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 Post subject: Question for Bill
Post #1 Posted: Tue Jun 13, 2017 2:37 am 
Oza

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Bill

This question was prompted by your current explanation of an endgame position from Mathematical Go. I'm making a different thread for what will become obvious reasons.

The topic here is 'bullying' (ijime). A few introductory things can be said about this concept. (1) It crops up probably several times in every pro game, although is not always mentioned. (2) It is nevertheless very commonly mentioned in Japanese texts. It may not be apparently so common in English texts but that may be because it gets lost in the swirl of different translations. (3) It has two aspects: actual execution of the bullying and pre-emptive action. (4) Pre-emptive action (i.e. gote) is by far, by miles, more apparent in pro games than in amateur games, and it is in fact this which makes it so common a feature in pro games. (5) Despite being so common, I have never seen an article on why pre-emptive action is so important. That's where you come in :)

Here is an example I have just come across, from a game between Iwamoto and Onoda.



White played first at the square point (the triangled exchange then followed). Iwamoto said this was because he feared that otherwise a Black peep at K9 would make his game insupportable. The word ijime was not used but can clearly be inferred. It is my sense that most amateur players, even (perhaps especially) strong ones would say that this White group has plenty of scope to make two eyes and so they would leave it. There is a thin group at the top, and if our amateur is in a rare pre-emptive mood he might play there, on the grounds that it may be a smaller group but for that very reason it needs more help - the big group can take care of itself ("big groups never die"). I suspect, however, that most amateurs would be looking for something on the right side.

Now, just in case someone raises the point that White's square move attacks Back above, so is not gote, let me repeat that it was followed by the triangled exchange, and it seems to me that the square move then is not doing anything other than pre-empting bullying.

Black now played A, an uncommented move which I find even harder to understand, and now White appeared to feel he was safe from bullying here. This was not quite true, as the subsequent play showed - White lived easily enough but in territory terms this group made about 6 points. White now played B, and again added a comment that he was pre-empting the (bullying) invasion.

Purely in terms of form I feel I know exactly what is going on, but in terms of actual substance I have virtually no feel for what is happening. Since pre-emptive bullying is a kind of reverse sente, it occurred to me that this concept, even though a middle game one, can perhaps be explained by reference to endgame play, and maybe by extending the corridor theory?

Another common term in this sort of position is that White is making himself thick (i.e. thicker in terms of eventual boundary plays), but again I'm wondering whether this can be subsumed in a more general explanation based on endgame theory.

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Post #2 Posted: Tue Jun 13, 2017 5:41 am 
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Interesting. I thought about how to apply this to other parts of the game, too.It seemed to me, that it would also be useful in the opening, were there is also often a struggle to get the last big point(tedomari), where you would mabe make a move that is slightly smaller then the alternative on paper, but it ensures you get the last big point afterwards.
I wasnt sure though, how to apply bills methods exactly, because it is stated that an infinitesimal is always woth less than any positive miai value, and I didt understand yet, how to include the fact that I might want moves of smaller miai value due to tedomari into the equation(also I might not want them, if I need to give up too much, so I need to weigh those things)

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Post #3 Posted: Tue Jun 13, 2017 8:44 am 
Oza

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Quote:
Is White's square move not an example of 'honte'? I.e., it prevents future problems while having a second purpose in diminishing Black's central strength.


I wouldn't say so, though there are some overlapping elements. A honte implies an usote, and choosing it means you are taking the safe option instead of the risky one. It's a tactical option. With a move that pre-empts bullying, there is not really a local option - it is a strategic choice.

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Post #4 Posted: Tue Jun 13, 2017 9:28 am 
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Interesting questions, John. I must say, though, that ijime is not something that I have studied, per se. The prevention of ijime is something that I noticed when I first started studying professional games: "Why is White protecting a live group?" for example. I concluded that the attack would have been too big. And that is my impression in this case, particularly for White's large group. An attack would allow Black to cash in on his overall thickness.

I expect that ijime has whole board implications. If it is only a local sente, who cares? It would not be anything special. The same is true for kikashi, OC. John, what is the relation between ijime and kikashi?

Along those lines, Sakata was known for playing kikashi early. Would you also say that playing ijime was a significant part of Sakata's style?

Thanks. :)

I'll address the relevance, if any, of Combinatorial Game Theory in my next note. :)

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Post #5 Posted: Tue Jun 13, 2017 10:48 am 
Oza

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John, what is the relation between ijime and kikashi?


