Life In 19x19

In this series we'll discuss Takagawa's approach to Go by reviewing some of his games first without, then with AI. The purpose of reviewing without AI first is to focus on his moves and not be biased by AI suggestions, but also to learn from my (or our, if others chime in) own analysis. The discussion takes the form of "testing hypotheses". From the description of his game style at Sensei's Library, these hypotheses are:

1 - "thick plays that enabled a constant flow of exchanges around the board"
2 - "preferred peaceful exchanges rather than head-on confrontations"
3 - "steadily squeeze his opponent's groups for small advantages" leading often to a "crop of center territory emerging in the late game"
4 - "emphasises balance based on counting"
5 - "drawn out games, confident in his endgame skills"

See https://senseis.xmp.net/?TakagawaKaku

The methods to test these will be

1 - how often did Takagawa choose a influence oriented move (high, connecting) over a territory oriented move (low, invading); how often did he reinforce a group rather than playing elsewhere
2 - how often did he choose a softer play instead of the sharpest play (AI will be needed here)
3 - how often did crops of center territory emerge (in the late game)
4 - here I'll attempt to make regular quantified positional judgments, which are expected to be close; AI will confirm (or not)
5 - are Takagawa's games indeed long(-er than average); are Takagawa's moves closer to "the best move" in the endgame (AI needed)

There are also psychological aspects of his game, like his time management and its impact on the opponent, which we can't evaluate from the game record

First a few aggregate observations from https://homepages.cwi.nl/~aeb/go/games/ ... agawa.html

From 1120 games

1) The median number of moves is 202, the average 203. According to https://homepages.cwi.nl/~aeb/go/misc/gostat.html the average number of moves in a go game is 211. Takagawa's average is close to the overall average. I would think the deviation is not significant. Takagawa's preference for long drawn out games is anyhow not supported by his average game length.
2) 722 games ended in resignation. Of these Takagawa won 364, being 50%. Of the 398 games that did not end in resignation, he won 250, being 63%. This does seem a significant difference and seems to support his superior endgame strength. Another explanation would be that he tended to resign more often than his opponents when being slightly behind, which would then account for his better counting skills.

Inferring stylish conclusions from aggregated data is always dangerous, so I won't dwell on this observation.

The selection of games to review, to avoid bias is:
From https://homepages.cwi.nl/~aeb/go/games/ ... agawa.html
In chronological order
The first game against an opponent I know by name
Repeat but remove opponents already reviewed

First game, against Fujisawa Hosai - no comments yet.

Your approach sounds formal. You have research questions and something of a methodology.

If your intention is really to investigate the things that you mention with the specific methodology then you might be better off with sampling a few games and investigate only those games, otherwise it is probably too much work. This way there would also be a predetermined end for the project when the selected games have been reviewed.

If your intention is to produce lot of reviews of a particular kind then I might be reading too much into how you described the method and questions to answer. If that is the case then it could be an idea to encourage others to review more games in a similar fashion and not the same games?

kvasir wrote:Your approach sounds formal. You have research questions and something of a methodology.

If your intention is really to investigate the things that you mention with the specific methodology then you might be better off with sampling a few games and investigate only those games, otherwise it is probably too much work. This way there would also be a predetermined end for the project when the selected games have been reviewed.

If your intention is to produce lot of reviews of a particular kind then I might be reading too much into how you described the method and questions to answer. If that is the case then it could be an idea to encourage others to review more games in a similar fashion and not the same games?

I'm about to publish the first review. I underestimated again how much work it is to review a single game in a way that holds up against the strong players (and strong debaters) on this forum. I thought I'd do 10 of them (your "sample approach") but I might run out of steam before long.

My intention is/was to give an idea of what it might mean to study a player with a particular style. If you think there's something particular about that player/style you can learn from, you need to focus on the style and build the reviews around that. If you don't, then there's no need to select such player for the review.

While I was pondering my approach for the first idea, I came across the possibility that the alleged style is not actually supported by the data, which makes it even more doubtful you can learn from it.

As you will see from the first review, Takagawa does play softer moves than the sharper ones brought about by AI, but that's to be expected from any pro. More unexpectedly, Takagawa makes a couple of adventurous choices, making the game more complex, while there were simplifying lines available, easier for me to understand, supported by AI, and giving a clear lead to someone who can accurately assess the score.

