A study of Takagawa

dust · **#21**

Knotwilg wrote:

A key point in the game is the peep at :w28:

, in this diagram :w1:

. Takagawa responded with the intuitive connection :b2:

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 :b4:

then Black has made a favorable exchange before connecting at :w3:

I think this may be another move where the strategic direction is more important than a few points. If Black lets White cut, then Black can make some profit in the corner but has less control in the centre with the three stones cut off. Having three stones cut off may not pose any immediate threat for Black, but it opens up possibilities for White to try to steer the direction of the game in a way they prefer and/or exploit the situation later on.

Knotwilg · **#22**

kvasir wrote:

If I understand correctly then you are saying that KataGo wants to play a? That is not the case for my setup, here it wants to play b.

I'll check again but indeed after some time A was the blue move. Around your B were many green moves too.

kvasir wrote:

Alternatively, maybe you meant that if black plays something else and white cuts at c then black can drive the cutting stone and give up the four stones, then he can finally play a?

Not what I meant - but it all boils down to the same thing. Playing the ko at some point gives more leverage than Takagawa's dull double empty triangle.

kvasir wrote:

My KataGo will instead do what I half expected and let white have the two stones if he still wants them but does play a first for good measures. For example the diagram, :b7:

is btw only one of many good moves.

Click Here To Show Diagram Code: [go]$$B For example $$ --------------------------------------- $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . . . O X . X . . . | $$ | . . . . O O . . . . . O . O X . . . . | $$ | . . O O . X O O . , . . . O . X . . . | $$ | . O X X . X X X O . O . . O . . . . . | $$ | . X . . . . . 4 X O . . . . . X . . . | $$ | . . . X . . . . X . . . . . O X . . . | $$ | . . . X O O O O . . . . . . . . . . . | $$ | . . . O X X O X 6 . . . . O . X . . . | $$ | . . X X X O 5 O . , . . . . 7 , X . . | $$ | . . . . . X O . . . . . . . . O X . . | $$ | . . . . O O O . . . . . . . . . . . . | $$ | . . O 2 O X X X . . . . . . O O O . . | $$ | . 3 1 O X X . . . . . . . . . X X . . | $$ | . . . X . O . . . . . . . . . . . . . | $$ | . . X , . X . . . , . . . . . X . . . | $$ | . . X O X X O . . O . . O . X . . . . | $$ | . . O . X O O . . . . b . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If we assume Takagawa's negative move was intentional then the other question besides style considerations is if this really is a good way to win in the position. Maybe playing b is easiest?

Any of

+

or

or

in this diagram or moves like b which harass the two space jump, are sharp ways to maintain the lead. Of those, :b5:

and

take White's growing center into account. With my own playing style, which is not so good at reducing moyos, I might pick :b7:

naturally, or :b5:

first if I noticed it.

kvasir · **#23**

BTW white can cut just fine.

Click Here To Show Diagram Code: [go]$$W Cutting in the random position (to make it white's move) $$ --------------------------------------- $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . . . . . . . . . . . O X . X . . . | $$ | . . . . O O . . . . . O . O X . . . . | $$ | . . O O . X O O . , . . . O . X . . . | $$ | . O X X . X X X O . O . . O . . . . . | $$ | . X . . 3 . . 1 X O . . . . . X . . . | $$ | . . . X . . . 2 X . . . . . O X . . . | $$ | . . . X O O O O . . . . . . . . . . . | $$ | . . . O X X O . O . . . . O . X . . . | $$ | . . X X X . X O . , . . . . . , X . . | $$ | . . . . . X O . . . . . . . . O X . . | $$ | . . . . O O O . . . . . . . . . . . . | $$ | . . O O O X X X . . . . . . O O O . . | $$ | . X X O X X . . . . . . . . . X X . . | $$ | . . . X . O . . . . . . . . . . . . . | $$ | . . X , . X . . . , . . . . . X . . . | $$ | . . X O X X O . . O . . O . X . . . . | $$ | . . O . X O O . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Playing the endgame in the corner has an effect on the cut.

Click Here To Show Diagram Code: [go]$$W Again making it white's move someway. $$ --------------------------------------- $$ | . . . . . . . . . . . O X X . . . . . | $$ | . . 3 . . . . . . . . . O X . X . . . | $$ | . O 2 . O O . . . . . O . O X . . . . | $$ | . X O O . X O O . , . . . O . X . . . | $$ | X . X X . X X X O . O . . O . . . . . | $$ | . X . . 5 . 6 1 X O . . . . . X . . . | $$ | . . . X . . . 4 X . . . . . O X . . . | $$ | . . . X O O O O . . . . . . . . . . . | $$ | . . . O X X O . O . . . . O . X . X . | $$ | . . X X X . X O . , . . . . . , X . O | $$ | . . . . . X O . . . . . . . . O X . . | $$ | . . . . O O O . . . . . . . . . . . . | $$ | . . O O O X X X . . . . . . O O O O . | $$ | . X X O X X . . . . . . . . . X X . . | $$ | . . . X . O . . . . . . . . . . . X . | $$ | . . X , . X . . . , . . . . . X . . . | $$ | . . X O X X O . . O . . O . X . . . . | $$ | . . O . X O O . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Endgame is so confusing without KataGo second guessing everything, trying to follow how KataGo plays endgame risks losing the marbles. I wonder if it is easier to understand if one wouldn't use same engine for black and white, it is maddening how black and white agree on everything when analyzing.

Knotwilg · **#24**

The key moves in this game are 31 to 39 where Takagawa is being reduced from both sides. This soft response to White's invasion and reduction is reversing the lead, from +2.5 due to the small komi to -3.5.
From 41 to 45 Black creates a weak group in the lower left

The upper left joseki then seems to turn out rather well for Black so that at 65 he could turn to the lower side again.

69: Instead Takagawa tries his usual tactic of creating a ko, at the upper side this time, to create an advantage elsewhere or attack White's center stones on a large scale.

83: Black does separate the center stones but the ko is still active and his upper side is weak

113-115: allows WHite to execute a squeeze, creating strength to kill the upper side or to capture the central cutting stones. Black saves them but then loses the top side depending on another ko fight. White doesn't even have to win it in order to win the game, so Takagawa resigns, seeing that White is in total control.

Knotwilg · **#25**

Click Here To Show Diagram Code: [go]$$W Moves 32 to 33 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . O O . O O O . | $$ | . . . O . . . . . , . . . . X X X O . | $$ | . . . . . . . . . . . . . . . . X X . | $$ | . . . . . . . . . . . . . . . X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . O . . . . . , . O 6 . . , . . . | $$ | . . . . . . . . . . . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . X . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . X X X . | $$ | . . . O . X . . . X . . . 4 X O O X . | $$ | . . . . . . . . . . . . . 2 1 . . O . | $$ | . . . . . . . . . . . . . . 3 . 5 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The double hane at :b2:

is intuitive and easy. It allows to take sente and enlarge the center at :b6:

Obviously KataGo is just a little keener on taking the 3-3 in the upper left, but let's put that aside
This diagram is the kind of straightforward Go an amateur would expect to learn from a pro.

Why Takagawa plays the softer game sequence may be because he expects to benefit from the aji later, perhaps in a ko.

Knotwilg · **#26**

Click Here To Show Diagram Code: [go]$$B Position at move 65 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O O O X X . . . . . . . . . . . . . | $$ | . . X X O O X . . X . a O O . O O O . | $$ | . . X O . . . . . , . . . . X X X O . | $$ | . . . O . O c . . . . . . . . . X X . | $$ | . . . O . . . . . . . . O . . X O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . 0 . . . . X . . . | $$ | . . . O . . . X . O 9 O O . . , . . . | $$ | . . . . . . . . . . b X X . X . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . X . . . . . . . . . . . . . . . | $$ | . . X O . X . . . . . . . . . . . . . | $$ | . . X . . 3 . . . . . . . . . X X X . | $$ | . . O O O X 2 . . X . . . X X O O X . | $$ | . . . . . O 1 5 7 . . X X O O . . O . | $$ | . . . . . . 4 6 . . . . O . . . 8 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Instead of A, Black could play at the bottom first. When the exit towards the left is blocked, White might take care of his corner at :w8:

. Then Black solidifies the center with :b9:

and next B.

This keeps the game very close. Black can play this way, recovering from his lukewarm opening, because White allowed him to settle at the top too easily. Later, Black can attach at C to move out, should he not be able to live locally.

This way of playing would again be in line with the alleged style of "keeping things simple and count on a superior endgame" while Takagawa again seeks complexity with A and for the third game in a row shows a preference for ko as a means to win the game by making major exchanges.

Knotwilg · **#27**

Comments inside the game. Move 91 is quite particular.

