An In-Depth Question About Bankroll Management

[AndrewtheBold]

I've been looking for a definitive answer on bankroll requirements and I have yet to find one. Typically, if you ask someone what kind of bankroll one needs to play limit hold'em, 300 big bets is the answer and the justification is that a winning player should not expect a losing streak of more than 300 BB.

Let's say that I have $3000 and I am ready to go play 5/10. Suppose I lose $300 and tomorrow I go looking for a game with my $2700. I am just as likely to go on a -300 BB streak, so in theory, I should not play 5/10. Therefore I must need far more than 300 BB to play.

On the other hand, lets say I'm willing to switch limits if I drop below 300 BB. Suppose my cardroom offers 1/2, 2/4, 3/6, 4/8, and 5/10. If I am no more likely to lose 300 BB at any one limit, then I could "spread" my bankroll, intending to switch limits whenever necessary. If I intended to maintain a 300 BB bankroll, it could be composed of 60 BB from each of the 5 limits, and thus I could play 5/10 with anything over 1800 (i.e. 180 BB).

With either of these models, it seems that a sort of "catch-22" can occur. On the one hand, I should not expect a losing streak of no more than 300 BB. On the other hand, at any given time (no matter how much I have already lost) a 300 BB losing streak is still possible, and thus I should quit playing long before I lose 300 BB. That means that my bankroll cannot sustain actually a 300 BB swing unless I have well over 300 BB.

Can anyone offer any thoughts on this matter?