One game review is no evidence or counter, but it told me I'll need a lot of time to make a decent assessment of the hypotheses, let alone derive a particular learning from Takagawa's alleged style.

1 - how often did Takagawa choose a influence oriented move (high, connecting) over a territory oriented move (low, invading); how often did he reinforce a group rather than playing elsewhere?
Moves 1, 3, 7, 25, 29, 31, 45, 47, 97, 109, 111 are influence oriented or honte-like thickness seeking moves
Moves 15, 27, 41, 113 were more profit oriented or fast paced developing moves

2 - how often did he choose a softer play instead of the sharpest play?
Moves 21, 93, 127 were soft, seeking compromise, for a smaller but more fathomable advantage; or simplifying for a fine victory
Moves 13, 43, 49, 71 wew uncompromising and complexifying, going for more than might be justified or easy to realize

3 - how often did crops of center territory emerge (in the late game)
not this time

4 - here I'll attempt to make regular quantified positional judgments, which are expected to be close?
At 111, Black's assessment to defend one group rather than the other, was 9 points off by KG's evaluation
Likewise at 127

5 - are Takagawa's games indeed long(-er than average); are Takagawa's moves closer to "the best move" in the endgame
no endgame

Instead, this game swung in major ways:

from 57 to 69, Fujisawa peeped many times in succession, to make Black heavy, but actually making him stronger
with moves 135 and 137, Takagawa may have misjudged the fighting conditions, turning himself into a prey rather than a hunter, turning a 9 pt lead into a 3 pt loss
from 170 to 176 Fujisawa may have missed the impact of his seeking life in enemy moyo, on the nearby unsettled position
from 182 to 188, a small loss turns into a 20+ loss for White, possibly due to misjudging the overall fighting condition

Click Here To Show Diagram Code

[go]$$B Moves 21 to 23
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . a O 2 . . |
$$ | . . . . . . . . . . . . . . . 1 X O . |
$$ | . . . . . . . . . . . O . X . X O c . |
$$ | . . . O . . . . . , . . . . . X O . . |
$$ | . . . . . X . . . X . O . b O 3 X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

is a soft move. Although Black lives after having multiple points to move out or make eyes, there's sharper play available

Click Here To Show Diagram Code

[go]$$B Sharper
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . a . . . |
$$ | . . . . . . . . . . . . . b . O 1 3 . |
$$ | . . . . . . . . . . . . c . . 2 X O 9 |
$$ | . . . . . . . . . . . O . X . X O 7 . |
$$ | . . . O . . . . . , . . . . . X O 8 . |
$$ | . . . . . X . . . X . O . . O 5 X 4 . |
$$ | . . . . . . . . . . . . . . 0 . d 6 . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Black forces White into a low connection with a-d as - .

If the previous was soft, here Takagawa seems to go against his style:

Click Here To Show Diagram Code

[go]$$B Moves 43 to 52
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . O X X X . . . . X . . . . . . . . |
$$ | . . . O . O X . . , . . . . X , . . . |
$$ | . . . . . O . . . . . . . . . . X . . |
$$ | . . O O . . . . . . . . . . . . . . . |
$$ | . . X B B . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . 6 4 . . . . |
$$ | . . O . . . . . . . . 2 . 5 3 O O . . |
$$ | . . . . . . . . . . . . . . . X X O . |
$$ | . . . . . 7 . 0 . 1 . O . X . X O . . |
$$ | . . . O . . . . . 9 . . . . . X O . . |
$$ | . . . . . X . O 8 X . O . . O X X . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

and set up multiple groups running into the center. Perhaps Takagawa wants to use his marked thickness here, but the outcome of this multi-running fight is not easy to predict.

Click Here To Show Diagram Code

[go]$$B Moves 43 to 52
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . c b 8 . . . . |
$$ | . . O . . . . . . . . 0 . 9 7 O O . . |
$$ | . . . . . . . 5 . . . . . . . X X O . |
$$ | . . . . . . 4 3 . a . O . X . X O . . |
$$ | . . . O . 6 . 2 1 . . . . . . X O . . |
$$ | . . . . . X . O . X . O . . O X X . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Instead, Black can (and probably should, per KataGo) sacrifice and create more central influence with . When White jumps out at , Black A is thick and next White B - Black C is a more severe cut for Black.

