Who says AI is territorial? (Joseki reevaluation)

[kvasir]

Is it possible that this is simply an error in Ishida's joseki dictionary? The most common type of error that I encounter in Go material is swapping black and white.

To me it does look good for black. I'd even go so far as to say black's two groups are strong. It is black to play right?

One model in Go is that it is good to make two strong groups around a singe group in the corner. Flying swallows?

My guess is that - to a pro of Ishida's generation -being squeezed as black is in that joseki sequence seems so unbearable and 'obviously wrong' that it affected the evaluation.

$$B Original diagram with move numbers removed $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X . , . . . . . , . . . . . , . . . | $$ | X . X X . . . . . . . . . . . . . . . | $$ | . X O O . . . . . . . . . . . . . . . | $$ | . O X O . O . . . . . . . . . . . . . | $$ | . . X O O O . . . . . . . . . . . . . | $$ | . O X O X X O X . . . . . . . . . . . | $$ | . . O X X X X . . , . . . . . X . . . | $$ | . . O O O X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------

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[go]$$B Original diagram with move numbers removed $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . X . , . . . . . , . . . . . , . . . | $$ | X . X X . . . . . . . . . . . . . . . | $$ | . X O O . . . . . . . . . . . . . . . | $$ | . O X O . O . . . . . . . . . . . . . | $$ | . . X O O O . . . . . . . . . . . . . | $$ | . O X O X X O X . . . . . . . . . . . | $$ | . . O X X X X . . , . . . . . X . . . | $$ | . . O O O X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

It looks like it was lost somewhere on me that this diagram isn't in Ishida, the next diagram is there. I have reversed the colors to keep in line with the rest of this topic. The comment is that black has almost collapsed and a and b are miai.

However, there is nothing at all about what happens if black lets white play a. There are also very few diagrams about the variation starting with the counter pincer in Ishida. The argument that Ishida would think black isn't good in the first diagram can't easily be connected to the the discussion in the book.

I have seen many cases of pros playing poorly in joseki, when those variations were new, it doesn't at all surprise me if some line like this have errors. However, I would expect it to be much more common when those lines have very few examples in databases. This is one such case doesn't appear to have been played much at the level when game recording starts. Maybe it is that joseki appeared fishy to pros?

$$B Diagram from Ishida, without move numbers. $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . X . . . . . . . $$ | . . a . . . . . . . . $$ | . . X O . O . . . . . $$ | . . X O O O . . . . . $$ | . . X O X X O . . . . $$ | . . O X X X X b . , . $$ | . . O O O X . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ +----------------------

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[go]$$B Diagram from Ishida, without move numbers. $$ | . . . . . . . . . . . $$ | . . . , . . . . . , . $$ | . . . X . . . . . . . $$ | . . a . . . . . . . . $$ | . . X O . O . . . . . $$ | . . X O O O . . . . . $$ | . . X O X X O . . . . $$ | . . O X X X X b . , . $$ | . . O O O X . . . . . $$ | . . . . . . . . . . . $$ | . . . . . . . . . . . $$ +----------------------[/go]

[xela]

...Maybe it is that joseki appeared fishy to pros?

Yes! Thank you. It appeared fishy to pros, and KataGo said: please look again.

I'm going to try once more with a different example. The first post wasn't an isolated incident. I keep running into this sort of thing during game reviews. If we can pause the conversations about "what does the word joseki mean anyway?" and "can you really trust AI on less than two point six squillion playouts?", I think there's an important principle struggling to emerge here.

This is Relentless chapter 1, variation 10, a sequence that didn't actually come up in the game:

$$Wc19 Can white cut? $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . X O . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . , . . . . . a X 2 . | $$ | . . . . . X . . . . . X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$Wc19 Can white cut? $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . X O . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . , . . . . . a X 2 . | $$ | . . . . . X . . . . . X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

