The key words here are "significant advances". I don't dispute that Berlekamp's results are mathematically interesting. With respect to go as it is played in competitive circumstances, however, it is trivial. Many of Berlekamp's examples are quite complicated and would certainly be hard to solve without familiarity with his theory. On the other hand they are artificial and involve only the very last moves of the game. Furthermore, there are examples of players who have solved similar problems during a game with the clock running. Ishida Yoshio in the early 70s, who, while all the pros watching the game were convinced he would lose by half a point, went on to win by a half point. This game earned him the accolade of "the computer". This was a good 20 years before Berlekamp's theory. Professional players have always had an intuitive grasp of Berlekamp's techniques as evidenced by problems in the literature over the last 200 years or so. A professional player who studied Berlekamp's theory would not increase his strength one iota as a result of his efforts, since he understands this theory intuitively anyway.
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Richard Bozulich
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-----Original Message-----
Joe Shipman
The World's Strongest Go players vs. God; Grishkin; Chess
>Bozulich says
"In the middle game and endgame, the top players 300 years ago like Dosaku, Osenchi, Jowa, Shuwa, Shusaku, Gennan Inseki, Ota Yuzo, etc., were as good or perhaps better than (especially Dosaku and Shusaku, who made very few mistakes and were more consistent in their play, compared to today's top pros) the top pros of today. It is true that opening theory has advanced considerably since Dosaku, but middle game and endgame is pretty much the same."
but he is wrong -- significant advances in the theory of Go endgames were made in the late 20th century by Berlekamp and others using the general theory of games developed by Berlekamp, Conway, and Guy. (John Horton Conway is the genius who invented this theory, Elwyn R. Berlekamp and Richard K. Guy extended it to Go and other games. Conway is in my professional opinion the most original mathematician in the world.)
Joe Shipman
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kiseido wrote:
Mr. Shipman says I am wrong because " `significant advances' in the theory of Go endgames were made in the late 20th century by Berlekamp . . . " The key words here are "significant advances". I don't dispute that Berlekamp's results are mathematically interesting. With respect to go as it is played in competitive circumstances, however, it is trivial. Many of Berlekamp's examples are quite complicated and would certainly be hard to solve without familiarity with his theory. On the other hand they are artificial and involve only the very last moves of the game. Furthermore, there are examples of players who have solved similar problems during a game with the clock running. Ishida Yoshio in the early 70s, who, while all the pros watching the game were convinced he would lose by half a point, went on to win by a half point. This game earned him the accolade of "the computer". This was a good 20 years before Berlekamp's theory. Professional players have always had an intuitive grasp of Berlekamp's techniques as evidenced by problems in the literature over the last 200 years or so. A professional player who studied Berlekamp's theory would not increase his strength one iota as a result of his efforts, since he understands this theory intuitively anyway. Richard Bozulich http://www.kiseido.com
I think the explicit development of a theory that covers in a way that ordinary players can understand problems that could previously only be solved in practical play by world-class players qualifies as "significant". Yes, people solved those problems in the literature over the last 200 years without reference to Berlekamp's theory -- but Berlekamp's theory makes the problems all solvable directly by an easy and rapid method. It is only applicable in the very final stages of the game, but I never claimed it wasn't. To take the "intuitive grasp" of professional players and make it clear and explicit is a big achievement.
Also, I think a professional player who studied Berlekamp's theory would indeed gain sufficient insight that he might at least be able to play difficult late endgames more quickly; if in time pressure it could make a difference.
A good analogy is the theory of corresponding squares in King-and-Pawn endgames in chess. Any given K+P ending with blocked pawns can be solved with a large amount of often confusing direct calculation (chess is a finite game after all); but the general method developed by Cheron and others allows all such endings to be solved in a uniform and efficient way, and this is a valuable theoretical advance. Just as in Go, it is possible to compose problems that are incredibly difficult to solve without the theory but easy with it, and just as in Go, the theory also helps occasionally in the less difficult positions that occur in practical play, by allowing them to be solved more systematically and quickly.
-- Joe Shipman
The basic question of this thread is "has go endgame (and middle-game) technique improved since Dosaku to Shusaku?" I think that Berlekamp's theory is extremely marginal to go technique as it is seen today or in yesteryears in the competitive arena.
I seriously doubt that any professional player, none of whom are mathematicians, who took the time and exerted the effort to read Berlekamp's "Mathematical Go", even if they could get through the arcane notation and glean some understanding, would improve their go technique. It is just too irrelevant to the main body of the game. And the frequency that a position relevant to this theory arises is extremely rare. So one cannot and should not put it on the same level of practicability as the theory of corresponding squares in chess. Even if a Berlekamp-type position does arise, a professional player, especially the strongest ones, have the ability to find the best move.
This is not meant to disparage Berlekamp's theory which is a solid mathematical achievement. But it doesn't have much application to the real world of winning a tournament game.
If you think it has application, then go through all the games in the year 2000 Kido Yearbook published by the Nihon Ki-in and show me how many lost games could have been won if Berlekamp's techniques were used and how many were won because they were played in conformity to Berlekamp's theory. I don't think you will find many and maybe none. I know that Berlekamp had a hard time finding examples back in the early 90s from thousands of games friends of his had gone through for him.
Respectfully,
Richard Bozulich
To Mr. Shipman:
Here are links: