You do not need a bigger bankroll for playing four tables than for one table provided you play the exact same way. As someone noted, you're not moving to four times your original stakes; you're just making the hands happen four times faster.

In practice, we all play a little differently with more tables. I feel most people play better with two tables than one (less temptation to limp in on poor cards.) Moving to three and then four will probably impact your play in the other direction, though, until you get used to occasionally being on four hands at once.

Since the quality of your play will go down, you might be wise to keep a slightly bigger bankroll.

As well, your possible swing size per hour will increase. You'll often get the good tables matching bad table to minimize the change, but you have the potential for much bigger gains and losses in short periods of times. This takes tougher psychological stuff to handle. That's another good reason for a bigger bankroll; a $500 loss feel awful on a $1000 bankroll, while it's easy to stomache against $2500.

Lastly, you also need to remember the 300BB guideline is based on a providing a decent likelihood of not losing it all, assuming you are a good player. Are you really good enough?

If you're good enough, the 300BB bankroll gives a strong likelihood of not tapping out. It's not a guarantee. In fact, there's a significant chance of tapping out a 300BB bankroll. It's small, but possible.

Tapping out a $1/$2 bankroll is not a crusher. It can be replaced from other earnings (flip burgers for a month.) But if your game is $5/$10 and you've built a $5/$10 bankroll which is way more dispsable income than you put away in many months, you do NOT want your bankroll to tap out, ever.

So, how much is the right bankroll for you?

If you are really a good player and adjust well to the new game, you're just fine with 300BB. If you could replace the bankroll by trimming a few weeks of paychecks, then you can run a little more risky -- such as playing at levels where you're not yet sure of your relative skill level, such as 4-tabling.

On the other hand, if you've only played, say, 20,000 hands, then you don't really know your win rate. You're pretty sure you're a winner, but not by how much. Consider your entire bankroll at risk playing at 300BB. And if the bankroll is so big relative to your earnings that you can't replace it, stick with more than 300BB no matter how good your are.