At the time, at was considered the usual move here. The book explains that after in this diagram, the reply at is a strong move, and "white can't expect a good result after cutting at a". The continuation is:

$$Wc19 Unfavourable capturing race $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O 7 . | $$ | . . . O . . . . . . . . . . . X 4 5 . | $$ | . . . . . . . . . . . . . . . X O O 6 | $$ | . . . O . . . . . , . . . . 2 1 X X . | $$ | . . . . . X . . . . . X . 0 9 3 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$Wc19 Unfavourable capturing race $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O 7 . | $$ | . . . O . . . . . . . . . . . X 4 5 . | $$ | . . . . . . . . . . . . . . . X O O 6 | $$ | . . . O . . . . . , . . . . 2 1 X X . | $$ | . . . . . X . . . . . X . 0 9 3 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

$$Wc19 The right time to tenuki: White stands better $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . c . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . . . X X O . | $$ | . . . . . . . . . . . . . . a X O O X | $$ | . . . O . . . . . , . . . b X O X X . | $$ | . . . . . X . . . . . X 2 X O O X . . | $$ | . . . . . . . . . . . . . 1 . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$Wc19 The right time to tenuki: White stands better $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . c . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . . . X X O . | $$ | . . . . . . . . . . . . . . a X O O X | $$ | . . . O . . . . . , . . . b X O X X . | $$ | . . . . . X . . . . . X 2 X O O X . . | $$ | . . . . . . . . . . . . . 1 . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

The book gives a few more moves and another variation to convince us that white loses the capturing race.

At this point, I think most humans would say something like: OK, if you cut at Q4 then you get captured, so the cut at Q4 doesn't work. There's no point cutting if your stone gets captured straight away. You're just helping the opponent to build up strength. A bit like mochikomi.

KataGo says: Hang on, just exchange white a for black b, then play white c, and I assess the position as favourable for white! What's more, cutting at Q4 and getting captured is significantly better than an early tenuki!

$$Wc19 Early tenuki: close to even $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 3 . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . X O . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . , . . . . . a X 2 . | $$ | . . . . . X . . . . . X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$Wc19 Early tenuki: close to even $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 3 . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . X O . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . , . . . . . a X 2 . | $$ | . . . . . X . . . . . X . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

This last diagram is assessed by KataGo as pretty much even, as compared with the previous diagram giving white an advantage. It looks like to cut first at a, get captured and give away a bunch of solid territory in the corner is not merely OK, it's positively better than not giving away that territory!

So how are we supposed to interpret this?

[kvasir]

This is Relentless chapter 1, variation 10, a sequence that didn't actually come up in the game:

Judging by how quickly pros appeared to churn through new variations in the mini- and micro-chinese openings then this should be a ripe field to find examples of questionable play by pros and it could also be understandable from the complexity of reading and judgment involved.

$$Wc19 Unfavourable capturing race $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O 7 . | $$ | . . . O . . . . . . . . . . . X 4 5 . | $$ | . . . . . . . . . . . . . . . X O O 6 | $$ | . . . O . . . . . , . . . . 2 1 X X . | $$ | . . . . . X . . . . . X . 0 9 3 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$Wc19 Unfavourable capturing race $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O 7 . | $$ | . . . O . . . . . . . . . . . X 4 5 . | $$ | . . . . . . . . . . . . . . . X O O 6 | $$ | . . . O . . . . . , . . . . 2 1 X X . | $$ | . . . . . X . . . . . X . 0 9 3 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

I question . This seems to fill black's own liberties.

$$W $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 3 O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . a . X X O . | $$ | . . . . . . . . . . . . . . 1 X O O X | $$ | . . . O . . . . . , . . . 2 X O X X . | $$ | . . . . . X . . . . . X X X O O X . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+

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[go]$$W $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . 3 O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . a . X X O . | $$ | . . . . . . . . . . . . . . 1 X O O X | $$ | . . . O . . . . . , . . . 2 X O X X . | $$ | . . . . . X . . . . . X X X O O X . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ +---------------------------------------+[/go]

White can play lot of plastering moves on the outside after to . Maybe white could consider other moves for , like a.

$$W $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . . . X X O . | $$ | . . . . . . . . . . . . . . . X O O X | $$ | . . . O . . . . . , . . . . X O X X . | $$ | . . . . . X . . . . . X X X O O X . . | $$ | . . . . . . . . . . . . . O . 3 1 2 5 | $$ | . . . . . . . . . . . . . . . . . 4 . | $$ +---------------------------------------+

Click Here To Show Diagram Code

[go]$$W $$ +---------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . . . . . . . . . . . . X O O . | $$ | . . . O . . . . . . . . . . . X X O . | $$ | . . . . . . . . . . . . . . . X O O X | $$ | . . . O . . . . . , . . . . X O X X . | $$ | . . . . . X . . . . . X X X O O X . . | $$ | . . . . . . . . . . . . . O . 3 1 2 5 | $$ | . . . . . . . . . . . . . . . . . 4 . | $$ +---------------------------------------+[/go]

White also appears to have a squeeze on the inside. If like this then black at least needs to read it to the end.

