The answer to this question is not-as simple as the one above. For instance, you may think of your bankroll as a completely separate financial entity that may be added to or removed from only at the poker table. If this is your view, then Mason Malmuth's research suggests you need about 300 big bets ($1800 for a $3-6 player) to ride out the inevitable downward swings.2
2If, of course, you're a winning player. If you're a losing player, no bankroll is big enough.
However, many people don't separate it out. If they have a few extra dollars, they might go play some poker. If they win, fine. If they lose, that's okay too. If that's how you prefer to manage your money, then you don't need a particular bankroll size - you simply replenish it (or withdraw from it) as you see fit.
By the way, I find the former approach (a separate bucket labeled "poker bankroll") to be an excellent disciplinary tool. Even if your financial circumstances permit you to add to the bankroll, it's healthy to monitor its growth (and shrinking), and keeping it separate will make that possible. It also attenuates the emotional swings associated with wins and losses. If you don't view a win as, "Oh boy, a new stereo!" or a loss as, "Oh dear, what of the rent?" then you'll play a better poker game all around.
I should note that I have many friends who have parlayed very small bankrolls in the $2-4 and $3-6 games into five-figure bankrolls with which they're playing serious mid-limit poker. This is not easy, and demands time, work, and a little luck. But if you start out with a reasonable bankroll for your low limit game (so you don't go busted when you lose a few times) then you, too, can do it.
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