The theme is opening study with KataGo, although I may include other topics. My intention is to play 1,000 openings against the Policy Weighted AI in KaTrain. The goal is not to win, but to avoid mistakes. I won't be posting the full openings here, only the main ideas I take away from each review. I'll number the games in order of posting, which is not necessarily chronological order (I have some saved up reviews I may post about later).

Some moves are deliberate style choices, which I won't regard as mistakes even if KataGo penalizes them. E.g. recently I play 3-3 fairly often in my openings.

I'll try to generalize a bit, but I may overgeneralize. I'd be delighted to hear disagreements, especially if you can offer counterexample positions.

Game 1, position 1

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O , b . . . . , . . . . a , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . c . O . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Here I played a, but b is a bit better and c is the best.

5-3 is a worse opening than 3-4. So we shouldn't allow the opponent to "fix the mistake" by making an enclosure. This is more important than making or preventing an enclosure from a 3-4 stone.

Game 1, position 2

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O O X . . . a . . . . . . . . . |
$$ | . . O , X X . . . , . . . . X , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]

This joseki should be finished with a low extension, given the upper-right enclosure.

Game 1, position 3

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O O X . a . . . . . . . . . . . |
$$ | . . O , X X . O . X . . . . X , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |[/go]

Instead, black played the high extension and white invaded. If this happens, black should force the connection at a.

Game 2, position 1

Click Here To Show Diagram Code

[go]$$Wc
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . O . . . . . X . . . . . . . . . |
$$ | . . O , O X . . . , . . b . . X . . . |
$$ | . . . O . X . . . a . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This position is a bit peculiar, but white would like to invade this framework. How to proceed? I thought a looks like a vital point to complete the framework, but I was too timid to invade there and played b instead, allowing black to seize a.

Continuation

Click Here To Show Diagram Code

[go]$$Wc
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . O . . . . . X . . . . . . . . . |
$$ | . . O , O X . . . , . . . . . X . . . |
$$ | . . . O . X . . . 3 . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 1 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

KataGo recommended this sequence. is a probe. If black defends the corner, then white plays at the vital point.

Game 2, position 2

Click Here To Show Diagram Code

[go]$$Bc
$$ --------------------
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . 1 a . O . . |
$$ , . . . . . , . . . |
$$ . . . . . . . b . . |
$$ . . . . . . 2 . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ . . . . . . . . . . |
$$ , . . . . . , . . . |[/go]

In response to black approaching the 3-3 point at , I haven't always been sure which extension to play. Based on KataGo's feedback I'll default to in the future. If the approach is instead at a, then respond at b.

This time my friend and I were studying the opening together. We played black against the AI.

Game 3, position 1

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . 5 . . . . |
$$ | . . . 2 . . . . . , . . . . . a 1 b . |
$$ | . . . . . . . . . . . . . . . c 6 d . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , 4 . . |
$$ | . . 3 . . . . . . . . . . . e . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

KataGo says should be at e, but let's focus on how black should respond to . I'd always thought that a–d are all reasonable moves, and indeed Josekipedia lists all four moves. My friend and I chose to play at d. But it seems that d is a terrible move!

Continuation

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . X . . . . |
$$ | . . . O . . . . . , . . . . . , X 3 . |
$$ | . . . . . . . . . . . . . . . 1 O . . |
$$ | . . . . . . . . . . . . . . . . 2 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . 4 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , O . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

is the correct move, after which we may expect the continuation shown above. KataGo's preference seems strong enough that, until I find a counterexample in play, I will assume this is the best joseki choice regardless of the outside board situation.

Game 3, position 2

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . X . . . .
$$ | . 3 X X X O 1 . . .
$$ | . . O O O 2 a . . ,
$$ | . . . . . . b . 4 .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

A 3-3 invasion joseki was played, ending with . We couldn't think of a good local follow-up for black. We thought about a, but if white responds at b we thought the result looks good for white, so we decided to tenuki.

Continuation

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . . . . . X . . . .
$$ | . X X X X O X 1 . .
$$ | . . O O O O a . . ,
$$ | . . . . . . . b O .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

However, black does have a good local continuation at . This threatens a follow-up at b, which white might contemplate preventing with a.

Game 4, position 1

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------------
$$ | . . . . . . . . . .
$$ | . X O a . . . . . .
$$ | . . X O . . . . . .
$$ | . b X O . . . . . ,
$$ | . 1 X O . . . . . .
$$ | . X O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

Another 3-3 invasion joseki. After , I responded at a, which is a big mistake. I was definitely thinking about b, but I vaguely remembered seeing something like a in a professional game; however, I'm pretty sure that position was actually quite different.

