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Two-by-three box
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    Keywords: Life & Death

1. No outside liberties

[Diagram]
No outside liberties

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


[Diagram]
Main line

After W3, Black can't play at a because of shortage of liberties. So, White can play there (or to the left of it) to kill the black stones (which she actually doesn't have to take off).

Andrew Grant: No! Black is already dead after 3: for White to play a or the point to the left is a waste of a move.


2. One outside liberty

[Diagram]
One outside liberty

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


[Diagram]
Main line

Black's throw in at B4 is necessary: if White gets to play there she makes it a bent four in the corner. W5 starts the ko. White can finish this ko by connecting at B4. Black captures four stones at a setting up another ko (see next diagram).


[Diagram]
Continuation

After the marked stone (Black a in the previous diagram), White sets up another ko with W1 and W3. She can finish the ko by connecting at W2, creating a bent three nakade. So, White has to win the ko twice to kill the corner and Black only once to live. [1]


[Diagram]
White's failure

With one outside liberty, this W1 fails. Black can play B4 because in this case he is not in atari.



3. Two or more outside liberties

[Diagram]
Two outside liberties

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


[Diagram]
Main line

The sequence is copied from the main line in the previous paragraph. Now Black can play the surprising move of B6 (oshitsubushi) because he still has at least two liberties. White cannot connect at B4 so Black will play there to make two eyes.



Addendum

In this diagram, Black is dead.

No, this is not a seki. Why?

[Diagram]
Explanation 1

After W1 and W3 fill up all the external liberties, the BC stones are caught in a connect-and-die.


[Diagram]
Explanation 2

If B1 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.



Footnote:

[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 B4 there; but then Black is the first to capture the second stage of the ko and here it is White (try to get first capture in a ko).


Authors:

WikiMasterEdited by Dieter. Original posts now at TwoByThreeBoxDiscussion.



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This is a copy of the living page "Two-by-three box" at Sensei's Library.
(OC) 2003 the Authors, published under the OpenContent License V1.0.