[John Fairbairn]

So how are we supposed to interpret this?

Make 2.6 squillion playouts?

At the more human level of interpretation, I think two points are missing in the analysis so far.

1. This really is a highly tactical position, and therefore not the sort of position we can easily (ever, even?) draw inferences from (and - am I right in assuming this? - therefore the sort of position where a different depth of analysis by katago could produce startlingly different variations.

There is even some human evidence of the highly tactical considerations. First, the Relentless commentary says the variation shown in the corner only works for Black because he has a stone at precisely M3. Second, the same joseki was played by Yi Se-tol later in the book (Chapter 34) except that he diverged a little and induced a big mistake by Black.

2. But if we do insist on trying to draw lessons from this position, I would say the first step is to get the language right. The sentence I would quibble with (strongly) is:

It looks like to cut first at a, get captured and give away a bunch of solid territory in the corner is not merely OK, it's positively better than not giving away that territory!

I don't see it at all as White giving away a lot of solid territory. I see it as ajitsuki - adding aji. Furthermore, White retains the option of adding even more aji here. The game in Chapter 34 illustrates the sort of aji that exists. I would even say that it is dangerous to call White Q4 a cut. Of course it is one, but using that word alone brings in too readily connotations of cut-and-capture or cut-and-kill. I would suggest the right way to express Q4 here would be to call it "a probe with the cut at Q4". I also infer that katago might think making this probe early is good because it is more likely that Black will play the hane on the outside instead of the inside (which seems like a plausible line, after all). So, is the result of this "probe" a loss for White? I hardly think so. The aji even at present definitely requires at least one but probably two repair moves from Black - maybe O5 at this stage and maybe Q2 later. If White enriches the aji, Black will surely have to add stones inside. So that will mean White has played four stones inside Black's area but Black will also have to play inside in his area to more or less the same extent. By tewari analysis, therefore, White has lost nothing - but has gained aji. White's bottle is not half empty. It is half full.

Changing the language like this can often change the evaluation.

[xela]

I don't see it at all as White giving away a lot of solid territory. I see it as ajitsuki - adding aji. Furthermore, White retains the option of adding even more aji here. The game in Chapter 34 illustrates the sort of aji that exists. I would even say that it is dangerous to call White Q4 a cut. Of course it is one, but using that word alone brings in too readily connotations of cut-and-capture or cut-and-kill. I would suggest the right way to express Q4 here would be to call it "a probe with the cut at Q4". I also infer that katago might think making this probe early is good because it is more likely that Black will play the hane on the outside instead of the inside (which seems like a plausible line, after all). So, is the result of this "probe" a loss for White? I hardly think so.

Thanks John, this is helpful.

My interpretation of the book is that they were giving these diagrams to show that white loses the capturing race after cutting, and it seems to me there was a clear implication that this is seen as a bad result. But your comments on aji and probing give some hints on how we might "understand" a different assessment.

Going back to our unreliable oracle:

• KataGo tells us not just the evaluation, but also the predicted ownership of each location on the board. Of course this is a poor proxy for "future territory": there's lots of scope for trades and other surprises. But here, after half a million playouts, the bottom right remains shaded dark grey (not absolutely black). My interpretation: KataGo is pretty confident that white has lost this capturing race, not even a ko to be seen, but there's still an outside chance that black might sacrifice the corner (for example, in response to an invasion at the bottom).
• The chapter 34 game is quite a different beast. There, KataGo starts out believing that white's cut at Q4 "works" in the human sense: thanks to the earlier shoulder hit, white can now cut and live inside. After move 33, after alleged mistakes from both sides, KataGo now shows the white stones as totally dead (no shades of grey here) but with the position overall rated as even, since white has a bunch of forcing moves on the outside. I find this easier to understand. But then the game move 34 saves the white stones in the corner according to KataGo, and is also rated as a small mistake by KataGo; sacrificing the stones and getting the forcing moves would have been better! At this point I'll stop: the variations are more intricate and it's too easy to get lost in the all the twists and turns.

