Life In 19x19http://lifein19x19.com/ Numerical evaluation theory of thicknesshttp://lifein19x19.com/viewtopic.php?f=15&t=18732 Page 2 of 2

 Author: dhu163 [ Thu Aug 11, 2022 12:10 pm ] Post subject: Re: Numerical evaluation theory of thickness What concepts are derivable from this sort of theory that isn't covered by sente/gote etc. ?Well, shielding is certainly one. Aji too (though the theory isn't strong enough to estimate it well, only informally tell you principles). Weak points as a key source of value of moves that gets split up as more moves are played. Each move is like splitting the area around into more independent endgames. If you take a vital point of life, it may be difficult for the opponent to make eyes in each independent region, so you may be "winning" in each, and profit arises from this.My better guesses for komi tune to the known k=7 for d=2. So suppose it takes d+1 moves to capture the corner.Perhaps m+n=(6d-4)/(4d-2). And m-n= 1-2*(-d-1)I think this m-n value is the closest I've come to JF's units of thickness/atsuiThenk=[4d-2 + d(6d-4)errf( (1-2*(-d-1)/(4-2/(2d-1))]/2Which predictsd=1k=1.5note that this is unreliable as (4d-2),(6d-4) break down for d<2. However, the answer does seem reasonable as any stone you place on the board that has 2 liberties lives.d=2k=7d=3k=15.7d=4k=27.8what goes wrong for the complete graph? well, the smallest group size, (4d-2) increases with degree and the number of neighbours, and it is larger than the whole board, so we can no longer talk about the "influence" such a group has on (6d-4) etc. because that is outside the board and so on.This tends to something a bit more than(3d^2+2d-2)/2which has roots at (-1 +/- sqrt(7))/3 . not quite golden ratio.Funny that d=0 gives k=-1 . There is only one intersection and play there is suicide.__next day: what?? please tell me this is a joke.7th letter of the English alphabet: G, 15th: O.