Risk of ruin when central limit theorem hasn't kicked in

[Izverg04]

I want to be able to calculate risk of ruin for non-normally distributed results.

The best example where I need this is calculating bankroll in video poker with positive expectation. If the return is reasonably large, let's say >1%, then the number of hands N over which we expect the largest negative swings is not yet large compared to 40,000, the average number of hands to get to the jackpot, thus the central limit theorem does not yet apply.

After searching this forum thoroughly, the best source I found is this article referenced by BruceZ in an old thread.

I understand the abstract, that they calculate the bounds on the risk of ruin using the first 4 moments of result probability distribution, but I get so lost thereafter that I can't even find the answer. If anyone is able to translate their results to me, I would really, really apreciate it. I understand that this is a fairly advanced question, but reading this forum give me hope that there are a few top-notch experts here.