I'm not sure there is one (except coincidentally). The underlying meaning of kikasu (ie the causative of kiku) is to make something effective. In other words, you play it now to ensure it has its full effect because it might lose its effect later. There is an element of judgement in there, and Sakata was obviously less sanguine than others about deferring such moves.

Also, kikashi tends to be a single move, maybe a couple sometimes, whereas ijime is a sustained Rottweiler attack. That said, in pro games ijime is not played just for the sake of it, but whenever there is a reason over and above bullying (e.g. you want to stop a possible connection). In that sense it has elements of forcing, but I consider that as a side effect.

For other readers, ijime (bullying or harassment) refers to moves against an enemy group that has to answer submissively, often just to make minimum life, and which typically ends up wholly enclosed. Every move by the persecutor is thus automatically adding value to his own position, either as territory or strength, and nothing is added for the victim. His group is shut out of the rest of the game and all he gets is to secure the few points he already had.

It can be allowed if there is sufficient compensation elsewhere. The persecuting side then has to find a way to make use of his local advantage, nevertheless, and for that reason the ijime episode, even though tactical, often comes to dominate the strategy in the rest of the plot.

However, ijime by itself like that is easy enough to understand. What I am asking about is the common pro habit of pre-empting ijime.

Switching from plain ignorance to a higher form of ignorance - speculation - I have long had the feeling that ijime (executive as well as pre-empted) in terms of identifiable nuggets has been more characteristic of older go than modern go. Hyperaggressive modern go often seems like a constant stream of ijime by both players! Or maybe that shows even more of my ignorance.


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Post #6 Posted: Tue Jun 13, 2017 11:46 am 
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Combinatorial Game Theory (CGT), in its modern form, was inspired by go, because, as play continues in a game of go, the board tends to break down into independent, or relatively independent regions of play. Either player could be the first to play in a given region, and either player might switch from the current region to another. We can thus consider each independent region as a game in itself, without saying which player will play first. The whole board, then, is a combination of such games, which we call combinatorial games. Combinatorial games differ from other turn-taking games where the first player is specified. The value of those games is determined by the results of minimax play. If we knew perfect play on the 19x19 board, the value of the game, with Black to play first, would be the komi. Our best guess for komi is currently 7. But by symmetry, we know that the mean value of go on the empty 19x19 board as a combinatorial game is 0. :)

Because of the tendency of a game of go to break up into a combination of independent or nearly independent games, many of the ideas of combinatorial game theory were foreshadowed in go theory. These include miai, getting the last play, and sente gaining nothing. The evaluation of a go region as a combinatorial game (without using such terminology, OC) goes back at least two centuries. :)

Given the history of CGT ideas in go, what does modern CGT offer go? IMHO, it offers better and more informative methods for evaluating positions and plays, especially for complicated ko positions, a deeper understanding of getting the last play and drops in temperature, and conceptual clarification. :)

What light can it shed on ijime? Not having studied ijime, I can't say, but I think not much. If, as I suppose, ijime is a whole board phenomenon, then strictly speaking, CGT has little to say about it. But even when regions of the board are not, strictly speaking, independent, their values, and the values of plays may be approximated, and may serve as guides to play. (OC, go players were aware of this long before CGT was developed. :)) One question, then, is how much the reverse sente to prevent ijime gains?

Now, given a number of independent regions where a gote or reverse sente gains the same amount, CGT tells us that, as a rule, it is best to take sente and, next, plays that threaten sente. It also tells us that if the gote are not miai, then it is better to take a gote before a reverse sente. We also know that these rules can be good guides, even if the sizes of plays are only approximately equal, and even if the regions are only approximately independent. If anything, then, CGT raises questions about playing reverse sente to prevent ijime.

One possible reason, which I think applies in this case, is that preventing ijime is just a large play. Another possible reason is that other large plays are miai, so that preventing ijime is a kind of last play.

But there is still the question of why pros prevent ijime so often. I assume that it is not an error to do so, as the pros estimate the size of plays and are aware of the value of getting the last big play. Do we see the same phenomenon in AlphaGo vs. AlphaGo games? Maybe not. In those games AlphaGo plays a very light style. If it is ready to sacrifice stones, how can it be bullied? And if it cannot be bullied, why bother to prevent bullying?

----

Thanks for your previous note, John, which I have just read, after writing the above. :) I am not sure how much I have just written here is pertinent, but here goes. ;)

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 Post subject: Re: Question for Bill
Post #7 Posted: Tue Jun 13, 2017 4:40 pm 
Oza

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Thanks, Bill. There is much to chew on in what you said, but what caught my eye most was:

Quote:
One possible reason, which I think applies in this case, is that preventing ijime is just a large play. Another possible reason is that other large plays are miai, so that preventing ijime is a kind of last play.