Game 4, position 2

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------
$$ | . . 3 . . . . . . .
$$ | . X W 1 . . . . . .
$$ | . 2 X O . a . . . .
$$ | . 4 X O . . . . . ,
$$ | . O X O . . . . . .
$$ | . X O b . . . . . .
$$ | . 6 . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

at the marked stone. This was the sequence resulting from my first mistake. The next mistake was to play the keima at a immediately, allowing white to connect at b.

Continuation

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------
$$ | . . X . . . . . . .
$$ | . X X X . . . . . .
$$ | . O X O . 7 . . . .
$$ | . O X O . 6 . . . ,
$$ | . O X O 3 . . . . .
$$ | . X O 1 4 . . . . .
$$ | . O 2 5 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

Instead, black should cut, which may result in something like the above continuation.

a is a joseki as well. If KataGo says it is a mistake, it is probably based on the whole board position it is occurring in. It is not hard to construct board positions where KataGo thinks a is the best move.

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------------
$$ | . . X . . . . . . .
$$ | . X X X . . . . . .
$$ | . O X O . X . . . .
$$ | . O X O . . . . . ,
$$ | . O X O . . . . . .
$$ | . X O X a W . . . .
$$ | . O O . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

This is a common ending shape for this joseki. White plays instead of a when the ladder doesn't work for white. If the ladder works for white, then playing at a gives white a favorable result.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------
$$ | . . X . . . . . . .
$$ | . X X X . . . . . .
$$ | . O X O . . . . . .
$$ | . O X O . . . . . ,
$$ | . O X O 1 . . . . .
$$ | . X O X 2 . . . . .
$$ | . O O 3 . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . , . . . . . ,[/go]

Black can play when the ladder favors white, white I imagine it did in your game. The results here can be more complicated. Perhaps KataGo thought this fight was also good for white in your case, which is why it wanted to play b in your original diagram.

_________________
We don't know who we are; we don't know where we are.
Each of us woke up one moment and here we were in the darkness.
We're nameless things with no memory; no knowledge of what went before,
No understanding of what is now, no knowledge of what will be.

Thanks for pointing this out. Yeah, after investigating some other positions it seems to be pretty situational. Maybe the ladder is a deciding factor?

BTW in the last couple weeks I've been focusing more on reviewing whole games. I will post some more openings here though at some point.

I've decided to continue this training regimen with some changes. Previously, I was playing the opening until move 30 or so. But my game analyses showed that I'm already making relatively few mistakes in that part of the game. In comparison, by move 50 I have usually made at least one huge mistake. So I will be practicing my openings until move 50.

Also, I will mix in some handicap games as well. I've found major deficiencies in my play when it comes to invading and reducing large frameworks. I think playing against a 9 stone handicap could be a helpful exercise. Studying handicap play could also help me enjoy handicap games more, which would be useful if I want to play on e.g. OGS where it's relatively hard to find an even game.

I've played some 9H games with KataGo already, which I may be posting some of later, but for the time being I'm posting about today's even game. I played black in this game. I lost 13 points by move 50.

Click Here To Show Diagram Code

[go]$$Wc Responses to white 1
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . a . . . |
$$ | . . . O . . . . . , . . . . . 1 X . . |
$$ | . . . . . . . . . . . . . . . c b . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In response to white 1 I've mostly played a in the past. However, it looks like c is superior when black has the ladder. There seem to be a lot of variations for c, which may be why I've stuck with a so far. But in the future I'll try playing c if the ladder looks good for me.

In the game, I went with a:

Click Here To Show Diagram Code

[go]$$Bc Joseki played in the game
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . 1 . . . |
$$ | . . . O . . . . . , . . . . 3 O X 5 . |
$$ | . . . . . . . . . . . . 9 7 6 4 2 . . |
$$ | . . . . . . . . . . . . . 8 . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Click Here To Show Diagram Code

[go]$$Wc Continuation
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . X a . . |
$$ | . . . O . . . . . , . . . . X O X X . |
$$ | . . . . . . . . . . . 2 X X O O O 4 . |
$$ | . . . . . . . . . b 6 3 1 O . . . . . |
$$ | . . . . . . . . . 8 7 . . . . . 5 . . |
$$ | . . . . . . . . . . 9 . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

It seems was a mistake, and white should have played at a. As black I felt like I must have also made some mistake by this point, but KataGo says everything is fine.

