In a hexagram produced by the traditional yarrow method, the probabilities from highest to lowest are:

static yin = 424399 / 939120 =~ 45%
static yang = 4051193 / 14556360 =~ 28%
moving yang = 5957 / 26832 =~ 22%
moving yin = 77 / 1612 =~5%

(Of course these "probabilities" assume the I Ching operates randomly through the yarrow stalks. The truth as we both know is it's a sentient oracle.)

I seem to recall you reviewed the math behind those numbers at one time. It was also independently reviewed by others at the request of Dick Kaser before he used some of my work as partial basis for his book I Ching in Ten Minutes.

Some interesting observations on the numbers (you may think of others; wanna co-author a scholarly paper?). For instance, the probability of a yin versus yang line in the initial hexagram (forget whether it's moving or not) is close to 50-50:

yin = 14546989 / 29112720 =~ .4997
yang = 14565761 / 29112720 =~ .5003

So just a tiny (almost imperceptible) yang bias in the initial hexagram. But look what happens after the moving lines change polarity! In the second hexagram of a reading, a huge yin bias emerges:

yin = 19619714 / 29112720 =~ .6739
yang = 9493006 / 29112720 =~ .3261

Not sure what this "means".

Another application is you can pigeonhole all 64 hexagrams into 7 probability sets, Yn where 0 <= n <= 6 is the number of Yang lines in a hexagram. Then for each set Yn, let y(n) be the frequency at which any one of its member hexagrams would occur if the yarrow method were random:

Y0 = {hx. 64}, y(0) =~ .0155647
Y1 = {hx. 58 thru 63}, y(1) =~ .0155848
Y2 = {hx. 43 thru 47}, y(2) =~ .0156049
Y3 = {hx. 22 thru 42}, y(3) =~ .0156251
Y4 = {hx. 8 thru 22}, y(4) =~ .0156451
Y5 = {hx. 2 thru 7}, y(5) =~ .0156653
Y6 = {hx 1}, y(6) =~ 0156855

So not only are the hexagrams ordered from fewest to most yang lines, but in the classic order they fall neatly into 7 sequential sets whose frequencies graph an almost perfect bell curve. (The 20 hexagrams of Y3 are the largest set and have the highest probability.)