I would suggest that the idea that preventing ijime is just a large play is, for amateurs, better expressed as "bigger than you think." And that brings to mind Sekiyama's concept of gote no sente, which he took from kendo. I think it's easier to see in sword-fighting than in go that a retreat which offers a new way forward is often better than pushing forward all the time. And the fact that he felt he had to coin a term for go suggests the concept was a bit murky in go anyway.

One reason it's harder to see the value of gote in go may be that, unlike in kendo, the switch back to aggression is not necessarily immediate. Patience, and often lots of it, is required. I think it is fair to say that pros can see the value of switching back to sente much further ahead than we amateurs can. In that sense, too, we could say that an ijime-blocking move is a large play (or "bigger than you think").

FWIW, because I have noticed ijime-blocking moves so much I have tried them sometimes in my own games. The effect is strange: it always brings to mind Michael Redmond's aphorism that go is an easy game. I can see exactly what he means. I may lack the technique to translate that into "100 victories in 100 battles" but my winning ratio zooms up to silly levels. If you ask why I don't play that way all the time, it's because on most of the few occasions I play go it is for relaxation or unwinding, and I don't want to have to think. Ijime-blocking requires thought. It's rather like the way that listening to classical music is probably most rewarding intellectually, but it can be quite hard work, so we all tend to listen to pop, rock or folk instead.

The idea of ijime-blocking as a possible tedomari doesn't gel with me yet, but it's an interesting idea so I will keep it in mind as I encounter new games.

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Post #8 Posted: Tue Jun 13, 2017 6:04 pm 
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John Fairbairn wrote:
FWIW, because I have noticed ijime-blocking moves so much I have tried them sometimes in my own games. The effect is strange: it always brings to mind Michael Redmond's aphorism that go is an easy game. I can see exactly what he means. I may lack the technique to translate that into "100 victories in 100 battles" but my winning ratio zooms up to silly levels.


I believe that. Allowing a weak group to form and then get pushed around is almost certainly the single most common reason I lose games at my level. This might be a productive way to think about reducing that tendency. Thanks.

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Post #9 Posted: Wed Jun 14, 2017 1:36 am 
Oza

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For example, in the diagram, the marked stone is a thick move that denies Black prospects - specifically, the approach that aims at the peep - on the upper side. It also aims at weaknesses in Black's formation. (This example is taken from 「厚く打つ」, "Playing thickly".)


marcel: Yes. Though in actual play this narabi move in this position is rather rare (and relatively recent - it is due to Iwasa Kei whose style was once described as "elegant simplicity"). By far the commonest play is to push up at N16, and even those who opt for thickness prefer R16 more often. But the narabi has virtues.

I think that what this tells us is that the narabi is a stylistic choice, but I'd go further and say that all amateurs should try a sustained period of playing thickly like this, because it teaches patience and so takes you much deeper into the game.

Another aspect is that thus playing thickly is not necessarily heavy. Go Seigen once pointed out that if you add a nobi to, say, a string of two stones in the right circumstances, you are adding one move but it now takes the opponent two more moves to capture the group. Even without capture being involved, it takes the opponent a lot longer to go round your group and he has no forcing moves to help him on his journey (which brings us back to pre-emptive moves).

The narabi/nobi complex of moves is often underestimated. It seems to have become more popular around Shin-Fuseki times, interestingly at the same time as Hypermodern chess, and when Nimzovich first propounded his concept of prophylaxis. I read recently that most of Nimzovich's ideas have not really survived into modern chess strategy, but a shining example is prophylaxis. Maybe the same realisation has occurred in go.

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Post #10 Posted: Wed Jun 14, 2017 2:01 am 
Judan

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John Fairbairn wrote:
Quote:
For example, in the diagram, the marked stone is a thick move that denies Black prospects - specifically, the approach that aims at the peep - on the upper side. It also aims at weaknesses in Black's formation. (This example is taken from 「厚く打つ」, "Playing thickly".)


marcel: Yes. Though in actual play this narabi move in this position is rather rare (and relatively recent - it is due to Iwasa Kei whose style was once described as "elegant simplicity"). By far the commonest play is to push up at N16, and even those who opt for thickness prefer R16 more often. But the narabi has virtues.


r17 is another thick move for white in that position, stopping black's attachment there and aiming at things like the r13 invasion (though with r10 present maybe that's not as powerful as in wider positions, or ones in which white has a pincer on that side and you have a counter-pincer fight going on so you are attacking the pressing wall). It's one of those patient but powerful moves I appreciate when I see pros play it, but I don't think I play it much (I think more that I tend not to get into such positions than I lack the patience to play it, though that could also be a problem).

