interesting to watch the money slowly go up for a time and then inevitably bottom out at nothing.
If you want to win in a casino, you should either get really good at poker or counting cards. You can’t out-probability any game.
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