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The usual recommendation is 300BB for limit hold'em game. If I'm 2-tabling, should I have 600BB?
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Your bankroll requirement for a given risk of ruin does not change when you multi-table as long as the quality of your play does not degrade, so that you have the same win rate and standard deviation on each table.
Also, 300 BB is a dumbed down rule of thumb for the mathematically illiterate, not for professors of chemistry, and it does not always apply. Use
these formulas to compute your bankroll requirement and risk of ruin.
Here is a recent post about multi-tabling.
Here is an old post with a theoretical discussion of multi-tabling bankroll requirements that you might find useful.