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Post #11 Posted: Wed Jun 14, 2017 7:32 am 
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Reminds me of this move, which I learned from Inseong:

Click Here To Show Diagram Code
[go]$$Bcm1
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . W . a . b . . . . . . . . . . . . |
$$ | . . O c . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O X . . . . . , . . . . . , . . . |
$$ | . . O X X O . X . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ----------------------------------------[/go]


After a move like this, even if black plays something like 'a', white can be free to play moves like 'b', etc. My inclination is usually to play something like 'c'.

When I learned this move, I called it the "Super Mario 2" move. That's because it reminded me of the special ability you have in Super Mario 2 to duck down for a couple of seconds, charge up, then jump higher than otherwise possible. It seems counterintuitive to duck down and wait in order to jump high, but it's the best way to really jump high.

Here, it seems counterintuitive to play solid and slow like this. But maybe it allows you to "jump higher" after building up power :-p

Image

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Post #12 Posted: Wed Jun 14, 2017 8:30 am 
Judan

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Amusing comparison Kirby; it seems your joseki has also jumped one line up the board ;-)


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Post #13 Posted: Wed Jun 14, 2017 8:31 am 
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Hi, Kirby. :)

Isn't this the diagram?

Click Here To Show Diagram Code
[go]$$Bcm1
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . W . a . b . . . . . . . . . . . . |
$$ | . . O c . . . . . . . . . . . . . . . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . O X . . . . . , . . . . . , . . . |
$$ | . . O X X O . X . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ----------------------------------------[/go]


Oh, darn! Uberdude beat me to it. :sad:

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Post #14 Posted: Wed Jun 14, 2017 9:17 am 
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John Fairbairn wrote:
Thanks, Bill. There is much to chew on in what you said, but what caught my eye most was:

Quote:
One possible reason, which I think applies in this case, is that preventing ijime is just a large play. Another possible reason is that other large plays are miai, so that preventing ijime is a kind of last play.


I would suggest that the idea that preventing ijime is just a large play is, for amateurs, better expressed as "bigger than you think."


There are a lot of bigger-than-they-look moves in go, including urgent plays and so-called double sente.

Quote:
The idea of ijime-blocking as a possible tedomari doesn't gel with me yet, but it's an interesting idea so I will keep it in mind as I encounter new games.


Well, they don't occur that often. :) I have noted prophylactic moves in the opening (whether they are anti-ijime moves or not) which leave the remaining ohba miai.

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Post #15 Posted: Wed Jun 14, 2017 9:17 am 
Honinbo

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Yup, that's what I meant.

I could blame the fact that I'm posting from a phone, but that's never stopped me before :-p

Indeed, I've been "squatting" from the go-study scene for too long, now.

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Post #16 Posted: Wed Jun 14, 2017 11:38 am 
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John Fairbairn wrote:
I'd go further and say that all amateurs should try a sustained period of playing thickly like this, because it teaches patience and so takes you much deeper into the game.


I heartily agree, as you know. :D

Quote:
The narabi/nobi complex of moves is often underestimated. It seems to have become more popular around Shin-Fuseki times, interestingly at the same time as Hypermodern chess, and when Nimzovich first propounded his concept of prophylaxis. I read recently that most of Nimzovich's ideas have not really survived into modern chess strategy, but a shining example is prophylaxis. Maybe the same realisation has occurred in go.


Oh, it seems to me that the idea of prophylaxis goes way back in go. Here is an example, from a Castle Game over 300 years ago:

Click Here To Show Diagram Code
[go]$$Bc Dosetsu (W) - Yasui Senkaku, 1698
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . 6 . . . . . . . . . 7 . . . . |
$$ | . . 0 , . . . . . , . . . . . , 5 . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . 1 , . . . . . , . . . . . , 8 . . |
$$ | . . . . 2 . . 3 . . 9 . . . 4 . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


:b1: - :b3: was the style in those days. :b9: is the prophylactic move, preventing a counter-pincer. I think that it was joseki back then, as it occurs in other contexts.

Click Here To Show Diagram Code
[go]$$Bcm11 Low extension
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O . . . . . . . . . X . . . . |
$$ | . . O , . . . . . , . . . . . , X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . 1 3 . . . . . . . . . . . . . . . |
$$ | . . . 2 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . 8 . . . . . . . . . . . . . . . |
$$ | . . . 4 7 . . . . . . . . . . . . . . |
$$ | . . X 5 6 . . . . , . . . . . , O . . |
$$ | . . . . O . . X . . X . . . O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Just a bit of the continuation. :) :b11: was joseki then, but it is too low. :w12: is a refutation. :b13: avoids getting pressed down, but then White has :w14:. I find it interesting that the ancients knew how to take advantage of :b11: without realizing that it was inferior. :)

The rest of the game is interesting. I like how White takes the bottom left corner, sacrificing a number of stones.


