This may not be exactly what you want, but I think it will go a long way toward answering your question.

The Variance (and standard deviation) of the True Count at various levels is given by a relatively simple formula. If N is the number of cards in the pack, and R is the number remaining cards (so that N-R) is the number which has been dealt, the the variance of the running count is given by

Var (RC) = s * R*(N-R) / (N-1)

where s is a constant that depends on the count system you are using. For HiLo, s is 10/13.

You can get the SD or the RC by taking the square root of the formula given above.

Note that our formula is symmetric between R and N-R. That is, the distribution of running counts after 1 deck ash been dealt is the same as it distribution when only 1 deck remains. (Do you see why ? ) This is obviously NOT the case for true counts.

We get the Var of the TC by dividing by R^2, and get

Var(TC) = S/(N-1) * (N-R)/R

I put all the constant together out front. The function (N-R)/R increases as R gets small.

By the way, I think these are the per card True Counts. If you want per deck TCs (which is what most of us use), you need to put in a factor of 52.