From my Bankroll thread:

Quote Originally Posted by I
To determine how long it will take for your average win to be 1 standard deviation, divide the square of your standard deviation for 1 hour by the square of your hourly rate.

hours to be ahead 84% of the time = (sigma/ev)^2.
*84% = the 68% of the time you will be +/- 1SD and the 16% you will be up more than 1SD.

This is one way to define the "long run". To find out how long it will take for your hourly rate to equal let's say 1.6 standard deviations, this is simply

hours to at least break even 95% of the time = (1.6*sigma/ev)^2.

At this point you have a 95% probability of being ahead.
To simplify the math lets assume a player with a winrate of 2BB/100hands and a Standard Deviation of 20BB/100hands

to have a 95% confidence of being ahead:
(1.6*20/2)^2 * 100 hands = 25,600 hands

now "ahead" doesn't mean at your true win rate... it just means >$0.