So these Markov deviation rates.

The coin tosses.

There is some binomial of (1/m + (m-1)/m = one, and m is dimensionsality.

And the Markov condition is a condition on the second term when the coin tosses equatiop, the current rate or Markov number.  The left side can be seen as a matching between three binomials with unfair coins, with only the second term considered.  The completed right side must also be a binomial, the best match to the three binomials on the left, emphasizing only the second term.  So all these coin tosses quickly trail off to terms greater than K+1, in which the matching cannot get more accurate, we should hit the Hurwitx finite limit. The deviation counts consists of two groups, the terms allowed (pit boss error, mainly) , the the terms corrected (adjust your bet). This must be the Boltzmann process, the path merging.  It is about matching the first three moments of the right side with the weighted sum of three binomial terms on the left.