Click Here To Show Diagram Code

[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?

Click Here To Show Diagram Code

[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]

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:

Click Here To Show Diagram Code

[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:

Click Here To Show Diagram Code

[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]

Click Here To Show Diagram Code

[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!

Click Here To Show Diagram Code

[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?

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.



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

Click Here To Show Diagram Code

[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.

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.

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:



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.

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.

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.

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.

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.

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".

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.

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.

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.

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]

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]

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?

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]

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.

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 .|
$$ . X X X O O X X X|
$$ . 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?!

I think your is a mistake. My proposal is:

Click Here To Show Diagram Code

[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]

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.

Click Here To Show Diagram Code

[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]

Click Here To Show Diagram Code

[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]

Click Here To Show Diagram Code

[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]

Click Here To Show Diagram Code

[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:

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 .|
$$ . X X X O O X b O|
$$ . . . 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?

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?

It is a little difficult to understand your figures without the corresponding varaitions.
Let me try to show you my result after some more analysis.

Click Here To Show Diagram Code

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

I agree with you. In that position white will probably play first in the corner. I hesitate between white "a" and white "b" but eventually I prefer white "a" because white "b" gives black local ko threats and, should white win the ko, then black should be able to block the white group on the bottom side.

As a consquence I consider that the following sente exchange will take place:

Click Here To Show Diagram Code

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

Now what is the value of the ko?

If black wins the ko then the result would be

Click Here To Show Diagram Code

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

and we can assume the following endgame

Click Here To Show Diagram Code

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

Click Here To Show Diagram Code

[go]$$W
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . O . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . X . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . X . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . , O . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . O . .|
$$ | . . . . . . . . . . . . . . . X O O .|
$$ | . . . O . . . . . . . . . . . X X O O|
$$ | . . . . . . . . . . . . . . O X O O 7|
$$ | . . . O . . . . . , . . . X X O X X 5|
$$ | . . . . . X . . . . . X X X O O X . 6|
$$ | . . . . . . . . . . . . . O O X . X X|
$$ | . . . . . . . . . . . . . . X . X X .|
$$ +--------------------------------------+[/go]

If white wins the ko then the result would be

Click Here To Show Diagram Code

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

Here the evaluation of the result on the lower side is not easy : in the middle game the white invasion at "a" threatens a connection and in the endgame, depending on the exact configuration reached white will be able to play in sente an ogeima or a keima.
Assuming simply that white will be able to play the ogeima in sente then the final result will be

Click Here To Show Diagram Code

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

Finally considering the area marked here under

Click Here To Show Diagram Code

[go]$$W
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . O . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . X . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . X . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . , O . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . O . .|
$$ | . . . . . . . . . . . . . . . X O O .|
$$ | . . . O . . . . . . . . . . . X X O P|
$$ | . . . . . . . . . . . . . . O X O O Z|
$$ | . . . O . . . . . , . . . X X P Z Z P|
$$ | . . . . . X . . . . . X X X P P Z M P|
$$ | . . . . . . . . . M M M M P P Z P Z M|
$$ | . . . . . . . . . M M M M M M P Z Z M|
$$ +--------------------------------------+[/go]

If I am not wrong:
if black wins the ko then B+26
if white wins the ko then B-20
The swing value of the ko is 46 and the miai value is about 15 points.
After the first sente exchange black has taken the ko => the count of the position B+11 (26 - 15).

I can see if I can add diagrams later but I'm not sure it is so interesting for me

Your analysis is similar to mine but I'm suspicious of choosing the larger ko and not assuming that white is playing it to win. Possible the difference between these two ko isn't enough to make a difference. I mean that it is possible white also shouldn't play the smaller ko unless he means to guarantee that he wins the ko and in that case it is likely better to win the larger ko. My point was about that black should or could wait for white to start the ko, for now. Black appears to gain a move if white plays first in the corner. White would after all be playing two moves in a row in the corner.

