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This is the Martingale system, it will 100% work if you have infinite money and can bet infinite amounts.
It won’t work on any table that has a 0 and/or 00. The reason those green numbers exist is to give the house an edge over high rollers who can sustain a martingale strategy.
It works even with 0 and 00 - but only if you have infinite money and there is no limit to bets. So long as there is finite money, or limited bets you will - statistically - hit a run of losses that exceeds your money.
Maximum bets and the fact that money is limited is what breaks this, once you hit the maximum bet odds are slightly against you winning on that next turn because of the 0 and 00; and so eventually you will lose as you hit running up to the max bet and then lose on that turn.
Lol this is irrelevant
Me: "bets 1 infinity dollars"
Loses
Me: "bets 3 infinities of dollars"
You can't have an infinite amount since past a certain mass it will collapse onto itself and create a black hole. (or other practical limits) So eventually you lose anyway.
I thought this was a pretty good in-depth explanation of the infinite case and the finite case: https://www.youtube.com/watch?v=zTsRGQj6VT4