Knotwilg · **#28**

Click Here To Show Diagram Code: [go]$$B Moves 35 to 35 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . O . . . . . . . . O O . . . . | $$ | . O O O . . O . X , . . O X . X . . . | $$ | . X X X . X . . 4 . . . . X . X . . . | $$ | . . . . . . . X . . . 2 . . . O X . . | $$ | . . . . . . . . . . . . . . . 3 . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . . . | $$ | . . X , . . . . . , . . W . O , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . X . . . . | $$ | . . . . O . . . . . . . . . . . . . . | $$ | . . X . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . O . . . , . . . . . X 1 . . | $$ | . . . . . . . . . O . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

A first key moment is when Black solidifies his territory with :b1:

after White has erased the left side and ran out at the marked move. This allows White to take the initiative with :w2:

and cut with :w4:

Click Here To Show Diagram Code: [go]$$B Moves 35 to 35 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . . . O . . . . . . . . O O . . . . | $$ | . O O O . . O . X , . . O X . X . . . | $$ | . X X X . X . . . . . . . X . X . 9 . | $$ | . . . . . . . X . . . . . . 6 O X . . | $$ | . . . . . . . . . . . . . a . 5 4 7 . | $$ | . . . . . . . . . . . . . . . . 8 0 . | $$ | . . . . . . . . . . . . . 1 . O . . . | $$ | . . X , . . . . . , . . O 2 O , . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . 3 . X . . . . | $$ | . . . . O . . . . . . . . . . . . . . | $$ | . . X . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . O b . . , . . . . . X . . . | $$ | . . . . . . . . . O . . X . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

It would have been more active to keep up the pressure here. If White now would play the keima from the previous diagram, his group will come under pressure. White can launch a skirmish in the upper right, which strengthens both weak groups. Black can further settle locally at A. KataGo would be audacious and play B.

Knotwilg · **#29**

Click Here To Show Diagram Code: [go]$$B Moves 79 to 79 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . O . . . . . . . . . O . . | $$ | . . . . O O . O . . . . . O O . . . . | $$ | . O O O . X O X X , . . O X . X . . . | $$ | . X X X . X . X O . . X O X . X . . . | $$ | . . . . . . . X . . . O O . . O X . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . O . | $$ | . . X , . X . . . , . . O . O , . X . | $$ | . . . . . . . 1 . . . . . . . X X X . | $$ | . . X . . . . . . . . . . . X . O O . | $$ | . X O . O . . . . . . . O . X . . . . | $$ | . O . O . . . . . . . . . . O X . . . | $$ | . . O . . . . . . . . . O . O . . . . | $$ | . X O O . O . . . , . . . X . X X . . | $$ | . X X O . . . . . O . . X . . . . . . | $$ | . X . X O . . . . . . . . . . . . . . | $$ | . . X . . . . . . . . . . . . . . . . | $$ ---------------------------------------[go] A second key move is this reduction/expansion. It's on the boundary of moyos indeed but the problem with it is that White's lower left is very strong and there are weaker areas that can use some attantion. [go] $$B Moves 79 to 79 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . O . . . . . . . . . O . . | $$ | . . . . O O . O . . . . . O O . . . . | $$ | . O O O . X O X X , . . O X . X . . . | $$ | . X X X . X . X O . . X O X . X . . . | $$ | . . . . . . . X . . . O O . . O X . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . O . | $$ | . . X , . X . . . , . . O . O , . X . | $$ | . . . . . . . 5 . . . . . . . X X X . | $$ | . . X . . . . . . . . . . . X . O O . | $$ | . X O . O . . . . . . . O . X . . . . | $$ | . O . O . . . . . . . . . . O X . . . | $$ | . . O . . . . . . . . . O . O . . . . | $$ | . X O O . O . . . , 4 . . X . X X . . | $$ | . X X O . . . . . O 3 . X . . . . . . | $$ | . X . X O . . . . 2 1 . . . . . . . . | $$ | . . X . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

If Black can reduce at the bottom in sente first, then his original move is better timed.

Click Here To Show Diagram Code: [go]$$B Moves 79 to 79 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . O . . . . . . . . 4 O . . | $$ | . . . . O O . O . . . . . O O 3 1 2 . | $$ | . O O O . X O X X , . . O X . X . 5 . | $$ | . X X X . X . X O . . X O X . X . . . | $$ | . . . . . . . X . . . O O . . O X . . | $$ | . . . . . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . O . | $$ | . . X , . X . . . , . . O . O , . X . | $$ | . . . . . . . 9 . . . . . . . X X X . | $$ | . . X . . . . . . . . . . . X . O O . | $$ | . X O . O . . . . . . . O . X . . . . | $$ | . O . O . . . . . . . . . . O X . . . | $$ | . . O . . . . . . . . . O . O . . . . | $$ | . X O O . O . . . , . . . X . X X . . | $$ | . X X O . . . . . O . 8 X . . . . . . | $$ | . X . X O . . . . . . 6 7 . . . . . . | $$ | . . X . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

In fact both Black and White could also respond on top of the respective keimas to make the situation a little more complicated but if we stick with the more mundane blocks, this i

In fact, KataGo seems to think of these reducing moves as miai and prefers making the upper right corner alive with points.

