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Beat Elf!
http://lifein19x19.com/viewtopic.php?f=15&t=16641		 Page 2 of 2
Author:  Bill Spight [ Sat Oct 19, 2019 8:51 am ]
Post subject:  Re: Beat Elf!
The third one comes from GoGoD 1996-01-31a, between Kobayashi Satoru (W) and Cho Chikun. I found it when I was looking for a game for How is your positional judgement? ( https://lifein19x19.com/viewtopic.php?f=15&t=16909 ). ;)

Earlier in the game.

Click Here To Show Diagram Code
[go]$$Bcm7 White blunders
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O 4 5 . . . |
$$ | . . . O . . . . . , . . 9 1 2 X 0 . . |
$$ | . . . . . . . . . . . . . . 3 6 7 . . |
$$ | . . . . . . . . . . . . . . . 8 a . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Cho played sanrensei and played the jump attachment, :b7:, against Kobayashi's approach. Kobayashi replied with the unorthodox wedge. (Elf's choice is 10.) I suspect that Cho set a trap for White with :b15:. If so, White fell into it with :w16:. In any event, :w16: is a blunder. According to Elf it loses 23% by comparison with a.

Click Here To Show Diagram Code
[go]$$Bcm17 A tale of two ladders
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O O X 1 . . |
$$ | . . . O . . . . . , . a X X O X O c . |
$$ | . . . . . . . . . . . . 4 2 X O X . . |
$$ | . . . . . . . . . . . . . . 3 O . . . |
$$ | . . . . . . . . . . . . . . b . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


With :w18: and :w20: Kobayashi set up two possible ladders at a and b. Elf recommends c instead. This two ladder setup is a common tactic when the shape is one line closer to the top side. I'm sure that Kobayashi had seen classical problems and ancient game records with Black's refutation. Maybe he was having a bad day. Elf's winrate estimate is skewed by the fact that Elf had perhaps never played the refutation against itself in its training. We can estimate White's loss at around 18%.

Click Here To Show Diagram Code
[go]$$Bcm21 Off with their heads!
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O O X X . . |
$$ | . . . O . . . . . , . . X X O X O . . |
$$ | . . . . . . . . . . . 1 O O X O X . . |
$$ | . . . . . . . . . . . 6 4 3 X O . . . |
$$ | . . . . . . . . . . 7 . . 5 2 a . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


The double ladder breaker, :b27:, was completely off Elf's radar (0 playouts). Elf's first choice was a (241.8k playouts), for a comparative loss of 18½%. Go Seigen criticized Cho Chikun for taking too much time in the opening. But in this case Cho might have played :b27: in two seconds flat.

It is obvious that :b27: breaks the ladder from the right, but where is this ladder from the top? Glad you asked. :cool:

Click Here To Show Diagram Code
[go]$$Wcm28 The other ladder
$$ ---------------------------------------
$$ | . . . . . . . . . . 9 8 . . . . . . . |
$$ | . . . . . . . . . . 7 6 3 . . . . . . |
$$ | . . . . . . . . . . 5 4 2 O O X X . . |
$$ | . . . O . . . . . , 0 1 X X O X O . . |
$$ | . . . . . . . . . . . X O O X O X . . |
$$ | . . . . . . . . . . . O O X X O . . . |
$$ | . . . . . . . . . . X . . X O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


White pushes Black to the edge, then :b37: captures :w28:.

Click Here To Show Diagram Code
[go]$$Wcm38 The other ladder, continued
$$ ---------------------------------------
$$ | . . . . . . . . . . O X 1 . . . . . . |
$$ | . . . . . . . . . . O X O . . . . . . |
$$ | . . . . . . . . . . O X X O O X X . . |
$$ | . . . O . . . . . 3 X 2 X X O X O . . |
$$ | . . . . . . . . . . 4 X O O X O X . . |
$$ | . . . . . . . . . . . O O X X O . . . |
$$ | . . . . . . . . . . B . . X O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


:w38: is atari. After :b39: fills, :w40: starts the ladder up again. This kind of ladder is called a spiral ladder ( https://senseis.xmp.net/?TurnaroundLadder ). Anyway, it is now obvious that :bc: breaks it. :D
Author:  bernds [ Sat Oct 19, 2019 8:58 am ]
Post subject:  Re: Beat Elf!
Bill Spight wrote:
I ran across this one the other day.

Click Here To Show Diagram Code
[go]$$Wcm26 Black to play.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . O O X X . . |
$$ | . . . O . . . . . , . . X X O X O . . |
$$ | . . . . . . . . . . . X O O X O X . . |
$$ | . . . . . . . . . . . O O X X O . . . |
$$ | . . . . . . . . . . . . . X O . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

One of my favourite games, and I like to use this position as an example sometimes: https://github.com/bernds/q5Go#database-support
Author:  Tryss [ Sat Oct 19, 2019 9:09 am ]
Post subject:  Re: Beat Elf!
:b27: was also off Katago radar. With 100k playout, it didn't explore it, and when played, it's a +25% move (or about 10 pts).

