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 Post subject: Go is a topological game
Post #1 Posted: Sat Sep 23, 2017 4:34 pm 
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This came up in the tanslation of commmentaries thread:

John Fairbairn wrote:
Quote:
As Matt Cocke UK 5d says, Go is a topological game.


Interesting and much underused concept* - possibly because it's too hard for humans but not for AlphaGo?. I first came across it through Paul Prescott at the London Go Centre (can't remember if he became British champion but he was at least a challenger). He studied topology (or a mathematical kind of it) at Cambridge, but in go he boiled it down in a simplistic but very powerful, which was something like preferring moves that did at least two things to moves that did one thing (or maybe better, moves that affected two or more groups instead of one).

How do you see topology working in go? And do you know how Matt sees it?

*There is a word, not common but not rare, in Japanese go 碁形 which is a nuisance to translate well: 'go shape' is obviously silly. It refers to the shapes in the game as a whole, but not in the sense of katachi. The sense is in fact the topography of the game, and the analogous word for topography in the geographical sense is 地形. I'm wondering, in the light of your comment and the changes in thinking being wrought by AlphaGo, whether we should be introducing the word 'topography' to go. What do you think?


I want to answer this, but not interrupt the flow of that thread (which has some great games). It's possible the ultimate source of my quote is also Paul Prescott. The quote is not original: I can't remember where I first heard it - possibly from Matthew MaFadyen, who amy well have heard it from Paul.

I generally think about in terms of large casle connectivity. It tends ot particularly relevant early in the game, and become less important the closer you get to the small endgame.

One of the games in that thread gives a very nice example:
dhu163 wrote:
the thickness concept vs two eyes comes up again here see :w49:



By move 50, the game looks topologically difficult for White. As the game progresses, white gets cut into more and more distinct groups. This casues inefficiencies, and so Master builds up a very solid lead without needing to kill anything. It seem to me that AlphaGo is very good at the topological aspect of the game - randomly scattered stones often link up miraculously to from a moyo or starat an attack.

Connecting groups is obviously fundamental. On the flip-side, cutting is great fun and rarely a mistake. To start with a trivial example:

Click Here To Show Diagram Code
[go]$$ Connecting is huge
$$ . . . . . .
$$ . . X . . .
$$ . O . O . .
$$ . . X . . .
$$ . . . . . .[/go]


Whoever plays first here gets a huge advantage. The reason is topological - one group versus two discsonnected groups.

To give a more non-trivial example:

Click Here To Show Diagram Code
[go]$$Wc 1 point jump
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . 1 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Black 2 is obviously a good move here.

Looking at it from a topological point of view, it can be regarded as attempting to maintain the connection between black's start point stones. So it's certainly consistent with viewing go as a topoliogcal game. White can disconnect the stones via an invasion, but if she invades too early her stones will come under a very fierce attack.

This raise the question as to whether this move is better topologically:

Click Here To Show Diagram Code
[go]$$Wc 2 point jump
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . 1 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


It will be harder for white to invade on the RHS, and so arguably the connectivity of this move is better than the 1-point jump. However, this move is less efficient than the 1 point jump in other areas. Suppose black gets sente to attack the white stone:


Click Here To Show Diagram Code
[go]$$Wc 2 point jump
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 3 . . . . . |
$$ | . . . O . . . . . 5 . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . 8 . . . 7 . X . . . |
$$ | . . . . . . . . . . . . . 1 6 . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


In this variation, 2 looks like it would be better as a 1-point jump. The issue is a topological one - black's 4-4 point and black 2 are quite far apart. So after white runs away on the outside, white has monkey business which could spearate the stones. Black could go back and defend, but then he's spent one more move connecting his bits than would have been necessary.

Efficieny is also why the move below is bad:
Click Here To Show Diagram Code
[go]$$Wc Eek!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . 3 . . . . . X . . . |
$$ | . . . . . . . . . . . . . 1 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


From a purely topological point of view, there may be some reason to play black 4. However, it's a horrible move which is only slightly better than passing. One interpretation is that if linking stones is important, it's very important to do it as efficiently as possible (and on as large a scale as possible).

There is a complex interaction between toplogocical considerations and sacrificinf stones. If stone are light, and can be scarificed, it can completely change the large-scale conncecity considerations. An example of this can be seen, for example, in this hamete:

Click Here To Show Diagram Code
[go]$$Bc Hamete
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . 1 . 2 . .
$$ | . . O , . . . . .
$$ | . . . 3 . . . . .
$$ | . . . . . . . . .
$$ | . . 4 . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


From a topology perspective, white 4 looks insane. However, if black plays naively, there is a trap waiting where white sacrifices a few stones for a wonderful result. (If people don't know the rip-off line, I've shown it below.)

Click Here To Show Diagram Code
[go]$$Bc Hamete
$$ ------------------
$$ | . . . . . . . . .
$$ | . . . . . . . . .
$$ | . . . . X . O . .
$$ | . 4 O 6 7 . . . .
$$ | . 2 1 X 8 0 . . .
$$ | . 3 5 . 9 . . . .
$$ | . . O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


Click Here To Show Diagram Code
[go]$$Bc Hamete
$$ ------------------
$$ | . . . . 9 . . . .
$$ | . . 1 5 6 7 . . .
$$ | . . . 4 X 8 O . .
$$ | . O O O X 0 . . .
$$ | . O X X O O . . .
$$ | 3 X X . X . . . .
$$ | . 2 O . . . . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]



Click Here To Show Diagram Code
[go]$$Bc Hamete
$$ ------------------
$$ | . . . . X . . . .
$$ | . . X X 1 X . . .
$$ | . 5 7 O X O O . .
$$ | 9 O O O X O . . .
$$ | . O X X O O . . .
$$ | X X X 3 X 8 . . .
$$ | . O O 2 6 4 . . .
$$ | . . . . . . . . .
$$ | . . . . . . . . .[/go]


Black gets 19 points, but white gets superb thickness worth way more than that. By sacrifcing some stones, white stayed connected. So reading is important to determine which stones are light, and connectivity is most important for non-light stones. (Of course, in this example black will not pay this way - for example attaching at G16 is in response to white's crazy move is a way out of this sequence.)


This post by drmwc was liked by 2 people: dust, Waylon
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