A slightly unusual Risk-Of-Ruin question

[NoSoup4U]

Over at another forum, a few of us have embarked on what we call a "silly quest." The rules of this quest are that you have to sit down at the lowest limit at a particular site with 20BBs and play that lmit until you either go broke or win enough to move up to the next limit with 20BBs. You then play with the same rules at that limit until you go broke or move up again. You can never drop limits or add money.

The question we have is how to calculate the risk of ruin over multiple levels of this quest. Let's pretend that the hero is very good and wins 3 bb/100 with an 18 sd/100. How about if he is 2 bb/100?

The Party version of this quest has 7 stages: .5/1, 1/2, 2/4, 3/6, 5/10, 10/20, 15/30. If one of you clever math guys can teach me how it works, I can translate to attempts with more levels.

We're ignoring the fact that the true winrate probably drops at higher levels. Our feeble attempts to calculate the RoR are resulting in extremely high numbers and I'd love for one you gurus to set me on the path to enlightenment.