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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Yes – that betting strategy will work fine as long as you have an infinite amount of money so that you can afford to keep going until you win.
Note that the odds of continuing a losing streak (e.g. continuing to land on red, if you’ve bet on black) don’t decrease exponentially, but instead stay exactly the same.
It’s like tossing a coin – even if you’ve had 100 “heads” in a row, the next toss it’s still 50/50 whether you get heads or tails since each toss (or spin of the roulette wheel) is independent of what came before. The coin doesn’t have any memory!
Long streaks of bad luck can happen quite regularly – was watching a Netflix documentary on a professional blackjack player (who have a slight advantage over the house) who was touring the states playing hours every day, and had a losing streak lasting for **months** … You better have a pretty large bankroll and disciplined betting strategy (better than I’ll keep doubling my bet) to stay solvent …
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