sooooo....unless you plan on playing for a REALLLLLLLLY long time, you needn't worry about quite so much about busting out as long as you are playing a winning game.
It's just the opposite. If you go broke, it will happen relatively early. Once you've survived a long time, your bankroll will have increased to the point where the risk of going broke becomes negligible.
if you bet an infinite number of times then this should account for ALL possibilities. this would include the extremely unlikely possibility that you will lose 1-billion bets in a row. obviously, the odds of this happening are ridiculously remote, however it needs to be remembered that infinity is pretty damn big.
It is true that you will eventually have negative swings as large as you please, but this does not mean that you will go broke. What is important is how rapidly your bankroll increases relative to these swings. If you are playing a winning game, you can make your risk of going broke as small as you like with a finite bankroll. See the
bankroll formulas in this thread.