In multi-table play, you will experience greater bankroll swings than playing at one table. There are much more hands played per hour and at times, you will lose at all tables, and at times you will win at all tables. You must prepare yourself to handle these swings. If winning is important to you, only play at multiple tables if you are already a winning player. Otherwise, you will just be increasing your losses.
There are some experts who caution players from playing at multiple tables because edge will decrease too much and that it is not worth playing multiple tables. They argue that you will lose a lot of edge by not giving your full attention and will lose money as a result. For experienced players this is misleading. Indeed, they are right that you lose out a certain edge per table, just as losing players will typically lose more money by playing at more tables.
However, there are three reasons why winning players will normally benefit from going up to multiple table play. Firstly, the total win-rate will be higher on an hourly basis, even if the winnings per table, per hour, are lower. Secondly, the swings increases when going from one table to two, but when adding more tables the swings actually decreases. (See next paragraph for further details.) Thirdly, playing at one table will eventually test the patience and many players have a hard time focusing, but playing multiple tables will keep their focus on the game.
By using standard risk formulas, it can be proved that playing at more than two tables does not increase volatility, rather it reduces it. For example, playing at four $5-$10 tables simultaneously yields a lower bankroll swing than playing at two tables. Hence, playing four tables at $5-$10 will give you a lower total volatility than playing at one $10-$20 table. This follows the simple logic that asset management is built upon: by having more assets with no or low correlation in their returns, you will maximize your overall return at a certain accepted level of risk exposure (volatility).
Hence, the best formula for many semi-professional players is to choose the limit where they have the highest hourly win-rate in absolute terms (such as $20 per hour, per table, on average), but not exceeding the limit their bankroll is suited for. For example, a player with a $5,000 bankroll should not play higher than $5-$10 in fixed limit Texas Hold'em at four tables simultaneously, as that bankroll would be equal to 500 times the big bet. If 300 times the big bet is reasonable at one table play, you will need to increase that number by about 50% for multiple table play, in order to handle the larger short-term fluctuations.
Remember that most players lack sufficient empirical data on their successes at higher limits. As a rule of thumb, you should play at least 200 hours at one limit to be able to draw any firm conclusions about your abilities at that limit. And, remember that your results are highly dependent on what type of opposition you face.
Most players do better while playing at the same type of table and limit at all simultaneous tables (for instance, at four full ring $5-$10 tables), whereas some short-handed specialists prefer to have one or two tables of multi-table tournaments open on the side, where they will only play maybe 10% of the hands in the first 2 hours without having to analyze too much. This way, they can pay full attention to the very demanding short-handed or heads-up games they are playing, but still work their way into the tournaments.