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All your math above is irrelevant and your last paragraph is completely wrong. Table limits are the reason this strategy won't work...
If you have a large enough bank roll and continuously double your bet after a loss, you can never lose without a table limit.
Source: data analyst.
Unless your bank roll is infinite, you always lose in the average case. My math was just an example to show the point with concrete numbers.
In truth it is trivial to prove that there is no winning strategy in roulette. If a strategy is just a series of bets, then the expected value is the sum of the expected value of the bets. Every bet in roulette has a negative expected value. Therefore, every strategy has a negative expected value as well. I'm not saying anything ground-breaking, you can read a better write-up of this idea in the wikipedia article.
If you don't think that's true, you are welcome to show your math which proves a positive expected value. Otherwise, saying I'm "completely wrong" means nothing.
This is just factually incorrect. Losing is always an option, even if you have a billion dollars so you can double your bet ~30 times, you could still lose the weighted coin toss 30 times. On top of that, all the money that's ever existed still only gets you like 50 spins on the roulette table, exponential growth is a bitch. OPs strategy of tripling their bet only goes for about 13 rounds before OP is slinging around a million dollars. Even if they just won the lottery, round 19 puts them out a cool billion.
Also this strategy is foolish in so many ways because you're just playing to hopefully break even, and like everything in a casino, the odds of you breaking even before running out of cash ALWAYS favors the house.
Source: Statistics.
Data scientist who does not know that 18/37 means you lose.