Knotwilg · **#30**

A two point win by Takagawa. Two kofights determine the game, the second making for a large swap that divides the board into two. Eventually the lead drops from about 8 to only 2 points.

Knotwilg · **#31**

Click Here To Show Diagram Code: [go]$$B Moves 69 to 78 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X 0 . . . . . . O . . . X . . . . | $$ | . O X O 9 . 3 2 6 X O . . O X . . X . | $$ | . 8 O X O O 4 1 O O X O . O X , X O . | $$ | . 7 O X . . . 5 . . X . . O X X O O . | $$ | . . X X . X . . . . . . . . X O X . . | $$ | . . . . . . . . . . . . . . . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . X . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O X . . . . . . . . X . O . . . | $$ | . . X X X X O O . . . . . . . . . . . | $$ | . . X O X O . . . X . . . X . , O . . | $$ | . . O O O . O . X . . . . . . X X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

First key moment: Black breaks through the top to set up a ko

Click Here To Show Diagram Code: [go]$$B Moves 79 to 88 $$ --------------------------------------- $$ | . . 2 . 4 7 6 . . . . . . . . . . . . | $$ | . O X O 1 8 3 . . . O . . . X . . . . | $$ | . O X O X 5 X O O X O . . O X . . X . | $$ | . O O X O O O X O O X O . O X , X O . | $$ | . X O X . . . X . . X . . O X X O O . | $$ | . . X X . X . . . . . . . . X O X . . | $$ | . . . . . . . . . . . . . . . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . X . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O X . . . . . . . . X . O . . . | $$ | . . X X X X O O . . . . . . . . . . . | $$ | . . X O X O . . . X . . . X . , O . . | $$ | . . O O O . O . X . . . . . . X X . . | $$ | . . . . . 9 0 . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

is the first ko threat. :w10:

shows an intention to lose the ko by making this local exchnage favorable for himself.

Click Here To Show Diagram Code: [go]$$B Moves 91 to 100 $$ --------------------------------------- $$ | . . O . O X O 1 . . . . . . . . . . . | $$ | . O . O X . X . . . O . . . X . . . . | $$ | . O . O X X X O O X O . . O X . . X . | $$ | . O O X O O O X O O X O . O X , X O . | $$ | . X O X . . . X . . X . . O X X O O . | $$ | . . X X . X . . . . . . . . X O X . . | $$ | . . . . . . . . . . . . . . . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . X . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O X . . . . . . . . X . O . . . | $$ | . . X X X X O O . . . . . . . . . . . | $$ | . . X O X O . . . X . . . X . , O . . | $$ | . 3 O O O . O . X . . . . . . X X W . | $$ | 9 4 5 6 . X O . . . . . . . . . . 2 . | $$ | 0 7 8 . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

After Black has recaptured the ko and White played the marked stone in the lower right, Black finishes the ko and White proceeds at :w2:

taking corner territory while reducing the lower side.

Then Black starts another ko, in the lower left, where previously White had taken some gain

Click Here To Show Diagram Code: [go]$$B Moves 101 to 110 $$ --------------------------------------- $$ | . . O . O X . X . . . . . . . . . . . | $$ | . O . O X . X . . . O . . . X . 6 . . | $$ | . O . O X X X O O X O . . O X . 4 X . | $$ | . O O X O O O X O O X O . O X , X O . | $$ | . X O X . . . X . . X . . O X X O O . | $$ | . . X X . X . . . . . . . . X O X . . | $$ | . . . . . . . . . . . . 8 . . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . X . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O X . . . 9 . . . . X . O . . . | $$ | . . X X X X O O . . . . . . . . . . . | $$ | . . X O X O 2 . . X . . . X . , O . . | $$ | . X O O O 1 O . X . . . . . . X X O . | $$ | X O 5 O . X O . . . . . . . . . . O . | $$ | O 3 O 7 . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Black plays a local ko threat, then ignores White's threat in the upper right and continues the ko at :b5. When White capitalizes on his threat, Black immediately resolves at :b7:

KataGo thinks this exchange favors White and the game is almost even now. BUT, White should not surround at :w8:

now.

Click Here To Show Diagram Code: [go]$$B Moves 101 to 110 $$ --------------------------------------- $$ | . . O . O X . X . . . . . . . . . . . | $$ | . O . O X . X . . . O . . . X . O . . | $$ | . O . O X X X O O X O . . O X . O X . | $$ | . O O X O O O X O O X O . O X , X O . | $$ | . X O X . . . X . . X . . O X X O O . | $$ | . . X X . X . . . . . . . . X O X . . | $$ | . . . . . . . . . . . . . a . O O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . X . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O X . . . . 0 . . . X . O . . . | $$ | . . X X X X O O . 8 9 . . . . . . . . | $$ | . . X O X O O . . X . . . X . , O . . | $$ | . X O O O X O . X . . . . . . X X O . | $$ | X . X O . X O . . . . . . . . . . O . | $$ | . X . X . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

Instead, White should settle here, creating sufficient influence towards an open center. If Black tries to escape with his group around A, the space through which he can do so is much more narrow.

