[BruceZ]

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This "question" is really two seperate questions:

1) What is the standard deviation for a typical winning limit hold-em player at middle limits? I have heard 10, 15 and 20 BB, so would anyone like to clarify?

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It depends on whether you're talking per hour or per 100 hands. When playing live, the benchmark has been 10 times your win rate per hour, so a win rate of 1 bb/hr would correspond to a SD of 10 bb. For 100 hands, this would correspond to a win rate of about 3 bb/100, and a SD of 17 bb, hence you might see SD values of 15-20 bb for 100 hands. It may be significantly higher if you are playing shorthanded, or in very aggressive games.


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2) Thinking back to my statistics classes I remembered this line, "The variance/mean of a sum of independent random variables is the sum of the individual variances/means." Now my question: would this theorem apply to multi-tabling? To elaborate, say I have a u=1/hr (mean) and a var=225/hr per table, and consequently a std. dev.=15/hr. Does that imply that two-tabling I would have a u=2/hr, var=450/hr, and std. dev.=21.21/hr? Thanks all.

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Correct. Note that by playing 2 tables at half the limit, you can reduce your standard deviation per hour without reducing your win rate, and hence greatly reduce your risk of ruin for a given bankroll, or cut your bankroll requirement in half for a given risk of ruin. This assumes that you can make the same number of bb/hr at each table at the lower limit as you did at the higher limit.