[kvasir]

• KataGo tells us not just the evaluation, but also the predicted ownership of each location on the board. Of course this is a poor proxy for "future territory": there's lots of scope for trades and other surprises. But here, after half a million playouts, the bottom right remains shaded dark grey (not absolutely black). My interpretation: KataGo is pretty confident that white has lost this capturing race, not even a ko to be seen, but there's still an outside chance that black might sacrifice the corner (for example, in response to an invasion at the bottom).

This interpretation is problematic.

It would be tremendously useful to have an estimate of territory that expresses how strong the each players grip on that territory is. If a value of 1 meant the territory is secure for black, 0 that it was secure for white and 0.5 that it could equally go either way, then that would match very well how most human players seem to think. I don't know exactly what values like 0.75 or 0.25 would mean but with some calibration they should have some useful meaning. However, this is not at all what KataGo estimates, it is estimating who owns each intersection after both players play the best moves.

Black's hold on the territory in the corner is conditional on black playing another move there. That move is not urgent but it still needs to be played eventually. We can interpret that to mean black has at least 50% chance of defending the territory later.

Now if KataGo plays first in the corner, which my KataGo thinks it should after unspecified number of playouts, then white gets a chance to start a ko. We can interpret that to mean there is a 25% chance that there will be a ko and 25% chance that black will defend here. Now we are at 75% black territory and 25% ko.

$$W Ko. KataGo prefers a to 9 by a very thin margin and switches from a to 3 after many playouts. Note that white's small lead is huge for computers. $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . 9| $$ | . . . . . . . . . . . . . O 7 . 3 4 .| $$ | . . . . . . . . . . . . . . . 5 8 6 .| $$ +--------------------------------------+

Click Here To Show Diagram Code

[go]$$W Ko. KataGo prefers a to 9 by a very thin margin and switches from a to 3 after many playouts. Note that white's small lead is huge for computers. $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . 9| $$ | . . . . . . . . . . . . . O 7 . 3 4 .| $$ | . . . . . . . . . . . . . . . 5 8 6 .| $$ +--------------------------------------+[/go]

Depending on the position ko can mean 100% black territory or 0%. One interpretation is that since black takes first in the ko then it is 33% black territory. Let's adopt that interpretation and say black has 83% of the territory (50% + 25% + 25% * 33%).

That isn't the end of it, white has some chance of controlling territory here. With a similar interpretation as before we have 25% chance to start a ko, which white is 67% of the way to turn into territory. White therefore owns 17% of the territory. Let's be clear about something,

It always amazes me that KataGo can (seemingly) solve such positions so quickly. Of course there are some errors but often it seems to find the right moves before it can show a primary variation that is convincing. I have ignored details about for example intersections that could be owned by black in some cases and never by white. If this is troubling, then you can imagine one of the intersections which do change hands in the ko fight. Anyway, I believe in the simplified case that there is 83% ownership by black and 17% by white. If we denote black and white probability of controlling by B and W then the ownership on scale -1 to 1, -1 meaning white 100% and 1 meaning black 100%, could be defined as ownership := B - W.

The ownership turns out to be 0.66 with simplified assumptions. If we had instead assumed black was closer to winning the ko we would have got a higher number, for example 0.84 if black was assumed to take immediately in the ko. We could also declare one or the other side will always win the ko, which is often what I see KataGo do.

If you read all the way here, and probably also if you didn't, then it should already be clear that it is necessary to make lot of assumptions before we decide who is the owner of the territory in the corner. When we assume gote moves and ko's can go either way in the course of the game we still get a value that is close to complete black ownership.

Why is this important? It shows how we can get a value close black owning most of the corner and white having almost no stake there despite there being a ko that white can force (according to KataGo). Playing the ko immediately is just slight worse than the primary variation. To put it differently, starting a ko and winning it isn't better than playing normal moves, but the ko is there waiting. This is an example of how there can be something that calls for immediate attention that doesn't affect the evaluation of by KataGo, it is therefore a counterexample for the claim that one can go backward from the ownership estimation by KataGo and say one side has a firm grip on the area. Black doesn't have a firm grip on the corner, instead black owes a move in the corner.

[John Fairbairn]

The following sentence from Shibano Toramaru in his latest scribblings on AI seems worth quoting in the context of this thread@

"The appearance of AI has vastly changed both how to think about the fuseki order of moves, and also the order of moves in josekis, as everyone will knows."