Knotwilg · **#32**

In the 6th game researched in this thread, against Maeda Nobuaki, the famous composer of tsumego, Takagawa holds a steady advantage around the komi in this no komi game. Contrary to his alleged style, Takagawa takes four corners and makes life with a central group to maintain the lead.

Click Here To Show Diagram Code: [go]$$B Moves 11 to 20 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . O . . . . . 2 . . . O . . . . | $$ | . . . , . . . . . , . . . . . , X . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 3 , 0 . . . . , . . . . . , O . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . 6 . . | $$ | . . 9 X . . . . . , . . . X . , 5 . . | $$ | . . . . . . 7 . 4 . . 8 . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

closes off the corner. :w10:

is a reducing capping move, taking influence.

Click Here To Show Diagram Code: [go]$$B Moves 41 to 50 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X X . . . . . . . . . . . . . | $$ | . . X X O O O . . . O . . . O . . . . | $$ | . . . O . . . . . , . . . . . , X . . | $$ | . X . O . . . . . . . . . . . X . . . | $$ | . . . O . . . . . . . . . . . . . . . | $$ | . 1 X 2 X . . . . . . . . . . . . . . | $$ | . O O X . . . . . . . . . . . . X . . | $$ | . O X X . 3 . . . . . . . . . . . . . | $$ | . O X , O . . . . , . . . . . , O . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . O . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X 5 7 9 . . , . . . X . , X . . | $$ | . . . . 4 6 X . O . . O . . . X . . . | $$ | . . . . 0 . 8 . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The weak group occurs after :w2:

cuts. Then :w4:

invades and Black calmly connects while taking influence towards his weak group. This is not just compromising, it's proper play.

Click Here To Show Diagram Code: [go]$$B Moves 61 to 70 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X X . . . . . . . . . O X . . | $$ | . . X X O O O . . . O . . . O X . . . | $$ | . . . O . . . . . , . . . . . , X . . | $$ | . X . O . . . . . . . . . O O X . . . | $$ | . . . O . . . . . . . . . . X 2 3 . . | $$ | . X X O X . 4 . . . . . . . . W 1 . . | $$ | . O O X . . . . . . . . . . . . X . . | $$ | . O X X . X . a . . . . . . . . . . . | $$ | . O X 9 O 8 . . . , . . . . . , O . . | $$ | . . O 5 7 . . . . . . . . . . . . . . | $$ | . . . 6 . . . . . . . . . . . . . . . | $$ | . . O . . 0 . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . . . | $$ | . . . . . . . . . . . . . . . . O . . | $$ | . . X X X X X . . , . . . X . , X . . | $$ | . . . O O O X . O . . O . . . X . . . | $$ | . . X X O . O . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

I thought the marked move and subsequent moves by White were overplays. :w8:

goes all out and :w10:

seems to attack from the wrong side. I head expected A instead, taking central profit while attacking.

Click Here To Show Diagram Code: [go]$$B Moves 101 to 110 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . X X . . . . . . . . . O X . . | $$ | . . X X O O O . . . O . . . O X . . . | $$ | . . . O . . . . . , . . . . O X X . . | $$ | . X . O . . . . O . . . . O O X . . . | $$ | . . . O . . O . . 2 1 6 . . X O X . . | $$ | . X X O X X O X . O X O 5 . . O X . . | $$ | . O O X X . . X O 4 O X . . . . X . . | $$ | . O X X O X X X . 3 O X . . 7 9 . . . | $$ | . O X X O O O X . X X X . O 8 , O . . | $$ | . . O X X . O . . . . . . . . . . . . | $$ | . . . O . . O . . O . . . . . . . . . | $$ | . . O . . O . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . O . . . | $$ | . O . . . . . . . . . . . . . . O . . | $$ | . X X X X X X . . , . . . X . , X 0 . | $$ | . . . O O O X . O . . O . . . X . . . | $$ | . . X X O . O . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The fight swerves to the right side, where Black links up his stones. Next Black defends his lower right corner. White's attacks didn't amount to anything.

Takagawa maintained a steady lead without doing any spectacular, except for making a clumsy shape with his weak group.

