Multi-tableing vs buy in requirements
When you're discussing bankroll management of say 20 buy-ins, are you referring to one (1) table. For example if I play 2 tables of 25NL, do I need a 20 buy-ins for each table, or 20 buy-ins for the two tables, thanks.
Regarding bankroll management, I have seen others recommend 20 buy-ins for one table of play, stating you should never have more than 5% of your bankroll in place at once. I disagree with that at the micro stakes, where win rates tend to be higher; moreover, you'll see how stop gaps play a major role in bankroll management below.
My recommendation is 20-40 buy-ins at the micro stakes regardless of if you're single tabling or multi-tabling; however, you have to use common sense and stop gaps as well. I multi-table up to 4 tables at once and having this amount of buy-ins hasn't been an issue for me; however, if you were mass tabling 16 tables, then you would definitely need a much larger bankroll.
Also you need to have stop gaps in place for each session. For example, "If I lose 3 buy-ins in this session, I will quit this session." Having a stop-gap in place is essential regardless if you're multi-tabling or single tabling because it reduces your risk of ruin of going broke. With a session stop gap in place, you'll effectively just be playing more hands per an hour multi-tabling versus single tabling if you always allow yourself to lose "x" amount of your bankroll before you force yourself to quit your session.
You also need to move down in stakes if your bankroll gets too small. For example, "If I fall below 15 buy-ins I will drop down in stakes until I reach 20 buy-ins."
Theoretically, you can go on a 20-40 buy-in downswing over a large sample of hands if you utilize variance calculators.
One last thing, if I am starting with 20 buy-ins, especially moving up in stakes, I'll play more conservative small-ball poker until I build up a larger bankroll so variance is smaller and I reduce the likelihood of having to move down in stakes.
But, all-in-all, what you choose is up to you and based upon how much the monetary amount of money means to you as well as your risk tolerance. If you are risk adverse, you'll want a bigger bankroll (40+ buy-ins), whereas if you're aren't then a smaller one is fine.
Hope this helps.