At this point I did feel a bit nervous about my cutting point at b, but I also thought that playing there now would be too slow, as it would give white time to erase the influence of the wall I had built.

Click Here To Show Diagram Code

[go]$$Bc Black 3 should be at 'a'
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . 1 . . . . . . . X . X . . . |
$$ | . . . O . . . . . , . . . . X O X X . |
$$ | . . . . . 3 . . . . . X X X O O O X . |
$$ | . . . . . . . . . a X O O O . . . . . |
$$ | . . . . . . . . . X O . . . . . O . . |
$$ | . . . . . . . . . . O . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . 2 . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

So I played this approach, and white played elsewhere. This would have been the perfect time to fix the weakness at a, but I played instead, which I think was slightly greedy (note, however, that is a perfectly good followup to play sometime after fixing at a).

Click Here To Show Diagram Code

[go]$$Wc White sets up a ladder breaker
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 4 . . |
$$ | . . . . . X . . . . . . . X . X 3 . . |
$$ | . . . O . . . . . , . . . . X O X X . |
$$ | . . . . . X . . . . 6 X X X O O O X . |
$$ | . . . . . . . . . 5 X O O O . . . . . |
$$ | . . . . . . . . 8 X O . . . . . O . . |
$$ | . . . . . . . . . . O . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . a 1 7 . . . . , . . . . . O . . . |
$$ | . . X 2 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

White then used an approach on my 3-3 stone to set up a ladder breaker. So I captured white's stone with . But this is the biggest mistake of the game so far. It's more urgent to help my corner, for example at a.

(Game 5 to be continued)

As for the rest of game 5, I made one fundamental mistake.

Click Here To Show Diagram Code

[go]$$Bc This corner is in danger
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . O O O O . . . ,
$$ | . a X X . X O . . .
$$ | . b . . . X O . . .
$$ | . . . . . . . . . .
$$ --------------------[/go]

I didn't realize how much trouble this corner is in. I think my thought process went like: "if at a, then at b, and now I'm done reading."

Click Here To Show Diagram Code

[go]$$Wc Variation: black dies
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . 3 O O O O . . . ,
$$ | . 1 X X . X O . . .
$$ | 4 2 . 9 6 X O . . .
$$ | . . . 5 8 7 . . . .
$$ --------------------[/go]

In the game, I ended up playing and dying. Actually black has a better option than .

Click Here To Show Diagram Code

[go]$$Bc Black can live
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . O O O O O . . . ,
$$ | . O X X 6 X O . . .
$$ | 3 X . 1 . X O . . .
$$ | . . 2 . 5 4 7 . . .
$$ --------------------[/go]

Actually above is not even the best move -- black would be better off sacrificing the corner to get a couple sente plays outside. But even saving part of the corner is better than my game result. Here's the rest of the sequence:

Click Here To Show Diagram Code

[go]$$Wc Conclusion -- black makes two eyes
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . O O O O O . . . ,
$$ | . O X X O X O . . .
$$ | X X . X 1 X O . . .
$$ | . 4 O 2 X . X 3 . .
$$ --------------------[/go]

Anyway, this is just making the best of a bad situation. This may be useful to know if I ever encounter this situation from white's point of view. But what I should have done was to defend early:

Click Here To Show Diagram Code

[go]$$Bc Black's defense
$$ | . . . , . . . . . ,
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . . . . . . . . . .
$$ | . 2 . . . . . . . .
$$ | . 1 O O O O . . . ,
$$ | . 3 X X . X O . . .
$$ | . . . . . X O . . .
$$ | . . . . . . . . . .
$$ --------------------[/go]

One final note. What was black doing while ignoring the situation in the corner?

Click Here To Show Diagram Code

[go]$$Bc A big move?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . X . . . . . . . X . X O . . |
$$ | . . . O . . . . . , . . . . X O X X . |
$$ | . . . . . X . . . . X X X X O O O X . |
$$ | . . . X . . . . . O X O O O . . . . . |
$$ | . . . . . . . . X X O . . . . . O . . |
$$ | . . . . . . . . . . O . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O O O . . . , . . . . . O . . . |
$$ | . . X X . X O . . . . . . . . . . . . |
$$ | . . . . . X O . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Actually, there are substantially bigger moves than this. To see them, I played out (even though is too slow for white) and then observed KataGo's recommendations:

