Knotwilg wrote:
Nice!
What you call the middle, I can relate to "Go Seigen groups", a concept introduced by John (again), due to Go Seigen writing & playing in this sense.
I'm not entirely sure the concept is a Go Seigen group, although I'd take your word for it if it was. The 'middle' or perhaps 'in-between' areas seem to figure differently into the games of strong players. I have sensed it with most pros, but it is more acute with the ultra-strong players like Shuei and AlphaGo.
I noticed it when I was flipping through printed copies of AlphaGo's 60-game match against online players. My copies are printed in only a single diagram, so you get a sense of the full board position at the end of the game. While flipping through the positions it struck me that the game records looked different than ones I'm used to seeing. When I started looking more, I realized that the in-between areas were qualitatively different, and that it was possible to make a good guess whether AlphaGo was playing black or white largely by looking at those regions. Here's a few examples:
- Click Here To Show Diagram Code
[go]$$ End of game. Observe the top right 'in-between'.
$$ ----------------
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . O . . O . . . . . . O . . X . . . . |
$$ | . O . O X . O . . O O O X X . O O . . |
$$ | . O . O . . . . . , X X . . X X . O . |
$$ | . X O O X . . . O . . . . . O X X O . |
$$ | X . X X . X . . . O X . . . . X O O . |
$$ | . X . . . . . . . O X . . . X O X O . |
$$ | . X O . X . X . . O O X . . X O X . . |
$$ | . X O X . X X O . X X . . . . O O O . |
$$ | . O . O X O X . . , . . . . X , . . . |
$$ | . . . O O O . . O . X . . X . . O X . |
$$ | . O . O X X . . . . . . X . X . X . . |
$$ | . O X X O X . . O . . X . X O X . . . |
$$ | . O O X O X . . . O X X X O . . . . . |
$$ | . X O O O X . . . . O X O O . . O . . |
$$ | X . X O . X O . O O . O X X O O X X . |
$$ | . X X . O X . . . . O O O X X X . . . |
$$ | . . . X . X . O . . . O X X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -------------------[/go]
- Click Here To Show Diagram Code
[go]$$ End of game. Observe the top left 'in-between'
$$ ---------------
$$ | . . . . . . . . . . . . O . O . O . . |
$$ | . . . . . . . . . . . . O . O O X O . |
$$ | . . . O O O . O O X . . O . O X X X . |
$$ | . . . , X X X . . X . O . O X X . . . |
$$ | . . X . . . . . X . . . O X . . . . . |
$$ | . . . . . . . . X O . . . O . . X . . |
$$ | . . . . X . . . . . . . . . O . X O . |
$$ | . . . . O X . . X . . . . . . X O O . |
$$ | . . O O X X . . . X . . . . . . . . . |
$$ | . . O , O . O . . , . O . . . , . . . |
$$ | . X X O O . O . O O . . . . . . O . . |
$$ | . . X X . X . X . X O O . . . O . . . |
$$ | . O O X . X . X . X X . . . X X O . . |
$$ | . . O O O O O . . X O O O . . . . . . |
$$ | . X O O . . O . O X X . . . . X . O . |
$$ | . O X O O O X . . X . . X . . X O . . |
$$ | . X X X X O X . . . . . . . . X . . . |
$$ | . . . X O X X . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ -------------[/go]
- Click Here To Show Diagram Code
[go]$$ End of game. Observe the top left 'in-between'
$$ -----------------------------
$$ | . . . . O . . O . . . . X O O O X . . |
$$ | . . O O X X X O O . . . . O O X X . . |
$$ | . . O X . . X X O O . . O O X X . . . |
$$ | . . O X . . . . X O O . X X O , X . . |
$$ | . O O O X X . . X O X O O O . O X . . |
$$ | O O X X O . . . X O X O . O X O X X X |
$$ | O X . . X . . . . X X O O X . X X O O |
$$ | X . X X O X . . . X X . O X X X X X O |
$$ | . X O O O X . X X X X O X . . O X O O |
$$ | . X X O O O X X O X O . X X X O X O O |
$$ | . X O O O X X O O O O O . O X X O O . |
$$ | . X O X O O O O . O X O O O X O X O . |
$$ | . . X X X O . O X X X X X O X O . . . |
$$ | . X X X X X X O X . . X O O O . O . . |
$$ | X X O X O O O X . . . . X X O . . . . |
$$ | X O O O . O X . X X . . X O O O . . . |
$$ | O O . . . O X X X . . . X X O X O O . |