Click Here To Show Diagram Code

[go]$$B Moves 97 to 106
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O X . . . . . . . . . . . . . . |
$$ | . . O X X X a 6 W 3 X . . . . . . . . |
$$ | . . . O . O X 4 1 2 . . . . X , . . . |
$$ | . . . . . O 8 7 5 . . . . . . . X . . |
$$ | . . O O . . . 9 . . O . . . . . . . . |
$$ | . . X X X . 0 . O . . . . . . . . . . |
$$ | . . . . . . . . . . X . . . . . . . . |
$$ | . . . . . . . . O . . X X . . . . . . |
$$ | . . X , . . . X O , X O . . . O . . . |
$$ | . . . O . . X O . X . O . . . . . . . |
$$ | . . . O X . . X . X O . . O O . . . . |
$$ | . X O X . X . O . X . O . X X O O . . |
$$ | . O O O X X O . . X O . . . . X X O . |
$$ | . . O X . X . O . X . O . X . X O . . |
$$ | . . . O O X . . . X . . . . . X O . . |
$$ | . . . . . X . O O X . O . . O X X . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

as a response to White's marked invasion, leads to a standard sequence.

emphasizes the center instead of capturing the top. If at A instead then Black at would capture the White junk stones on a large scale and also strengthens the left side.

Click Here To Show Diagram Code

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

forces Black to spend more moves on the capture. Locally Black A (or fancier moves on the first line) is necessary but Takagawa decides to make a netting move at . KataGo thinks this is a mistake, because it doesn't really reduce White's squeezing potential in the center and it offers to lose the capturing race at the top.

reinforces the center again and now the whole board represents a complex set of related possible cuts, attacks and captures.

Click Here To Show Diagram Code

[go]$$ Position at move 112
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O X . O . . . . . . . . . . . . |
$$ | . . O X X X X O O X X . . . . . . . . |
$$ | . . . O . O X O X O . . . . X , . . . |
$$ | . . . . . O O X X . X . . . . . X . . |
$$ | . . O O . . O X . . O . . . . . . . . |
$$ | . . X X X . O . O . . . . . . . . . . |
$$ | . . . . . . . . . . X . . . . . . . . |
$$ | . . . . . b . . O . . X X . . . h . . |
$$ | . . X a . . . X O , X O . . . O . . . |
$$ | . . . O . . X O . X . O . . . . . . . |
$$ | . . . O X . c X . X O . f O O . . g . |
$$ | . X O X . X . O . X . O . X X O O . . |
$$ | . O O O X X O . . X O . . . . X X O . |
$$ | . . O X . X . O . X . O . X . X O . . |
$$ | . . . O O X . . . X . . . . . X O . . |
$$ | . . . . . X . O O X . O . . O X X . . |
$$ | . . . O d . . e . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

A takes profit and threatens to cut off the whole left side at B
C is a lingering threat for White to cut off the stones at the lower left
D would firmly capture the bottom stones, while E saves them in miai
Black can hane at F and threaten to cut the funny zigzag group.
Black G and H attack the white stones on a large scale. However, Black must be wary of weakening his corner's life & death condition.

Click Here To Show Diagram Code

[go]$$B Moves 111 to 112
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O O X . O . . . . . . . . . . . . |
$$ | . . O X X X X O O X X . . . . . . . . |
$$ | . . . O . O X O X O . . . . X , . . . |
$$ | . . . . . O O X X . X . . . . . X . . |
$$ | . . O O . . O X . . O . . . . . . . . |
$$ | . . X X X . O . O . . . . . . . . . . |
$$ | . . . . . . . . . . X . . . . . . . . |
$$ | . . . . . 1 . . O . . X X . . . . . . |
$$ | . . X , . . . X O , X O . . . O . . . |
$$ | . . . O . . X O . X . O . . . . . . . |
$$ | . . . O X . . X . X O . . O O . . . . |
$$ | . X O X . X . O . X . O . X X O O . . |
$$ | . O O O X X O . . X O . . . . X X O . |
$$ | . . O X . X . O . X . O . X . X O . . |
$$ | . . . O O X . . . X . . . . . X O . . |
$$ | . . . . . X . O O X . O . . O X X . . |
$$ | . . . O . . . 2 . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

