RobertJasiek wrote:
Bill, I know too little about history of research in using counts and move values for evaluating gote and sente after Sakauchi Jun Ei and until 2016. CGT (and Mathematical Go Endgames) studies a lot but, AFAIK, not in terms of count and move value, as go players use them: unchilled, without infinitesimals. Has everything in between been your invention? I wonder because everything I read had been written by you: comparing counts or move values, gains, distinguishing types, conditions for move order in environments etc. What of that has been your invention and what has been invented by others (whom)?
Among the first go books I bought were Sakata's
Killer of Go series and Takagawa's
Go Reader series. One of the Sakata books deals with tsumego and yose, one of the Takagawa books is about the yose. Both mention miai counting, but Sakata regards it as useful only in special cases. Takagawa is clearer, and simply mentions both deiri and miai counting. Both authors, however, start with finding the count. Neither mention the problems with double sente.
My own efforts were mainly based upon my understanding of Takagawa. Most go books start out with assuming that a play is a double gote (sic!), a one-way sente (sic!), or a double sente (sick!
), and make the calculations accordingly. On my own I discovered that if you start out assuming that all plays were simple gote, you could derive a contradiction when the value of the opponent's reply was larger than the assumed value of the supposed gote. Then you got a sequence of plays that was sente or gote depending upon when the size of the plays dropped below that of the original play. With this method I was able to get all the temperatures and mean values of non-ko thermography, a few years before thermography was invented. I don't know whether I improved on Takagawa or not, since I had donated the
Go Reader set to the Yale library before I concentrated on yose calculation. It took me a few years before I abandoned the idea of local double sente. I had never actually calculated one, only assuming that plays that had humungous follow-ups for both players were double sente. But I managed to prove, to my satisfaction, that they did not exist. (Before 1976.) I even sent an article to the Go World saying that they did not exist, but Bozulich did not bite.
I developed my own theory of ko evaluation, but it is not very practical. You have to know too much to apply it, as a rule. I touch on it at the start of
This 'n' That. It is at the root of the CGT idea of
komonster, and my classification of types of ko threats, and the idea of the ko ensemble.
After studying CGT I came up with the idea of ambiguous plays. I also discovered how to evaluate multiple kos and superkos, in 1998. And a few years later I discovered the relation between simple approach kos and Fibonacci numbers (Edit: in a neutral threat environment). (Edit: Earlier I had regarded approach kos as a kind of sente. In an environment with sparse ko threats, that might be more accurate.
For instance, the proverb says that a three move approach ko is no ko at all. In an NTE, it is worth 1/13 of the swing, which is often worth fighting. As a sente, it is worth 1/24 of the swing, which is closer to 0.)
Talking about how much a play gains, on average, is just another way of talking about miai values. Less scary and unfamiliar, I think. Colored thermographs add a bit of clarity. They make it easy to describe
privilege, for instance.
I owe a lot to Takagawa's clarity. I doubt if I would have gotten very far on my own without that. Like most players, I probably would have remained mired in deiri values, deciding between sente and gote by the seat of my pants.