The Molesworthian "any fule kno" made me smile because, even if it's true, not everyone applies that knowledge. For good reason of course. It's damn hard to know WHY to change move orders, and even harder to know when to take leave of absence from an ongoing joseki and when to return to it later, something AI bots do all the time and something I've never seen pros talk about in any significant way. In fact, I've often wondered if it's part of a randomising function in the bots to ensure they don't play the same way every time =- something that was the bane of early chess computers.

[RobertJasiek]

know when to take leave of absence from an ongoing joseki and when to return to it later, something AI bots do all the time [...] I've often wondered if it's part of a randomising function in the bots

No.

With sufficient playouts, Katago "knows why" to play elsewhere and when to return. Having studied also this during the previous 6 months, I could often understand it in terms of human reasoning. If only I invest sufficient time for analysis and my thinking, I always find some explanation convincing for myself. Often, such explanations are preliminary because they depend on hard evaluation of move values during the opening or middle game. In such cases, I learn "this kind of action is more urgent than that one".

[Gérard TAILLE]

Black's hold on the territory in the corner is conditional on black playing another move there. That move is not urgent but it still needs to be played eventually. We can interpret that to mean black has at least 50% chance of defending the territory later.

Now if KataGo plays first in the corner, which my KataGo thinks it should after unspecified number of playouts, then white gets a chance to start a ko. We can interpret that to mean there is a 25% chance that there will be a ko and 25% chance that black will defend here. Now we are at 75% black territory and 25% ko.

I do not understand how black can kill white with only one move. I think if black plays first then the position becomes yose ko and white has still a chance to live.
OC if white plays first the resulting position is a simple ko.

[kvasir]

Black's hold on the territory in the corner is conditional on black playing another move there. That move is not urgent but it still needs to be played eventually. We can interpret that to mean black has at least 50% chance of defending the territory later.

Now if KataGo plays first in the corner, which my KataGo thinks it should after unspecified number of playouts, then white gets a chance to start a ko. We can interpret that to mean there is a 25% chance that there will be a ko and 25% chance that black will defend here. Now we are at 75% black territory and 25% ko.

I do not understand how black can kill white with only one move. I think if black plays first then the position becomes yose ko and white has still a chance to live.
OC if white plays first the resulting position is a simple ko.

I see my post could use some editing, but I'm tired

This comment about black owing a move is for the initial position. Let's say white makes the forcing move as in the diagram but after that there is a choice between a or b. If white plays a, then black is left owing a move to protect against b. KataGo realizes after quite a few playouts that it can also play b as a forcing move and lock-in the ko aji.

$$W $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . .| $$ | . . . . . . . . . . . . . O . . b . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ +--------------------------------------+

Click Here To Show Diagram Code

[go]$$W $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . .| $$ | . . . . . . . . . . . . . O . . b . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ +--------------------------------------+[/go]

Either or can be points to tenuki if you look at the diagram in my previous post. The example of ownership does not take into account that the decisions to skip or is correlated in some way. I also don't mention that the whole corner is shown as white when white starts the ko. The example is too complicated as it stands.

Let me copy the diagram here.

$$W Ko. KataGo prefers a to 9 by a very thin margin and switches from a to 3 after many playouts. Note that white's small lead is huge for computers. $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . 9| $$ | . . . . . . . . . . . . . O 7 . 3 4 .| $$ | . . . . . . . . . . . . . . . 5 8 6 .| $$ +--------------------------------------+

Click Here To Show Diagram Code

[go]$$W Ko. KataGo prefers a to 9 by a very thin margin and switches from a to 3 after many playouts. Note that white's small lead is huge for computers. $$ +--------------------------------------+ $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . O . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . X . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . a . . . . . . . . . . . . . X . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . , . . . . . , . . . . . , O . .| $$ | . . . . . . . . . . . . . . . . . . .| $$ | . . . . . . . . . . . . . . . . O . .| $$ | . . . . . . . . . . . . . . . X O O .| $$ | . . . O . . . . . . . . . . . X X O .| $$ | . . . . . . . . . . . . . . 1 X O O X| $$ | . . . O . . . . . , . . . 2 X O X X .| $$ | . . . . . X . . . . . X X X O O X . 9| $$ | . . . . . . . . . . . . . O 7 . 3 4 .| $$ | . . . . . . . . . . . . . . . 5 8 6 .| $$ +--------------------------------------+[/go]

The point is that the ownership shows something that depends on the principle variation, not on all the possibilities. Despite that KataGo predicts black controls or owns the corner, the aji of starting a ko in the corner is very real.