In the game, saves the left side and saves the bottom side. While this type of compromise might fit into Takegawa's style to make the count easier, it makes the situation more complex. KataGo offers to simplify as follows:

Click Here To Show Diagram Code

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

Black resolves the top, forcing White to reinforce at which also captures the left side on a grand scale. And then captures the bottom.
This reduces the complexity and shifts the focus of the game to the right side, where Black has the better prospects and only has to take the corner status into account plus the aji at A.

Throughout his life, Takagawa played Sakata Eio most of all opponents. Sakata was by far his superior with 19-72 or a win percentage for Takagawa of only 21%. Hashimoto Shoji was another nemesis (6-14). He fared a bit better against the great Go Seigen (19-26 or 44%). He recorded comparable percentages over at least 15 matches against Otake, Fujisawa Shuko, Rin Kaiho and Akira Hasegawa. On the upside were Fujisawa Hosai (55%), Kitani Minoru (58%), Maeda Nobuaki (65%) and Kaoru Iwamoto (67%). One man beat him three times while the reverse never happened: Cho Chikun. Takagawa was often able to present a perfect balance sheet himself. He defeated Sato Sunao no less than seven times without succumbing once.

Next up: Hashimoto

Following Disraeli, we might say that there are lies, damned lies and go statistics.

The glaring example here is to quote Takagawa in his 60s playing Cho Chikun in his early 20s. That's why we have a charity called Age Concern. We also have to take account of quick promotees and high dans having to play lots more handicap games in the days of the Oteai. Or high dans involved in title games or finals having to play the creme de la creme all the time, and rarely the get to enjoy the fat-free yoghurts in the preliminaries.

Nevertheless, I think it is true that Takagawa does lag a little behind the other big names of his day in overall percentages. His official career record was 1179-661-509-6-3 or about 59%. That is a smidgeon below Otake (60%) and Rin (60%) but above Fujisawa Hideyuki (57%). Sakata is out in front on 64%. We can't compare Go Seigen because he only has 325 official games with the Nihon Ki-in, but many years ago I did a count of my own and he came out at about 69% or 70% (again, most often giving handicaps). And he did beat Sakata down, remember.

However, I've been more struck over the years by how often players with great percentages fail at the final hurdle of title matches. They are always the best man and never the bridegroom. Yet players with moderate percentages can often win titles through having that extra bit of mental steel. If we look at Takagawa, he played at a time when there were very few titles. The bulk only started coming on stream around 1955 when he was past his peak (born 1915), yet he still won over 20 titles. The younger Sakata bested him there, too, of course, getting to over 70. So, that's another way to measure, but it still seems iffy to me.

Surely the only sane approach, in the present context, is to assess how easy it is to copy one professional's style compared to another as a way for an amateur to improve. That means irrespective of results. But it might fit for Takawaga, especially as he wrote more than most about his style. Yet I am also dubious about that, because I remember Michael Redmond telling me that you recognise a player's distinctive style by seeing which moves he makes and other players don't. By that definition, it seems to me that you will end up making unusual moves all the time (which somehow doesn't seem right ), unless you extend your models to a largish group of apparently similar players.

And that really is a LOT of work! If we looked at study styles of amateurs, I think we would find that avoiding hard work is the most charactersitic feature. Nevertheless, if we spent as much time on that as we do on looking for magic formulas or free videos, we might actually improve one day!

John Fairbairn wrote: Surely the only sane approach, in the present context, is to assess how easy it is to copy one professional's style compared to another as a way for an amateur to improve. That means irrespective of results. But it might fit for Takawaga, especially as he wrote more than most about his style. Yet I am also dubious about that, because I remember Michael Redmond telling me that you recognise a player's distinctive style by seeing which moves he makes and other players don't. By that definition, it seems to me that you will end up making unusual moves all the time (which somehow doesn't seem right ), unless you extend your models to a largish group of apparently similar players.