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Post #17 Posted: Fri Jun 16, 2017 1:48 am 
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A detailed positional judgement, sophisticated analysis or arcane terms for what simply is attack and defense are not needed. Even the roughest count tells us W leads on territory. To maintain his lead, he must defend some of his 3 weak groups. He defends the central weak group so as to also indirectly defend his other two weak groups. If instead he defended one of his other weak groups, he would be indirectly defending only one further weak group. Defending 3 is better than defending 2 weak important groups.

Simple.

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Post #18 Posted: Fri Jun 16, 2017 3:47 am 
Oza

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Quote:
Even the roughest count tells us W leads on territory. To maintain his lead...


But White lost, and there were no special tactical excitements such as kos or captures, and no mistakes were mentioned. Instead, Black said, shortly after this position, "I was confident" and White said, a little later, "I thought the game was close but I just didn't have enough."

Of course White was only a Japanese 9-dan, but I expect he and Black saw the bad aji on the lower side (where White got only 24 points and Black got a huge right corner). The bad aji is exacerbated by the continuing weakness in White's left centre group forcing him to defend in a way that let Black connect his own left centre group at J5.

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 Post subject: Re: Question for Bill
Post #19 Posted: Fri Jun 16, 2017 4:14 am 
Judan

Posts: 6725
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Rank: UK 4 dan
KGS: Uberdude 4d
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This position under discussion reminds me of a decision I faced recently in the British Challengers' league vs Andrew Kay:
I was white and black had just connected at the marked point following my invasion of the lower side (full game at http://eidogo.com/1XbHEBGLq ). The two main moves I was considering were a, a prophylactic move for my centre group, and b, solidly completing the lower side shape and in theory meaning the 3-3 is killable but with bad aji along the right side. If I don't play a move there black c is quite annoying: if I then answer at b black can comfortably live in the corner, and if I hane in the corner my 5 stones can get in trouble so I didn't actually gain much from invading the lower side. Taking gote to finish off is I believe usually considered a good result for white who gained a lot of territory, the issue is how much profit can black make from them attacking/bullying the white centre group with the thickness I have him. My initial feeling was to defend the centre group with a move at a, but after some thought I decided I didn't like that as 1) black d was still sente and I couldn't find an answer better than e which felt slack shape (and d is useful for black against white invasion at f later) and 2) wantd to get real profit at lower right. I also thought about white d or attach, but didn't like either. So in the end I played b for cash, daring black to attack, which he did at d and I answered with a fancy-pants attach. I wasn't particularly happy with the shape I got in the game, what do people think would be best or am I already in trouble? Perhaps my invasion of the lower side was not good, or move 36 (e8) should have been one line further at e9.
Click Here To Show Diagram Code
[go]$$Bc British Challengers 2017 round 5: Andrew Simons (me) 4d white vs Andrew Kay 4d black.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O X . . |
$$ | . . . . . . . . . O . . O . . O X . . |
$$ | . . . X . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . X . X . |
$$ | . . . X . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . f . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . X . d . a . , . . . . . O . . . |
$$ | . . . . . . e . . . . . . . . . . . . |
$$ | . . X . O . . . . . . . . . . . . . . |
$$ | . X . . . . O . . . . . . . . . . . . |
$$ | . X O O O . . O . . . . . . . . O . . |
$$ | . O X X . X . . . B X X . . . . . . . |
$$ | O . O X . . X . . X O X O b . O . . . |
$$ | . O O X . . . . . X O O O X . c . . . |
$$ | . O X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

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 Post subject: Re: Question for Bill
Post #20 Posted: Fri Jun 16, 2017 4:51 am 
Judan

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John Fairbairn wrote:
White lost, and there were no special tactical excitements such as kos or captures, and no mistakes were mentioned. Instead, Black said, shortly after this position, "I was confident" and White said, a little later, "I thought the game was close but I just didn't have enough."

Of course White was only a Japanese 9-dan,


If we see the game sequence, we can replace such nullarguments and failure to point out mistakes by mentioning some.

Quote:
but I expect he and Black saw the bad aji on the lower side (where White got only 24 points


24 is expected.

Quote:
and Black got a huge right corner).


Of course, Black gets something from the still weak W groups.

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