[RobertJasiek]

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X 2| $$ . X X X O O X 3 O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+

Click Here To Show Diagram Code

[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X 2| $$ . X X X O O X 3 O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+[/go]

$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O 3| $$ . . . . O X O O X| $$ . . . X X O X X 1| $$ . X X X O O X X 2| $$ . . . O O . O X X| $$ . . . . . O X X .| $$ -----------------+

Click Here To Show Diagram Code

[go]$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O 3| $$ . . . . O X O O X| $$ . . . X X O X X 1| $$ . X X X O O X X 2| $$ . . . O O . O X X| $$ . . . . . O X X .| $$ -----------------+[/go]

$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . . . O O . O X X| $$ . . . . . O X X .| $$ -----------------+

Click Here To Show Diagram Code

[go]$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . . . O O . O X X| $$ . . . . . O X X .| $$ -----------------+[/go]

What ko? White is dead in perpetual ko, no? Or what else?

$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . 2 1 O O . O X X| $$ 4 3 . 5 . O X X .| $$ -----------------+

Click Here To Show Diagram Code

[go]$$W $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . 2 1 O O . O X X| $$ 4 3 . 5 . O X X .| $$ -----------------+[/go]

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ 1 X O O O . O X X| $$ X O . O . O X X .| $$ -----------------+

Click Here To Show Diagram Code

[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ 1 X O O O . O X X| $$ X O . O . O X X .| $$ -----------------+[/go]

Suppose Black connects. Not triple ko but White dead. Sort of. To avoid dame, Black needs to dissolve before the game end after filling all other dames to avoid J1989-in-seki. Usually, Black can.

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . X O O O . O X X| $$ X O 1 O . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X X X| $$ . X O O O . O X X| $$ X O 1 O . O X X .| $$ -----------------+[/go]

Suppose Black ko captures. Better. Afterwards, White cannot remove the big black string but Black can remove the big white string. White is dead in perpetual ko. So again: what ko?!

[Gérard TAILLE]

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X 2| $$ . X X X O O X 3 O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X 2| $$ . X X X O O X 3 O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+[/go]

Suppose Black ko captures. Better. Afterwards, White cannot remove the big black string but Black can remove the big white string. White is dead in perpetual ko. So again: what ko?!

I think your is a mistake. My proposal is:

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O . O X 1| $$ . . . . . O X X .| $$ -----------------+[/go]

[kvasir]

At first impression there appears to be this ko. White has local threats. I learned long ago that with ko it is not about finding the ko as much as it is about finding the right ko.

Oh no, Gerard beat me to posting this.

$$B $$ . . . . . 4 O . .| $$ . . . . 5 X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O 3 O X 1| $$ . . . . . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . 4 O . .| $$ . . . . 5 X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O 3 O X 1| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Wm6 $$ . . . . . O O . .| $$ . . . . X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X 3| $$ . X X X O O X 2 O| $$ . . . O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Wm6 $$ . . . . . O O . .| $$ . . . . X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X 3| $$ . X X X O O X 2 O| $$ . . . O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Bm9 $$ . . . . 5 O O . .| $$ . . . 4 X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 1| $$ . . . X X O X X 2| $$ . X X X O O X X .| $$ . . . O O 3 . X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Bm9 $$ . . . . 5 O O . .| $$ . . . 4 X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 1| $$ . . . X X O X X 2| $$ . X X X O O X X .| $$ . . . O O 3 . X X| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Wm14 $$ . . . . X O O . .| $$ . . . O X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 3| $$ . . . X X O X X O| $$ . X X X O O X X .| $$ . . 2 O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Wm14 $$ . . . . X O O . .| $$ . . . O X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 3| $$ . . . X X O X X O| $$ . X X X O O X X .| $$ . . 2 O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+[/go]

[Gérard TAILLE]

At first impression there appears to be this ko. White has local threats. I learned long ago that with ko it is not about finding the ko as much as it is about finding the right ko.