And that really is a LOT of work! If we looked at study styles of amateurs, I think we would find that avoiding hard work is the most charactersitic feature. Nevertheless, if we spent as much time on that as we do on looking for magic formulas or free videos, we might actually improve one day!

I don't actually believe in it myself but I thought trying it out is a more interesting expenditure of my time than trying to convince someone verbally. Unfortunately we haven't seen the OP yet participate in this spin-off.

Thanks John for staying tuned as long as I've not run out of steam

I'm going to be much shorter on this review than the previous one, because of time management and because much less happened in this game, which was played without komi and Takagawa never really was in trouble, winning eventually by 8 points.

We can see the influence oriented style at work throughout the opening. At 50 Hashimoto makes a point losing ko threat, allowing Takagawa to take a corner and give up the ko at 53.

Two games is still too few to see a pattern but in the previous review Takagawa's usage of ko to get a favorable exchange already reminded me of Go Seigen. In a distant past I replayed many of Go's games and ko was one of the main features.

At 97 however he almost shows off his "lack of brilliance" by connecting what seem to be two stones of small value, with an empty triangle for Go's sake. It's a move you can't fathom Go Seigen ever playing - and Katago says it loses 4.5 points. Then 99 loses about the same amount, reducing his 13-ish point lead to the 5.5 he started with.

But from then onwards he keeps that lead until the very end, as if he wanted to show he can but doesn't need to play that well.

Overall this game is much more of a confirmation of his portrayed style, being influence oriented, keeping the count, throwing in a dull or even incomprehensibly soft move once in a while.

I keep in mind though that he might be just as much a master of ko as the GOAT - to be continued!

In the review you'll see labels A/B/C all the time, these were my candidates for the next moves, as a test for my ability to spot good candidates, not in terms of predicting Takagawa, rather good moves in my own view.

Knotwilg wrote:If the previous was soft, here Takagawa seems to go against his style:

It looks to me like Takagawa's style.

The situation feels unclear only to begin with. Takagawa plays one space jumps and then it feels like Takagawa has to win the game (look at the sequence I have conveniently hidden to save space). The only thing he did was to find time to play six one space jumps and make a table shape. It is as if he looked for the path of least resistance and played that -- like he is water

After all he is described as playing by the Chinese motto "running water doesn't compete for first place". That is a message about perseverance and humility. In this game he is ahead from the outset, a no komi game, and he almost clinches the game playing some of the least assuming moves imaginable. The game is almost over before move 100 and if it weren't for some inexplicably adventurous play starting with move 133 there would never be a chance for white (maybe there wasn't a real chance, these guys weren't computers).

Takagawa was apparently a fan of running water or rivers. If that is a metaphor for his style then it could be useful to recall words of the ancient river admirer, Heraclitus, who said "you never step into the same river twice". In a similar way you might not find Takagawa's (or any player's) style to be the same twice.

Click Here To Show Diagram Code

[go]$$W Moves 28 to 29
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O . . . . . . . . . . . . . . |
$$ | . . O O . . O . . , . . . . . X . . . |
$$ | . . X X . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , X O . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O O O . . . . . . . . . . . . |
$$ | . . O . O X X X . . . . . . . . . . . |
$$ | . . . . X 2 . . . . . . . . . . . . . |
$$ | . . . X . 1 . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . X . . . |
$$ | . . X O . . O . . . . . . . . . . . . |
$$ | . a O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

A key point in the game is the peep at , in this diagram . Takagawa responded with the intuitive connection

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[go]$$W Moves 28 to 29
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O . . . . . . . . . . . . . . |
$$ | . . O O . . O . . , . . . . . X . . . |
$$ | . . X X . X . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X , X O . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . O O O . . . . . . . . . . . . |
$$ | . . O . O X X X . . . . . . . . . . . |
$$ | . . . . X 3 . . . . . . . . . . . . . |
$$ | . . . X . 1 . . . . . . . . . . . . . |
$$ | . . X , . . . . . , . . . . . X . . . |
$$ | . . X O . . O . . . . . . . . . . . . |
$$ | . 2 O 4 . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

KataGo says that in this case, the proverbial moron should not connect against the peep. Black can instead play :b2:here. If White cuts, Black makes life in profit in the corner and the three stones are out. If White instead connects at then Black has made a favorable exchange before connecting at