Great! I was fearing you were in the gambler's fallacy :-)
May I ask you why you are so interested in the busting probability of funny martingales?
You can ask, but I don't know what to tell you.
I'm interested in mathematics, and this seems like it should have a neat solution.
I don't know that you can call it a "martingale" by the way, since it doesn't reset on a win.