In the game here, White should have played 52 at A. It is impossible to say exactly what that move is worth, but pros seem to agree it is worth more than 18 points.
Ishida Yoshio wrote a book on this topic. It was called "Kono te, nanmoku" (How much is this move worth?) [Nihon Bungei-sha, 1992, ISBN 4-537-01563-2]. Interestingly it was sub-titled "Breaking the 3-dan barrier."
Ishida was writing when komi was 5.5 points, so perhaps some readjustment is needed. Nevertheless, he started with the assumption that any move in the very early opening was worth 20 points. As positions formed some shorter extensions dropped in value to maybe 17 points. But big points and urgent points, as they emerged, took on greater value. As a rule of thumb he treated big points as worth 20 and urgent points as 25.
It seems pretty obvious that Ishida (The "Computer") would have played A.
We realise that we finger-counters at GoGoD are playing with fire here, with so many mathematicians out there. If we have misrepresented the arguments, it's our fault. But we still have no doubt that the various articles and books mentioned are worth buying.
If you want something below the 3-dan level, there seems to be nothing in English beyond Sensei's Library that discusses counting in the full pro deiri, miai way, but a good basic primer in Japanese and Korean exists by Yi Ch'ang-ho. The Japanese edition, "Watashi no Keisei Handan" (How I count) is ISBN 4-416-79948-9 (Seibundo, 2000), and you may need to know his name is I Chanho in Japanese.
This useful follow-up came from Bill Spight on rec.games.go:
Thanks for the interesting article. :-)
However, Satoshi's article is not the latest word on ko evaluation. Professor Berlekamp pointed out in "Games of No Chance" several years ago that kos like approach kos cannot be evaluated without regard to the ko threat situation. Satoshi's suggested divisor for a one-move approach ko of 4 is appropriate in only certain situations, when one player is komaster.
A more realistic rule of thumb, when the expectation is that there will be an exchange for the ko and that neither player has a clear advantage, is to divide by 5 for a one-move approach ko, by 8 for a two-move approach ko, by 13 for a three-move approach ko, etc. (It's a Fibonacci sequence! ;-)) You can see my slides from my 2002 talk on this topic at http://hometown.aol.com/billspight/myhomepage/NTE.htm .
There is a proverb that says that a three-move approach ko is no ko. That is more in line with a divisor of 13 than with a divisor of 6.
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