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KanazawaSolution24
KanazawaSolution69
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Two By Three Box
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    Keywords: Life & Death

1. No outside liberties

[Diagram]
Diag.: No outside liberties

If there are no outside liberties, White can kill Black unconditionally by playing at 'a'.


[Diagram]
Diag.: Main line

After White 3, Black can't play at 'a' because of damezumari. So, White can play there (or to the left of it) to capture the black stones (which she actually doesn't have to execute).



2. One outside liberty

[Diagram]
Diag.: One outside liberty

When there is exactly 1 outside liberty, the best white can do is to make it a (two stage) ko. The vital point is at 'a'.


[Diagram]
Diag.: Main line

Black's throw in at 4 is necessary: if White gets to play there she makes it a bent four in the corner. White 5 starts the ko. White can "finish" this ko by connecting at 4. Black captures four stones at 'a' setting up another ko (see next diagram).


[Diagram]
Diag.: Continuation

After the marked stone (Black 'a' in the previous diagram), White sets up another ko with 1 and 3. She can finish the ko by connecting at 2, creating a bent three nakade. So, White has to win the ko two times to kill the corner and Black only once to live. [1]


[Diagram]
Diag.: White's failure

With one outside liberty, this White 1 fails. Black can play 4 because now he is not in atari.



3. Two or more outside liberties

[Diagram]
Diag.: Two outside liberties

When there are at least two outside liberties, Black is unconditionally alive.


[Diagram]
Diag.: Main line

The sequence is copied from the main line in the previous paragraph. Only now Black can play the surprising move of 6 because he still has two (or more) liberties. White cannot connect at 4 so Black will play there to make two eyes.


Addendum

In this diagram, black is dead.

No, this is not a seki. Why?

[Diagram]
Diag.: Explanation 1.

After white 1 and 3 fills up all the external liberties, the marked black stones are caught in a connect-and-die.


[Diagram]
Diag.: Explanation 2.

If black 1 prevents the connect-and-die at any point of the game, he turns his group into a straight three big eye instead and dies in gote.



Footnode:

[1]: One could argue that, this being the case, White might as well fill the outside liberty in the main line diagram instead of connecting at 4 there, but then Black is the first to capture the second stage of the ko and here it is White.


Authors:

WikiMasterEdited by Dieter. Original posts now at TwoByThreeBoxDiscussion.



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