If you have a large enough bank roll and continuously double your bet after a loss, you can never lose without a table limit.
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.
Imagine you were asked to start speaking a new language, eg Chinese. Your brain happens to work quite differently to the rest of us. You have immense capabilities for memorization and computation but not much else. You can’t really learn Chinese with this kind of mind, but you have an idea that plays right into your strengths. You will listen to millions of conversations by real Chinese speakers and mimic their patterns. You make notes like “when one person says A, the most common response by the other person is B”, or “most often after someone says X, they follow it up with Y”. So you go into conversations with Chinese speakers and just perform these patterns. It’s all just sounds to you. You don’t recognize words and you can’t even tell from context what’s happening. If you do that well enough you are technically speaking Chinese but you will never have any intent or understanding behind what you say. That’s basically LLMs.