$$ | . . . . O O O X . . . . X . X X X O . |
$$ | . . . . . O X X . . . . . X X O O O . |
$$ -------------------------------[/go]
- Click Here To Show Diagram Code
[go]$$ End of game. Observe the bottom right 'in-between'
$$ --------------------------------------
$$ | . . . . . . . O . X . . X O . O X . . |
$$ | . . . X O O O . O O X X X X O X X . . |
$$ | . . . X X . O . O X X O X O O . . . . |
$$ | . . . , . . O O X O O O O X . X . . . |
$$ | . . X X . . O X X . X O . . . . . . . |
$$ | . . . O . O . . . . X X O . X X X . . |
$$ | . X . . . . . . . . . O O O X O . X . |
$$ | . . . X . . X . X X . O X O O . X O . |
$$ | . X . . O . . . . O . O X O . X X O . |
$$ | . O O O X X . X X O . O X X X X O X . |
$$ | . . O X . . . X O . . . O O X O O X O |
$$ | . O X X . X . . O . . . . X O X O O . |
$$ | . . O O X . . . . . . . . . O X . . . |
$$ | . . . . O X . O O . . . . . O . O . . |
$$ | . . . . . . O . X O O . . . . . . O . |
$$ | . . O O . X . . O X O . O . . O O . O |
$$ | . . O . O O X X X X X X O . . . X O . |
$$ | . . . O X X . . . . X O . O X X . X X |
$$ | . . . . O . X . . . . . O . X . . . . |
$$ -------------------------------------[/go]
Compare to a random human game:
- Click Here To Show Diagram Code
[go]$$ End of game.
$$ ---------------------------------------
$$ | . . . . . O . . . . . . . . . . . . . |
$$ | . . . X O X O . . . . . . X . X O X . |
$$ | . . X X X X O . O O . O O O O X . X . |
$$ | . . . O . X X O O , O X X . O O X . . |
$$ | . O O X . X . X O O X . . . O X . . . |
$$ | . X X O O X X O X . X . X O O X . . . |
$$ | . X O . O O O O X . X . . O X X . X . |
$$ | . . X O . O X X X O . . . O X O O O . |
$$ | . . X X O . O O . . X X X O O X X X . |
$$ | . . . O . . O . X X . . O X X , X . X |
$$ | . . O O O O O X . O X . O . . X . X . |
$$ | . . X X . O O O . O . X O . X . . . X |
$$ | . . . X . . O X . . . . O O O X X X . |
$$ | . . X O X . O X O O O . O . X O O O . |
$$ | . X O O . O O X . X O X X O O . . . . |
$$ | . X X O . . X . X X O . . O X X X X . |
$$ | . X O O . . X . X O O X X X O O O X . |
$$ | . . . . . . X X X O . X O O . O . O . |
$$ | . . . . . . . . X . . . . . . . . . . |
$$ ---------------------------------------[/go]
In each case, AlphaGo has accumulated nontrivial points in these in-between regions, and its position in these regions look qualitatively different than those of human pros. Human games tend to fill those areas in with strings of stones. There might be a few eyes made in those area, but generally there aren't a lot of hefty territories. In AlphaGo's case, its territorial boundaries extend much further in the centre (i.e., the in-between) than we would normally expect, but it also uses those area for safety. See the second position, for example, where that area forms the critical eyespace for the Black group. This would seem to line up with John's comment about extending boundaries into the centre.
Now in Shuei's case, he wasn't building territories quite like AlphaGo. But he did seem to play differently in these in-between regions than many pros. He certainly picked up points there, and the regions often turned out to be critical for group safety. I'm afraid my insights are like trying peer through a dense fog--it seems like there's something there, but it's tough to elucidate. Perhaps it has something to do with the fact that many of his games were handicapped, but I have to wonder if the ultra-strong players--the Meijins--have a deeper understanding of those areas than a lesser pro. Certainly I'm paying more attention to those areas now.
If some numerically inclined soul wanted to make an effort, it would be possible to load a series of SGF files and determine how often a given intersection on the board became territory (or should become territory, in the case of a resignation). There may be a difference in the way the AIs accumulate points, particularly the location of those points.