system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why can’t people go to the casino playing roulette and bet on black, and if they lose, double what they lost and bet on black again until they win?

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.
gpt
You're right, your odds of loosing 6 consecutive plays at roulette playing black are slim. Yes. But to get to that point you'll have had to lose 5 consecutive plays, which would require you to have bet $100, then $200, then $400, then $800, then $1,600 for a total of $3,100. Then still have $3,200 left over to bet the sixth time.

This strategy is known as the martingale strategy and only works if you have an infinite bankroll, which you don't.

EDIT: And you'd by stymied by the table limit, too.

EDIT2: Some elaboration on the Martingale Strategy based on some comments.

1. Given an infinite bankroll and no table limit, it *is* a valid strategy that is guaranteed to win. What prevents it from being implemented in real life is the lack of an infinite bankroll and the existence of table limits.
2. It does *not* rely on the gambler's fallacy. It doesn't assume that the odds of any given play changes, but rather exploits the fact that any non-zero chance of winning becomes a guarantee on an infinite time line. At some point, you *will* win. And, when you do, your bets are structured as to cover all previous losses plus profit.
3. It doesn't care about the odds of winning. OP already notes the odds are less than 50/50 (because of the zeros on the wheel). But the odds of winning don't impact the validity of Martingale, they just alter how long on average you might have to play to realize that guaranteed win. What *does* affect Martingale is the payout structure. For roulette, the odds are less than 50/50 but the payout *is* 50/50 (e.g. you win what you bet). This is why Martingale says to double. If the payout structure was different, you're subsequent bets would be different (better payouts mean smaller increases, worse payouts mean larger increases).