HET's Journal

How close are Go professionals to perfect play?  This question came up
on rec.games.go with a different phrasing:  what would happen if
today's professionals played against God.  


From: Tweedie 

Many years ago I had the honor or meeting Go Sei-gen (Wu Ching-yuen). During
dinner I asked him how close 9 Dan professionals were from perfect play. He 
said that if he played a Go game with God, and played black with a 2 stone
handicap the outcome would not be certain. He felt he had a better chance of
winning, but he would not bet his life. With a 3 stone handicap he was sure
he would win, but he would not be comfortable and would not bet his life on
the outcome. However, with a 4 stone handicap he was confident of the outcome,
and he would bet his life.

About a year later I asked Fukuda 6 Dan professional the same question. His
answer was rather interesting. He said that even if he held black and put a
9 stone handicap against a raw beginner he would never bet his life on the 
outcome of the game. I asked "Why not?", and he said, "I might lose".    :-)



From:Jan van der Steen

Many years ago an article has been published in the German Go
Magazine which reported on some research done by a German
professor in Mathematics. I posted an excerpt (from memory)
on this newsgroup in 1992. I guess it's ok to include it once
more below. I don't have the original article so please don't
ask me for more details. Maybe one of our German readers can
dig up the original article. I would be interested in a copy as well.

Jan van der Steen

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

A German professor Mathematics did some research on the variation
in the results of Go games versus the strength of the players.
Amongst other things, he discovered that the variation relates
proportional to the strength of the players involved:

        ^           |
        |           |
        |           |
     variation      |..............*
                15  |              .
                    |              .
                    |.........*    .
                    |         .    .
                10  |         .    .
                    |....*    .    .
                    |    .    .    .
                    |    .    .    .
                 5  *    .    .    .
                    |    .    .    .
                    |    .    .    .
                    |    .    .    .
                    -----------------------------------
                    9p   6d   3d   1k   4k  strength ->


An interesting extrapolation is to see which strength relates to
perfect Go (variation equals zero since games between two perfect
players will always have the same result):

        ^           |
        |           |
        |           |
     variation      |..............*
                15  |              .
                    |              .
                    |.........*    .
                    |         .    .
                10  |         .    .
                    |....*    .    .
                    |    .    .    .
                    |    .    .    .
                 5  *    .    .    .
                    |    .    .    .
                    |    .    .    .
                    |    .    .    .
             *------------------------------------------
                    9p   6d   3d   1k   4k  strength ->


So, it seems that the perfect player can give a 9 dan prof 3 stones (!).

I once showed this graph to Miyamoto Naoki 9 dan (known in the West
by his game analysis in "Shusaku, the Invincible") and asked his opinion:

    "I fully agree", he said, "but if my life depends on it
     I want to have 4 stones handicap against god!".



From: law20065@leonis.nus.sg (KOH KEW SOON)

Back in an ancient dynasty, the best player in the whole of China (and 
presumably the rest of the world as well) was this scholar who was friends 
with the emperor who also liked go. Of course he would always lose to the 
emperor (even though he could give the emperor h-4). This guy, whom we 
shall call Da Guo Shou, was travelling through rural China one day when 
he was stranded at night and sought shelter at a remote village farm. 
While he was sleeping that night, he heard the familiar sound of go stones 
being placed on a board, which sounded like divine music to his ears. He 
got up, crept towards the sounds, and saw, under the moonlight, an old 
woman playing with her daughter-in-law. There were only a dozen stones on 
the board, but the configuration of the stones struck Da Guo Shou as 
being unfamiliar yet celestially beautiful.
 
The daughter, having just made a move, sighed and proclaimed, "Alas, 
mother, you are too good for me, I have again lost by 5 points."
The old woman admonished her, "Have you now grown so careless? You should 
see that it is clearly a difference of 8.5 points." She proceeded to 
analyse the *entire game*, displaying variations and placements that Da 
Guo Shou would not have thought of in his wildest dreams. As the two 
peasant women discussed the game, Da Guo Shou felt faint. His head swam 
with all the marvellous moves and he fell unconscious.

Alas, when he awoke the next day, he found that he could not remember any 
of the moves he had seen, and the two peasants could not be found 
anywhere. A fruitless search of the surrounding area revealed that he had 
slept not in a farm but in a desolate mountain area. And nearby, was a 
large slab of stone with carvings that ressembled a go board, with heaps 
of pebbles around it.

After this incident, Da Guo Shou renounced his claim as a go master and 
retired to be a teacher. Some say that he later became a hermit and went 
to live in the mountains, hoping to find the Immortals whom he believed 
he had chanced upon that day. Others say that when he was striken near 
death, he had cried that the stars themselves had descended from heaven 
and danced on the go board of the Earth, and mumbled deliriously about 
man's hopeless insignificance.

Perhaps this story was true. It shows that if there really was a GOD, or 
any being who could foresee *every* variation on the go board, then go 
becomes an inevitable process. The closer to the ending, the lesser the 
variations and the easier to predict the end. When that day comes, 
perhaps it is time for Go 3D.