Knotwilg · **#33**

This seventh game was played in the 1939 Oteai, against Kajiwara Takeo. We can safely call this a masterpiece by Takagawa: he overcame the disadvantage of a no komi game into a five point victory by White, without Kajiwara making any glaring mistake. A first AI analysis suggests that all moves stay safely within the 4 point error margin, only Takagawa finds real good moves way more often.

This is also a good game to study the endgame and see how good Takagawa's endgame could be.

Knotwilg · **#34**

Click Here To Show Diagram Code: [go]$$B Moves 21 to 30 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . O X . . . . | $$ | . . . O . . . . . , . . . O X , X . . | $$ | . . . . . . . . . . . . . O . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . 1 . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . 3 O O . . . | $$ | . . . . . . . . . . . . . 4 X O . . . | $$ | . . . . . . . . . . . . 2 . X X O . . | $$ | . . X , . . . . . , . . 8 7 . , O . . | $$ | . . . . O . . . X . . 0 5 6 . X X . . | $$ | . . . . . . . . . . . . . 9 . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

is awkward shape and AI Sensei thinks it’s worse than the table shape at :w6:

We’ll see later that the bad shape will haunt Black.

Click Here To Show Diagram Code: [go]$$B Moves 71 to 80 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . O . . . . O X . . . . | $$ | . . . O . O . . . , . . . O X , X . . | $$ | . . O . . . . . . . . . . O . . . . . | $$ | . . X X . 9 . 0 . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . X . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . 5 X X . 7 . . . . . . . . . . . . | $$ | . . O O . 4 8 6 . , . . . . . , . . . | $$ | . . . 2 . . . . . . . . . X . O . . . | $$ | . . O X . . . . . X . . . . . . . . . | $$ | . . 1 O X . O . . . O X X X O O . . . | $$ | . . . 3 . X . O X X X O . O X O . . . | $$ | . . . X X O O . O O O . O . X X O . . | $$ | . . X , O X O . . , . . O X . , O . . | $$ | . . . . O . . . X . O O X O . X X . . | $$ | . . . . . . . . . X . X X X . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

and

are overconcentrated. White had previously played at the top and ignored left side and center. Being allowed to move out with :b4:

and :b6 is too good. With :w10:

Takagawa takes the initiative.

Knotwilg · **#35**

Click Here To Show Diagram Code: [go]$$B Moves 111 to 111 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . X . . . . | $$ | . . X O . . . . O . . . . O X . . . . | $$ | . O . O . O . O . , . . . O X , X . . | $$ | . X O . . . X . . . . . . O . . . . . | $$ | . X X X . X . O . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . O . X X . | $$ | . . . . . . . . . . . . . O X 1 O X . | $$ | . . X X X . X . . . . . . O X . . O . | $$ | . . O O . O O O . , . . X O X , O . . | $$ | . . . O . . . . . . . O O X X O . . . | $$ | . . O X . . . . . X . . . . X . . . . | $$ | . . X . X . O . . . O X X X O O . . . | $$ | . . . X . X . O X X X O X O . O . . . | $$ | . . . X X O O . O O O . O O . . O . . | $$ | . . X , O X O . . , . . O X O O O . . | $$ | . . . . O . . . X . O O X . X X X . . | $$ | . . . . . . . . . X . X X X . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

After

all groups are safe, so we get an early endgame. Still, White's top side to center territory has not been clearly delimited.

Click Here To Show Diagram Code: [go]$$B Moves 111 to 116 $$ --------------------------------------- $$ | . . . . . . . . . . . . 4 3 5 . . . . | $$ | . . . . . . . . . . . 6 . 2 X . . . . | $$ | . a X O . . . . O . . . . O X . . . . | $$ | . O . O . O . O . , . . . O X , X . . | $$ | . X O . . . X . . . . . . O . . . . . | $$ | . X X X . X . O . . . . . . . d . . . | $$ | . . . . . . . . . . . . . . O . X X . | $$ | . . . . . . . . b . . . . O X 1 O X . | $$ | . . X X X . X . . . . . . O X . e O . | $$ | . . O O . O O O . c . . X O X , O . . | $$ | . . . O . . . . . . . O O X X O . . . | $$ | . i O X . . . . . X . . . . X . . . . | $$ | . . X . X . O . . . O X X X O O . . . | $$ | . . . X . X . O X X X O X O . O . . . | $$ | . . . X X O O . O O O . O O . . O . . | $$ | . . X , O X O . . , . . O X O O O . . | $$ | . . . . O . . . X . O O X . X X X f . | $$ | . . h . . . g . . X . X X X . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

When

walls off the top, :b3:

is almost forced, since locally double sente. From White's perspective A now takes the corner, B enlarges the top, C after B even more, D might become sente on the big black group, E definitely is, F is big endgame and so are G, H and I

Knotwilg · **#36**

Knotwilg · **#37**

The game against Go Seigen (White) showed a rapid reduction of the Black advantage in this no komi game. Coming out of the fighting in the lower left Black restored the advantage. When White not only settled easily in his lower right moyo but was allowed to reduce the bottom - while Black played slow moves in the upper left - White took a 10 point lead. Black tried a heavy ko to come back but couldn't win it and resigned.