Click Here To Show Diagram Code

[go]$$Bc Some actual big moves
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . d . . X . . . . . . . X . X O . . |
$$ | . . . O . . . . . , . . . . X O X X . |
$$ | . . . . . X . . . . X X X X O O O X . |
$$ | . . . X . . . . . O X O O O . . . . . |
$$ | . . . . . . . . X X O . . . . . O . . |
$$ | . . . . . . . . . . O . . . . . . . . |
$$ | . . . . . . . . a . . . . . . c . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . e . . . . . . |
$$ | . . 4 . . . . . . . . . . . . O . . . |
$$ | . 2 . . . . . . . . . . . . . . . . . |
$$ | . 1 O O O O . . . , . . . . . O . . . |
$$ | . 3 X X . X O . . . . . . b . . . . . |
$$ | . . . . . X O . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

I believe b is similar in spirit to the move I played. It is simply approaching the wider side instead of the narrower side. And a is playing at the boundary of the two frameworks instead of invading deep into white's framework. Perhaps one of these moves could become my first intuition.

Click Here To Show Diagram Code

[go]$$Wc 10 = a
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . 8 7 9 . . c d |
$$ | . . . . . . . . . . . . . X . 5 3 b . |
$$ | . . . O . . . . . , . . . . 4 1 X . . |
$$ | . . . . . . . . . . . . a . . 2 6 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Although Black 2 at 5 or 6 are also possible, I frequently play this variation.

Black plays two excess stones but gets a wall on both sides and the ko aji B-C-D remains.

Click Here To Show Diagram Code

[go]$$Wc result
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . X O O . . . . |
$$ | . . . . . . . . . . . . . X . O O . . |
$$ | . . . O . . . . . , . . . . X O X . . |
$$ | . . . . . . . . . . . . X . . X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Thanks. I haven't seen this joseki before. In fact until recently I didn't play the large knight's enclosure much at all, so much of this is new to me.

It seems that KataGo doesn't like this joseki very much though. In your first diagram, KaTrain shows move 4 as a 3.3 point loss and move 6 as a 1 point loss.

Instead, KataGo recommends something like this:

Click Here To Show Diagram Code

[go]$$Bc Black gets territory and white is still unsettled
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X 5 3 2 . . |
$$ | . . . O . . . . . , . . . . 4 O X 9 . |
$$ | . . . . . . . . . . . . . . . 1 8 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 6 . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

ISTM black is making good use of the diagonal fuseki in this variation. White needs to exchange , which seems locally unfavorable, in order to threaten (not even realize) a ladder. Meanwhile black is getting solid territory in both corners.

I also looked at a parallel fuseki:

Click Here To Show Diagram Code

[go]$$Wc Still loses 2.7 points
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . X . 5 3 . . |
$$ | . . . O . . . . . , . . . . 4 1 X . . |
$$ | . . . . . . . . . . . . . . . 2 6 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In this case, loses 1.6 points and loses 1.1 points. So this is about 1.6 points better than the same joseki in a diagonal fuseki context. I would guess there are two effects in play here: the absence of a ladder breaker makes cutting less valuable for black, and the 4-4 stone in the adjacent corner increases the value of black's wall a bit.

So I haven't yet seen a position where this joseki choice is actually optimal for black.

This is not the most recent game, but KataGo's advice in this game contrasts confusingly with another game I am planning to share soon, so maybe a quick discussion can help me find enlightenment.

I played black in this game. By move 50 I had made about 7 points' worth of mistakes.

Game 6, position 1

Click Here To Show Diagram Code

[go]$$Bc Black should have approached at a or b
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . 1 , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . b a . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

One of my goals in publishing this journal is to avoid making the same mistake twice. Yet here I have made a mistake I already discussed in game 1. The 5-3 stone is really not such a great opening, so it's important for black to approach before white can rectify the situation by making an enclosure.

Game 6, position 2

Click Here To Show Diagram Code

[go]$$Bc High extension is slightly better
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . 6 . . . . . . . . . . . . . |
$$ | . . 4 , . . . . . , . . . . X , X . . |
$$ | . . 2 1 . . . . . . . . . . . . . . . |
$$ | . . 3 5 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 7 a . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

It's a small difference, but black should have played the extension on the 4th line here. I made the reverse mistake in game 1. My feeling now is that the high extension should be played in most situations, and the low extension should be used only when there is some obvious synergy with other stones nearby.

