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Yes that is true... if you end at a "random" point (running out of money for example). But if you can always end at a win (particularly a large one after a string of many losses) then that changes things, the odds become much less relevant because you are manipulating them.*
The problem is that consistently doing so would require genuinely unlimited money and no betting limits, since the number of losses-that-can-happen-in-a-row is itself unlimited. With that little detail the Martingale system would actually work.
Then again if you have unlimited money then why bother to gamble?
*(Actually I sorta take back my first comment in this thread, the odds aren't why to triple, just growing the pot faster each win is)