Oh no, Gerard beat me to posting this.

$$B $$ . . . . . 4 O . .| $$ . . . . 5 X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O 3 O X 1| $$ . . . . . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . 4 O . .| $$ . . . . 5 X O O .| $$ . . . . . X X O 2| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X . O| $$ . . . O O 3 O X 1| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Wm6 $$ . . . . . O O . .| $$ . . . . X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X 3| $$ . X X X O O X 2 O| $$ . . . O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Wm6 $$ . . . . . O O . .| $$ . . . . X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O X| $$ . . . X X O X X 3| $$ . X X X O O X 2 O| $$ . . . O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Bm9 $$ . . . . 5 O O . .| $$ . . . 4 X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 1| $$ . . . X X O X X 2| $$ . X X X O O X X .| $$ . . . O O 3 . X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Bm9 $$ . . . . 5 O O . .| $$ . . . 4 X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 1| $$ . . . X X O X X 2| $$ . X X X O O X X .| $$ . . . O O 3 . X X| $$ . . . . . O X X .| $$ -----------------+[/go]

$$Wm14 $$ . . . . X O O . .| $$ . . . O X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 3| $$ . . . X X O X X O| $$ . X X X O O X X .| $$ . . 2 O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+

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[go]$$Wm14 $$ . . . . X O O . .| $$ . . . O X X O O .| $$ . . . . . X X O O| $$ . . . . O X O O 3| $$ . . . X X O X X O| $$ . X X X O O X X .| $$ . . 2 O O X 1 X X| $$ . . . . . O X X .| $$ -----------------+[/go]

The position is not easy to analyse. My point here is that I do not understand why white needs ko threats!
My view is the following:

$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X b O| $$ . . . O O . O X a| $$ . . . . . O X X .| $$ -----------------+

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[go]$$B $$ . . . . . . O . .| $$ . . . . . X O O .| $$ . . . . . X X O .| $$ . . . . O X O O X| $$ . . . X X O X X .| $$ . X X X O O X b O| $$ . . . O O . O X a| $$ . . . . . O X X .| $$ -----------------+[/go]

In the position above the local temperature is about 9 points (?)
If black plays first by a move at "a" I think the temperature remains equal to about 9 points. As a consequence if you assume the ambiant temperature equal to 13 points then you do not need ko threats to fight the ko. IOW black at "a" is a mistake if ambiant temperature if greater than 9.
On the other hand if white plays first by playing at "b" then the temperature increases up to about 14 points.
My expectation is the following. White will start the ko very soon and will probably win the ko and kill black group in the corner. In exchange black will be able to play tenuki two times. If the ambiant temperature is equal to 13 that means that black can consider he has 26 ( 2 * 13) points in the corner.

Maybe I am wrong but what is your own evaluation of the local temperature?

[kvasir]

Maybe I am wrong but what is your own evaluation of the local temperature?

It is one of those cases when it is moderately hard to calculate but knowing if you got the right answer is much harder. So I can calculate for you but it would take too much effort to verify beyond my intuition about what is happening. It is good practice so I'll humor you

I only noted down some numbers but otherwise did it without playing out variations. Since I did this in my head we have to go backwards and I'm not going to explain how I reached the conclusion which I'll try to summarize.

The way I see it, if black takes and wins the ko he is at +17 but if white starts the ko there are two choices. White can choose a big ko to drive up the value per move or a small ko. The thing is that if he chooses the big ko he will forego an endgame move here but if he chooses the small ko he gets that endgame as part of starting the ko.

Most ko are trades, I assume this one is also, therefore I don't want to give up that endgame to drive up the value per move. The small ko then it is.

I have black at +16 if he ends the small ko, I have white at -17 if he ends the same ko. I'll ignore fractions and say the value of the ko will be at +4 when white plays to start it.

How about if black stars a ko immediately? In that case he can win the ko to be at +16 (not sure why I got one less here, I'll just go with it). White, however, can only go back to needing a move to start the small ko.

We, therefore, have a situation of black being able to move to +17 in two moves and white being able to move to +4 in one move. The value of a move in this situation is just 4 or 8 as you like to say

Black won't make a move here for a long time.

OK, OK, I'm ignoring that there is an approach ko but I doubt it is a good idea for black when the situation otherwise isn't urgent. I'm ignoring the approach ko for the reason that white doesn't need to spend an extra move, white in fact gains a move but needs to come up with lot of threats.

There is something important that I have saved for last. Which is the territory in the corner. Since the move was worth ~4 and white were to move to +4 then the territory would seem to be +8 but that is for an arbitrary region. I think we can count some naive +25 points in the corner before white locked-in the aji. Now it is +8, some naive 17 points are already erased. Maybe it is no wonder that the score evaluation is -3 to -4?