Probability of obtaining a high true count

As an experienced BJ counter, I can definitely attest to having a noticeable and remarkable edge with true counts exceeding ~3 or 4 -- and I am happy to make bets as large as 5-7x the base bet in those instances, even if I know (and accept) that I may not win every hand despite the high count.

However, I've also experienced BJ sessions during which it takes a very long time -- 3-4 hours -- of very boring min-bet play before the shoe starts getting interesting with a high count. So my question is: for a randomly shuffled 6-deck shoe, what is the probability that the true count will, at some point exceed 2,3,4 ... ? Is it the same as the probability that it will be less than -2,-3,-4/etc? What about the probability that it will just sit and hover around 0? Thanks!

Off the top of my head I believe I recall that true count of +3 appears roughly 10% of the time.

So in a given average hour you might expect about six minutes.

Typing this from my phone however so I'm sure others may chime in here with more specific references and/or data proof, my recollection may be flawed...

-DBJT

http://blackjackincolor.com/truecount1.htm