Fun little paper on the Gambler's ruin problem that you can play around with: http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GR.pdf

Of course these equations need some modification to take into account the varying max bet size, but I figure there's only a 0.9% chance of someone with a bankroll equal to the house's winning 90% of the bankroll before losing 90% of his bankroll at a 1% max bet and 2x payout.