Non-randomness of BJ "sampling" ???

From Stanford Wong's BJ21

Posted by MathProf on 15 Dec 1997, at 5:22 p.m., in response to Re: variance of shoe, posted by Don Schlesinger on 15 Dec 1997, at 9:35 a.m.

Just to add some clarification to my remarks. The formula I gave for the "Variance of a Shoe" above, was actually not the Varaince of a BJ Shoe. I was addessing the problem: if you randomly cut off the last part of a Shoe, and measured its True Count, what would the variance be. The formula I listed gives expresses that variance in terms of the Number of Cards in that Remainder.

I also stated that the TC would be symmetrical about 0. (I am assumming that if your rounding, that you do it in a symmetrical manner).

Now BJ is not random. (No I am a Patterson disciple) While the distribution of cards in the pack may be random, where a dound ends is determined by the hitting and standing behavior of the players involved. Which is what I beleive Don was alluding to when he said

Actually, this statement is not exactly true. For any given absolute value of count, the frequency of the
negative TC will be somewhat higher than the frequency of the corresponding positive TC. This is a well-known fact, although the magnitude of the differences is not very important.

The same comment, that what I have said is note exactly true, whill also apply to the Variance formula above. Indeed, I am not sure that tehre is an closed formula for the Varaiance of an actual BJ SHoe. However what I have said will give you a good idea of what is going on.
If I am misinterpretting Don's remarks, then I hope he will correct me.