Game 6, position 3

Click Here To Show Diagram Code

[go]$$Bc should be at a or b
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . X , X . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . a . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . X X X . . |
$$ | . . . O . . . . . . . . 1 X O O O b . |
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This position is my main reason for posting this game. It seems loses a whole point here. In a world where AI disapproves of side-oriented strategies like san-ren-sei, it's rather delightful to come across a position where the side extension is favored over a corner move.

This leads me to a hypothesis: the correct timing for a side extension is when both corners are exerting significant influence towards the side.

I may continue game 6 later, but I wanted to skip ahead to a position from game 7 that presents a confusing contrast. I played white in this game.

Click Here To Show Diagram Code

[go]$$Wc Should white play a, b, or c?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . O . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . c . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . O O O . . |
$$ | . . . X . . . . . . . . a O X X X b . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Recalling KataGo's advice on position 3 of game 6, I chose to play c here. But KataGo says that is a bad move, and I should play a! I really don't see how a is different from the move I was admonished for playing in the previous game. I would be super happy if anyone has thoughts that can clarify this.

In the meantime perhaps my best bet is to just play b, which is at least regarded as nearly optimal in both cases.

Click Here To Show Diagram Code

[go]$$Wc result
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . X O O . . . . |
$$ | . . . . . . . . . . . . . X . O O . . |
$$ | . . . O . . . . . , . . . . X O X . . |
$$ | . . . . . . . . . . . . X . . X X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

"KataGo doesn't like this joseki"

What is KataGo's difference of percentages at the game start and at this position from Black's view?

And does it see the ko at this moment?

First, a is not just a corner play. It has influence on the bottom side.

Second, in general Black has more leeway than White in the opening, despite the somewhat large komi.

Third, in this game all four sides are undeveloped, so developing one of them is not so urgent. In the other game the left side is developed, so if Black develops the right side there is more to the idea of leaving the top and bottom side as miai. In general, extending on the side to make a moyo is a second tier play in the opening. The later in the opening, the more likely the extension is to be a good play.

Fourth, and related in particular to the second point. Despite the large komi White's job in the opening is more to thwart Black's development than to pursue his own development.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I haven't got the answers, but I have a feeling that I know where the answers lie. I have come to this feeling after having recently looked at a lot of old Chinese commentaries where the terms used are rather different from the ones the Japanese and thus we tend to use. They are looking at similar positions but through a different prism. It is often startling how much difference that makes. Another related thing that affects perception is different emphasis. The old Chinese seem to stress timing far more than the modern commentators.

I suspect therefore that, to make progress with learning from AI, we are going to have to devise a new vocabulary.

Click Here To Show Diagram Code

[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . O . . . . . . . . . . . . . |
$$ | . . O , . . . . . , . . . . X , X . . |
$$ | . . O X . . . . . . . . . . . . . . . |
$$ | . . X X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . a . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . X X X . . |
$$ | . . . O . . . . . . . . 1 X O O O b . |
$$ | . . . . . . . . . . . . . O . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

For example, in your example above (which I will call Diagram 1), you talk (as we all would) get away from the concept of extensions: "both corners are exerting significant influence towards the side."

But, as you also note, that way of talking lets us down in the following case (Diagram 2):

Click Here To Show Diagram Code

[go]$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . O . . . . . |
$$ | . . . , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . c . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . O O O . . |
$$ | . . . X . . . . . . . . a O X X X b . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Extensions are rarely mentioned in old Chinese, expect in the very limited sense of two- or three-space extensions. That tells us straightaway that we don't actually have to talk about extensions at all! The Chinese put the emphasis instead on expanding "power" (势) or what we might call a sphere of influence. For similar reasons they don't talk about thickness, so again that tells us we don't have to, either.

Let us therefore try to look at Diagrams 1 and 2 by eschewing the concept of extensions, but without going overboard and trying to apply the Chinese world view. Let us use the western concept (Matthew Macfadyen's) of "virtual territory."

The basis of VT is that you map out a large area that is big enough to be divided in two, and say that, "If he invases on one side - I don't care which - he will live small but I will get a large confirmed territory on the other side.

This does work out that way in practice, but the theory doesn't seem very popular. In think that's because it may work as predicted but doesn't give good overall results. I think AI shows why.

If we look at Diagram 2, the VT area can essentially be divided into two areas. Bad.

But if we look at Diagram 1, the VT area can be divided into three areas. Good.

My speculation about what is happening (which seems to fit with games by pros who study with AI) is that the gain from a VT area split in two is not enough. The lone "safe" area that results after an invasion of the other side is still subject to erasure and so on. You end up over-protecting your investment.

