[AlanBostick]

Read Gambling Theory and Other Topics by Mason Malmuth, particularly the section titled "How Much Do You Need?"

Mason doesn't give this formula outright but if you know a bit of algebra you can pull it out of what he wrote. If S is your hourly standard deviation -- the square root of the variance your play records show you experience in one hour's play -- and W is how much you expect to win in one hour's play, then the minimum bankroll you need to play with negligible risk of going broke is:

BR = 9/4 * S*S/W

Typical values for W are in the range of 1-2BB and a typical value for S would be 10. This results with a bankroll requirement of but 225 BB for a win rate of 1 BB/hour and only 113 BB for a win rate of 2 BB/hour.

Mason warns of "non-self-weighting" effects of running bad (when your cards are cold, he says, your opponents notice you losing and take shots at you, so your win rate ) and reccomends increasing this by a margin of safety 20 to 30%. The 300 BB number I often see presumably includes a 50% margin of safety, and Mark Blade's 400 BB number is a 100% margin of safety.

1. Multitabling should increase your win rate by a factor of the number of tables you play, and it should increase your standard deviation by the square root of the number of tables. If your hourly win at one table is W and your hourly standard deviation is S, then your hourly win playing four tables should be 4*W and your hourly standard deviation should be 2*W. Interestingly enough, in the bankroll formula I give above, those factors cancel, and the bankroll requirement stays the same. (This makes sense, because playing four tables at once for one hour is the equivalent of playing one table for four hours.)

2. It's not unreasonable; but I personally would track each table as a separate session.

3. The uncertainty of your win rate -- the likely difference between your actual results and your "true" win rate, is given by U = S/sqrt(T), where T is the total number of hours of play that you've recorded. To trust your results, you want U to be small compared to W. With W ~ 1 and S ~ 10, after a hundred hours, U ~ 1, the same size as W, and there's about 1 chance in 6 that we're actually a losing player. After 900 hours, U ~ 1/3, and so we are rather more confident about the value of W.

4. Typical hourly standard deviations, as I've said, are in the neighborhood of 10 BB.

5. See the start of this message.

6. As I've said, Gambling Theory and Other Topics by Mason Malmuth.