This is how Katago try to salvage the situation :

Click Here To Show Diagram Code
[go]$$Wcm28 Katago choice (38-39-40 at a-b-c)
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . a 7 1 . . . . . 0 . |
$$ | . . . . . . . . 8 . 6 . . O O X X 9 . |
$$ | . . . O . . . . . , . 2 X X O X O 3 . |
$$ | . . . . . . . . . . . X O O X O X 4 . |
$$ | . . . . . . . . c . 5 O O X X O . . . |
$$ | . . . . . . . . . . X . . X O b . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . O . . . . . , . . . . . X . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


And it put white at 30% winrate, with -9 pts
Author:  Bill Spight [ Wed Dec 23, 2020 11:29 am ]
Post subject:  Re: Beat Elf!
A whopper for Elf, according to itself. ;)

Click Here To Show Diagram Code
[go]$$Bcm15 Elf's choice for move 115
$$ ---------------------------------------
$$ | . . . . . . . . . . . . X X X X . . . |
$$ | . . . . . . . . . . . X O X O X O O . |
$$ | . . . O . . X . . . X . O X O X O . O |
$$ | . . O , O . . . . , . . O X O X X O . |
$$ | . . X . X X . . . X X O O O O X . X . |
$$ | . . . . . . . . . . O X X 1 . O X . . |
$$ | . . . . . . . . . . O . . X O O . . . |
$$ | . . . . . . . . . . . O . X . O X . . |
$$ | . . O . . . . . O . . . X . X O O . . |
$$ | . . . , . . . . . O X O . . . , X . . |
$$ | . . . . . . . . . O O X . . X . O . . |
$$ | . . O . . . . . . X X . X X O O . . . |
$$ | . . . . . . . X . . . . . O X O . . . |
$$ | . . . O . . . X O O . X O . X . . . . |
$$ | . . O . O . X O X . . O . . O O . . . |
$$ | . . X O O . . . X , O . X X . , O . . |
$$ | . . X X O . . X . . . . . O . X O . . |
$$ | . . . . X . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Elf's peep, by its own reckoning, loses 28% to Rittetsu's play.

If you can find it, you're a better man than I am. ;)

Click Here To Show Diagram Code
[go]$$Bcm15 Mainline for W116
$$ ---------------------------------------
$$ | . . . . . . . . . . . . X X X X . . . |
$$ | . . . . . . . . . . . X O X O X O O . |
$$ | . . . O . . X . . . X . O X O X O . O |
$$ | . . O , O . . . . , . . O X O X X O . |
$$ | . . X . X X . . . X X O O O O X 0 X . |
$$ | . . . . . . . . . . O X X . . O X 8 9 |
$$ | . . . . . . . . . . O . . X O O 6 . . |
$$ | . . . . . . . . . . . O . X . O X . . |
$$ | . . O . . . . . O . . . X . X O O . . |
$$ | . . . , . . . . . O X O . . . 7 X 5 . |
$$ | . . . . . . . . . O O X . . X 3 O . . |
$$ | . . O . . . . . . X X . X X O O 4 . . |
$$ | . . . . . . . X . . . . . O X O . . . |
$$ | . . . O . . . X O O . X O . X 1 2 . . |
$$ | . . O . O . X O X . . O . . O O . . . |
$$ | . . X O O . . . X , O . X X . , O . . |
$$ | . . X X O . . X . . . . . O . X O . . |
$$ | . . . . X . . . . . . . . . X . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

Rittetsu made quite a play!

Elf reckons that Jowa made the wrong reply by not accepting the sacrifice.

The game record, with some of Elf's variations, is below. :)

The fraction is Black's winrate estimate (assuming komi), and the number below is the number of rollouts. Tesuji just means Good move.
Author:  Bill Spight [ Sun Dec 27, 2020 8:50 am ]
Post subject:  Re: Beat Elf!
On the third day of Christmas

Click Here To Show Diagram Code
[go]$$Bcm33 Kato Masao (W) - Cho Chikun, one prisoner each
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . O 1 . . . . . . . . . . . . . . . |
$$ | . O X O . . . . . . . . . . . . . . . |
$$ | . X . X O O . . . , . . . . . X . . . |
$$ | . . X X O . . . . . . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . O . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . X . . . . . , X . . O . O X . . |
$$ | . . . . . X . . . . . . . . . O X . . |
$$ | . . . . . . . . . . . . . . . O O X . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

:b33: is Elf's choice, but it thinks that Cho Chikun's actual move is 15% better.

Enjoy! :)
Author:  Harleqin [ Mon Dec 28, 2020 7:29 pm ]
Post subject:  Re: Beat Elf!
Maybe first attach at B13. If White hane on the inside, Black has gained something even if the ko is resolved to a white corner. If White hane on the outside, Black has several threats to connect.
Author:  Uberdude [ Tue Dec 29, 2020 3:02 am ]
Post subject:  Re: Beat Elf!
What's going on with that lower right corner? With Elf's 33 is black going to play ko threats there? My thinking is maybe black should start there and perhaps even push and cut with q5 as ko threat amplification technique before starting the ko, trying to up the stakes of the subsequent ko threat after only starting top right ko later (which white can't resolve in a good aji way in 1 move anyway).
Author:  Knotwilg [ Tue Dec 29, 2020 12:11 pm ]
Post subject:  Re: Beat Elf!
Both the top left and the lower right look urgent. Let's examine the lower right first.

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


If Black solves the lower right in this active fashion, White gets good shape and sente to kill the upper left. Aji remains at ''a'' but this was a severe cutting point to start with. Having all of that resolved by a capture looks too good for White.

Passively resolving the lower right is even worse.

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


If Black passively protects the upper left, White can ignore and turn to the lower right. Black can defend in two ways.

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


In this variation, White kills, A and B being miai.


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


The second variation is very similar.

So it looks like actively resolving the upper left is the only option


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


Besides Elf's move there's this way. Black has a nose tesuji to sacrifice.

I must say, if this weren't a problem statement from a pro game, I'd hate to be Black. Perhaps I'misreading the lower right?


Edit:

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


Maybe the plot is to cut this way. White can't bail out of this ko. If he does, there's still a ko left at A and the cut at B becomes sharper.
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