With a three-area VT, however, you end up two safe-to-safish areas after invasion of the other, and instead of the opponent being able to apply pressure at his leisure on your one big nest egg, he ends up instead having to chase two rabbits at once.

If there is anything in that or a similar theory, it seems to be that we should get a away from the idea of talking about extensions, which have strong connotations about territoru on the side. Instead, we should find a term that forces us to think about potential territory in a more VT or "sphere of influence" way, and to use terms such as fence post or claim markers, or whatever. It may be that a move chosen that way coincides with the spot chosen for an extension, but the mindset is very different. In particular, the VT or SOI mindset might usefully lead you to reject a move on an extension point and, indeed, encourage to play moves on points you never looked at before because they were not extensions.

I think this language-controlled mindset comes up in other ways. In Diagram 2, for example, generations of us, pros included, have always assumed that a Black move at 'a' is only natural. That is because we have been bombarded with testosterone-laden advice. We must apply "kiai", we mustn't let White play 'a' and "force" us to connect. we must "bully" the opponent and "press" him into the corner, etc etc.

But if we strip away all of that language and look at the position dispassionately, we could alternatively say White 'a' "helps" Black to connect. We could note that there is no loss because it is the exchange of a third -line move for a fourth-line move, which we know to be normally equal. And of course, not playing 'a' means Black gets sente to play elsewhere first. Bots do that a lot. Old Chinese commentaries stress that a lot. A recurring phrase in OC commentaries which you don't see in Japanese commentaries is 'fighting for the initiative' 争先.

The Jesuits used to say, give me the child and I will give you the man. The main tool in their armoury to achieve that result was, quite simply, words.

Using new words in go may be like switching from using a donkey to power a grinding stone to using a two-stroke engine. One small step for man. A large leap for donkeys.

Here is a matrix of KataGo's policy intuition for whether to play on the side around the b area instead of extending at a, if we vary the two corner enclosures. These were derived from me eyeballing the policy probabilities with the particular random symmetries for one run of analysis, rounding them, and giving partial credit if there were multiple side moves that each individually were not preferred, but together took up some more of the policy mass.

Click Here To Show Diagram Code

[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . 3 3 . . . . |
$$ | . . . , . . . . . , . . . 3 3 1 1 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . b b . . |
$$ | . . . , . . . . . , . . . . . b b . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 4 4 . . . . . . . . . . . . . . . |
$$ | . . 4 4 . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . , . . . . O O O . . |
$$ | . . . 2 . . . . . . . . a O X X X . . |
$$ | . . . . . . . . . . . . . X . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Note that KataGo's search sometimes disagrees with the above policy - sometimes the policy probabilities would be lower yet the search decided the side move was best, sometimes they were higher yet the search decided the move at 'a' was best. But whereas the search will be giving a more accurate answer for this exact position, considering the combinatorics of the possible followup sequences, the policy might be more general in the sense of representing the net's intuition for side extensions averaged across a wide variety of openings "like" this one, so I'd actually like to pay more attention to the raw policy in this case here.

Anyways, the raw policy's intuition appears to show a pretty clear gradient of "power to support a good side framework" for different corner enclosures where the 3-4 OP is at the top, the 3-4 TP is next, and the 4-4 SK is at the bottom, and the rest are in the middle. As black's "side framework support power" increases, KataGo's intuition increasingly prefers "a", to reduce black's potential. As white's "side framework support power" increases, KataGo's intuition increasingly prefers the side extension for white to build their own potential.

We can't ask KataGo directly "why" it has this ranking, but in retrospect the rough ranking matches with some of my intuition as lowly amateur dan. The "side framework support power" here seems to correspond to roughly a notion of influence towards the side plus lack of annoying forcing moves or approach moves against the corner enclosure that would help in invasion/reduction of that side later.

The exact ranking also differs black vs white here, which a-priori isn't shocking since the position isn't symmetric. Probably would need to experiment in many more positions to tease out what the "second factor" is that causes these subtle ordering variations on top of the primary factor of this side influence power. I think there' a chance the "second factor" might also be human-comprehendable, like this "primary factor".

By the way, anyone else who likes this should feel free to do studies like this as well, or like the earlier study I did on conjectured optimal komi by board size and ruleset, or other positional studies. I think there could be some more interesting insights to be gained by taking different patterns and varying the stones and seeing how the policy and evaluations respond.

All it took was me clicking through the 36 possibilities in Lizzie while looking at the numbers and writing them down (hit 'b' in Lizzie to toggle the raw policy probabilities). Anyone else could do things like this too.