thanks simi - i was looking for that
The thing about blackjack, and statistics in general, is that there is usually isn't ever a 'sure' thing. There's pretty sure, and pretty surer. Even stuff outside the 3SD margin that's commonly used can happen and will happen.
Breaking even is one exact slice of the distribution. The win rate isn't suppose to tell you what will happen, but what will happen on average--it is the mean win rate of the distribution (everything that can possibly happen). Winning twice the win rate, or a dollar more or less, doesn't invalidate the win rate because the number was never meant to apply to an instance, but to the group as a whole.
The Law of Large numbers does say that as the number of samples approaches infinity that the average of your variable will approach expectation (the theoretical average). That approach can happen many ways though, but the more you play, the more likely you'll be close to expectation.
I'm a bit new to N0 myself, but from what I understand, it has nothing to do with bankroll size. It's just EV and SD. How likely you are to get to N0 in the first place seems to be affected by bankroll size though.
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