Key point #1

Click Here To Show Diagram Code: [go]$$B Moves 21 to 30 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . 6 5 b . . 3 c . . . . . . . . . . . | $$ | . . a . B . X O . . . . . O X X . . . | $$ | . . O , . . . W . , . . O O O , X . . | $$ | . . . O O X . . . . . . . X 0 X . . . | $$ | . . . . X 1 . 4 . . . . . . . . . . . | $$ | . . 2 . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . 8 . . . . . . . . . . . 7 . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . O . . . . . 9 . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

The upper left skirmish is the result of a marked pincer on an approach. B5 and W6 are both urgent to establish or challenge the opponent's base. Even :b7:

and subsequent black moves should be at A, says KataGo and likewise W8 and subsequent should capture at B. After A Black can stabilize at C any time. :b9:

is an obvious point for mutual development but when :w10:

pushes through, White has already made the game close.

Reinforcing or pressuring unsettled groups in a corner is bigger here than developing unchallenged corners or build towards the side. This is a tough balance: sometimes playing away to develop a corner is bigger.

Knotwilg · **#38**

Key point #2

Click Here To Show Diagram Code: [go]$$B Moves 41 to 41 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . 2 . . | $$ | . . . . X . X O . . . . . O X X O 1 . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X 3 . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . . . . . . . . . . X X X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . O . . . . . X . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

loses sente. Instead

Click Here To Show Diagram Code: [go]$$B Better $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . . . . | $$ | . . a . X . X O . . . . . O X X 2 4 . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X . 3 . | $$ | . . . . X X . O . . . . . . X O O O 1 | $$ | . . O . . . . . . . . . . . . X X X . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . O . . . . . . . . . . . X . . . | $$ | . . . , . . . . . , . . . . . , . . . | $$ | . . . O . . . . . X . . . . . X . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ | . . . . . . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

here would force White to add :w4 so that Black can play first in the upper left again.

Knotwilg · **#39**

Key point #3

Click Here To Show Diagram Code: [go]$$W Moves 98 to 99 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . X X . . . . . . . X X X . | $$ | . . . O O . . . . . . . . . . . . . . | $$ | . . O . X . O . . . . . . . . . . . . | $$ | . O . O . . . . . , . . . . . , . . . | $$ | . . O X X . O d . . . . . . . . . . . | $$ | . . . . . . X . O . . . . . . . . . . | $$ | . b X X X . X . . . . . . . . . . . . | $$ | . X O X O O O O . . . . . . . . . . . | $$ | X O O O X O . . . . . . . . . X . . . | $$ | . O O X X O X X . , . . . . . , . . . | $$ | . O X X X O X O X X . . . . . X . . . | $$ | . O . X . X O O c . . . . . . . . . . | $$ | . . 1 2 X a . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

After this exchange, White has a two staged ko available, starting with throwing in at A. The presence of this ko is tightly linked to the capture or conection at B. If Black wins that ko or reinforces at C, then Black B klls the corner. Otherwise said, Black B now makes the ko heavy for White, while White B makes the ko heavy for Black.

At the same time, D is a vital point for the black and white groups running into the center. The relative strength in the center moreover affects the urgency for Black to live locally in the upper left.

Click Here To Show Diagram Code: [go]$$W Mistake $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . X X . . . . . . . X X X . | $$ | . . . O O . . . . . . . . . . . . . . | $$ | . . O . X . O . . . . . . . . . . . . | $$ | . O . O . . . . . , . . . . . , . . . | $$ | . . O X X . O 2 . . . . . . . . . . . | $$ | . . . . . . X . O . . . . . . . . . . | $$ | . 1 X X X . X . . . . . . . . . . . . | $$ | . X O X O O O O . . . . . . . . . . . | $$ | X O O O X O . . . . . . . . . X . . . | $$ | . O O X X O X X . , . . . . . , . . . | $$ | . O X X X O X O X X . . . . . X . . . | $$ | . O . X . X O O . . . . . . . . . . . | $$ | . . W B X . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

White decided to secure his corner, activating the ko potential at the bottom. However, this allowed Black to take the vital point in the center.