Click Here To Show Diagram Code

[go]$$B Black plays away, white has choice between a larger ko with A and a smaller one with B, and of course tenuki.
$$ +--------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . O . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . X . . .|
$$ | . . X . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . X . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . , . . . . . , . . . . . , O . .|
$$ | . . . . . . . . . . . . . . . . . . .|
$$ | . . . . . . . . . . . . . . . . O . .|
$$ | . . . . . . . . . . . . . . . X O O .|
$$ | . . . O . . . . . . . . . . . X X O .|
$$ | . . . . . . . . . . . . . . O X O O X|
$$ | . . . O . . . . . , . . . X X O X X b|
$$ | . . . . . X . . . . . X X X O O X a O|
$$ | . . . . . . . . . . . . . O O . O X .|
$$ | . . . . . . . . . . . . . . . O X X .|
$$ +--------------------------------------+[/go]

We both used the method of finding a value for the ko and value per move but the calculus would change if we assume one or the other player could win the ko using good threats. I think white is close to being there, maybe he could win the ko. I did assume that white can't guarantee this outcome and is interested in a fair trade. Possibly this assumption is not good but it was what I thought was a reasonable assumption but these ko are large

It still seems likely to me that black shouldn't play first in the corner. They say every dog has its day, but usually you can't make up for playing more moves when less would have done. Without checking the principle variation that KataGo provides I can only guess at what happens if white tries to win the large ko.

Now that the questions have become so complicated I have began to wonder what KataGo says. I looked at it briefly before and recall that these questions weren't critical. Now that I'm checking again it appears they are even less critical than what I recalled.

I agree with you kvasir.
Remember what I said in my post https://lifein19x19.com/viewtopic.php?p=280202#p280202 :
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.

Let's expect that white will be able to play first in the corner and will be able to win the ko.
The question is now the following: when white will start the ko?
The question is difficult indeed. If the ambiant temperature is T then, in compensation for the corner killed by white, black will play tenuki two times and will gain 2*T points. That means that white wish to wait for a ambiant temperature as low as possible. In the other hand, if white wait too long then her good ko threats could disappear and black could also build her own ko threats.
In addition, if white wait too long then a difficult fight may take place elsewhere on the board and the temperature could stay quite high.
For those reasons I think white should start the ko quite early in order to win this ko and let black play tenuki two times.

It is not only a difficult question, it's a question that starts from lot of assumptions.

I'm very suspicious about arguments that start by declaring something like "white will win every ko". If you assume this, then ko becomes a one sided move that black can't play. If you state instead "white will win every ko while <some-condition> is true", then there is still a very strong assumption there.

Why not instead assume the player that starts the ko wins it? Possibly by ignoring a ko threat. When we do this we would eliminate capturing in the ko on the two conditions:

• If winning the ko in this way is not better than other moves in the game. We'd say it's dominated by some other move.
• If winning the ko ends up being worse than letting the other player play. We'd say it is reversed.

It is not clear which of these condition applies when we say that white will win the ko. Maybe that is why it appears as if white's fortunes could suddenly change if few moves later we say that black will win the ko? I can't relate this argument directly to this complex position but I think it is likely that if starting the ko immediately isn't white's strategic choice, then the change in who we say is winning the ko is somewhat fictious.

Take for example a gote endgame move. What happens if we declare white will play this move and then declare a few moves later that black will play there? We can often make good arguments about who is likely to play an endgame move. In this case nothing really happened unless either player made a mistake, our argument about who will play first might help us identify some mistakes but it isn't an assumption that we strictly require. It is also an argument that can lead us astray if we turn it into an assumption.

At the risk of relativize the argument one can also ask what happened in this case if it was never part of white's strategy to be certain about who wins this ko? In this position it doesn't seem reasonable to claim to know what the optimal strategy is or to claim that we could discover it. I think we need to be very careful when optimal strategy is so subtle.

I ran KataGo for 1 million playout on the four most interesting candidates. For some reason the playout statistics sums to a higher number in the following screenshots but it was the same 1 million in each case. Take a look at the attached image.

Seeing your post it appears that the move here after is part of top moves for black.

Click Here To Show Diagram Code

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

We previously concluded that it was not a good idea for black to play first in the bottom left corner. Does that mean that something was wrong in our analysis? I believed that the value of this black move was far smaller than 15 but it must be wrong. How do you calculate such value (without trying to be very accurate OC)?