Dan Mathematics
It is a common joke among Finnish players, that one's dan rating is a direct measure of his/her counting ability. That is, a shodan can count to one, 2-dan can count to two and so on.
Try it: listen to a dan player while his groups are involved in a complicated battle. If he goes "one-two-three-*duh*, one-two-three-*duh", you can be quite sure he is a 3-dan.
Of course, this would mean that kyu players cannot count at all, which is not too far from the truth. Extending from the above principle, you possibly could estimate a kyu rank by measuring how many mistakes happen between correct moves. This will sound like "*duh*-*duh*-*duh*-*duh*-one" for a 4 kyu.
Since this page is called Dan Mathematics, here's another:
We once had four player next to a computer, and were wondering what strength should we report to the go server.
The individual players' strengths were 3-dan, 1-kyu, 1-kyu and 2-kyu. So, just adding them up (3-dan being interpreted as -2 kyu, which produces the correct handicap) we got -2-kyu + 1-kyu + 1 kyu + 2kyu = 2 kyu.
The fun part is, when evaluating this same sum in "dan mathematics", the result is 3-dan + 0-dan + 0-dan + -1-dan = 2-dan.
So, clearly we were both 2-kyu and 2-dan at the same time..
No wonder the roman numerals caused the collapse of their empire.
--Bass
Actually, you forgot to average it. Since it was four people, the result would be .5 dan and .5 kyu, or exactly halfway between one kyu and one dan.
I thought if you were white you get an extra 5.5 (or whatever it is these days) komi. ~srn347