[Darryl_P]

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If you play against either a finite number of players who have an infinite number of chips, or a potentially infinite number of players with a finite (or infinite) number of chips each, then you will eventually lose all your chips.

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This is simply not true. The only assumptions you need are the 3BB/100 advantage you have and the fact that you are at least an average player (something which IMO can be assumed from the way in which the question was posed).

That 3BB/100 advantage automatically limits the variance with which your opponents can play because there is a level above which your EV necessarily becomes higher with nothing more than average play.

This limiting variance will still be very small compared to your bankroll so you will still be able to define an amount like a million BB say which you will have a greater than 50% chance of doubling before losing. And here the random walk model applies and so the probability of EVER going broke is very small indeed.

The trouble with your reasoning is that whatever bad run you mention (say 1 trillion hands in row of quads over boat, which of course must happen eventually), the expected amount of money I will have grinded out from my 3BB/100 advantage will cover it more than enough trillion times for it to be a threat to my bankroll.

Of course such a run CAN happen before I've managed to grind out the cover for it but that has a probability of less than 0.0000000001% of happening, as shown by the random walk model.