From what I recall reading, 300 big bets is the standard minimum bankroll for limit poker games. Of course, if you play games where 4 raises are possible (most sites cap it at a bet and 3 raises) or something like that, you might consider having a slightly larger bankroll.
I also think there is nothing wrong with playing below your bankroll. So if you want to play $0.50/$1.00 with a $12,000 bankroll... that's fine. But normally, $300 should be enough to handle the swings.
I forget where I originally read this but I believe it was discussed on another forum where they were talking about "Risk of Ruin" and assumed an average 'winning' limit player.
If you are a losing player, no bankroll will be large enough to avoid going broke eventually. But if you're break-even or a winning player, 300xBB should be fine. More is always better.
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