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In limit poker, you should expect to see convergence after a few hundred hands. If after a few hundred hands or maybe 1000 hands, your losing at a limit table, its because your behind in skill not luck.



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AAAAAAAAAHAHAHAHAHAHAHAHAHAHAH!!!!!!!!!! Man, for a second there I thought you were serious.



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The mean value of a random poker hand, excluding skill factor, is zero (or slightly negative if you include rake). Poker is a zero sum game, thus excluding skill, the EV over a series of hands will also be zero.

Thus, we know the expected mean of any series of poker hands. Variance is measured by distance from the mean. Say you play $1/2 limit poker, the average win or loss is about $13. Its rare to have outliers beyond $20 or so.

Given that distance from the mean is bounded, variance is bounded, and should converge fairly rapidly. If necessary I can calculate it more precisely than my original guesstimate, but unless your going to spend some time crunching numbers to prove that my guesstimate is far too low or provide a more accurate assessment (thereby enlightening all of us), i'm not going to waste the time.