Click Here To Show Diagram Code: [go]$$W Connect $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . X X . . . . . . . X X X . | $$ | . . . O O . . . . . . . . . . . . . . | $$ | . . O . X . O . . . . . . . . . . . . | $$ | . O . O . . . . . , . . . . . , . . . | $$ | . . O X X . O 1 . . . . . . . . . . . | $$ | . . . . . . X . O . . . b . . . . . . | $$ | . . X X X . X 0 8 . . . . . . . . . . | $$ | . X O X O O O O . 2 . . . . . . . . . | $$ | X O O O X O . . . . . . . . . X . . . | $$ | . O O X X O X X . , . . . . . , . . . | $$ | . O X X X O X O X X . . . . . X . . . | $$ | . O a X 9 X O O 6 . . . . . . . . . . | $$ | . . O X X 3 4 5 . . . . . . . . . . . | $$ ---------------------------------------[/go]

What if

here?

puts pressure on White. Black can use ko threats to connect, sacrifice the stones in the corner (:w11: at A) and build a moyo around B. This is White's best sequence still and the game is close.

Click Here To Show Diagram Code: [go]$$W Mistake $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . X X . . . . . . . X X X . | $$ | . . . O O . . . . . . . . . . . . . . | $$ | . . O . X . O . . . . . . . . . . . . | $$ | . O . O . . . . . , . . . . . , . . . | $$ | . . O X X . O 1 . . . . . . . . . . . | $$ | . a . . . . X . O . . . . . . . . . . | $$ | . . X X X . X . 3 . . . . . . . . . . | $$ | . X O X O O O O . 2 . . . . . . . . . | $$ | X O O O X O . . . . . . . . . X . . . | $$ | . O O X X O X X . , . . . . . , . . . | $$ | . O X X X O X O X X . . . . . X . . . | $$ | . O . X . X O O b . . . . . . . . . . | $$ | . . W B X . . . . . . . . . . . . . . | $$ ---------------------------------------[/go]

White can of course increase the value of the lower left fighting by connecting at :w3:

but that turns :b2:

into a very favorable sente by Black, who builds up the bottom. Black can now raise at A, or capture at B and sacrifice the left side, in order to further expand the moyo on the right side.

Knotwilg · **#40**

Key point #4

Click Here To Show Diagram Code: [go]$$B Moves 121 to 130 $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X 7 . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O . . . . . . X O O O . | $$ | . . O . . . X X 6 . . . . . . X X X . | $$ | . . . O O . . . . 0 . . . . . . . . . | $$ | . . O . X . O . 3 2 . . . . . . . . . | $$ | . O . O . . O O 4 9 . . . . . , . . . | $$ | . . O X X X O X X 5 . . . . . . . . . | $$ | . . . . . . X X O O 8 . . . . . . . . | $$ | . O X X X . X . X . . . . . . . . . . | $$ | . X O X O O O O O . . . . . . . . . . | $$ | X O O O X O O O O . O . . . . X . . . | $$ | . O O X X O . . O X . . . . . , . . . | $$ | . O X X X O . O X X . . 1 . . X . . . | $$ | . O . X . X O O O X . . . . . . . . . | $$ | . . O X X . X X X . . . . . . . . . . | $$ ---------------------------------------[/go]

When

threatens to fully surround the top left, Black bails out with :b7:

. This allows White to reinforce the center, which will later help reducing Black's right side and bottom.

Click Here To Show Diagram Code: [go]$$B Better $$ --------------------------------------- $$ | . . . . . . . . . . . . . . . . . . . | $$ | . O X . . . X . . . . . . . . . O . . | $$ | . . . . X . X O . . . . . O X X O X . | $$ | . . O , . . . O . , . . O O O O X . . | $$ | . . . O O X . . . . . . . X O X X X . | $$ | . . . . X X . O 5 . . . . . X O O O . | $$ | . . O . . . X X O . . . . . . X X X . | $$ | . . . O O 4 . . . 2 . . . . . . . . . | $$ | . . O . X 3 O . X O . . . . . . . . . | $$ | . O . O . . O O O 1 . . . . . , . . . | $$ | . . O X X X O X X X . . . . . . . . . | $$ | . . . . . . X X O O . . . . . . . . . | $$ | . O X X X . X . X . . . . . . . . . . | $$ | . X O X O O O O O . . . . . . . . . . | $$ | X O O O X O O O O . O . . . . X . . . | $$ | . O O X X O a . O X . . . . . , . . . | $$ | . O X X X O . O X X . . X . . X . . . | $$ | . O . X . X O O O X . . . . . . . . . | $$ | . . O X X . X X X . . . . . . . . . . | $$ ---------------------------------------[/go]

KataGo thinks Black can seize the upper hand in the fighting this way

A study of Takagawa

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