Rectangular six in the corner

    Keywords: Life & Death

Chinese: 盘角板六 (pan2 jiao3 ban3 liu4)
Japanese: 隅の板六 (sumi no itaroku)
Korean: -

Readers are advised to study the bent four in the corner and the rectangular six (if they have not mastered them) before reading the contents of this page.

Table of contents


1. No outside liberties

[Diagram]
No outside liberties  

If there are no outside liberties:

Black can live with 5 points of territory by playing either a or b,

White can kill Black unconditionally by playing at a.

[Diagram]
White to kill  

After W3, Black can't play at a or b because of shortage of liberties. Black is dead.


2. One outside liberty

[Diagram]
One outside liberty  

When there is exactly one outside liberty, the best White can do is to make it an approach 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. If Black wins this ko, by playing again at B4 and then playing at a capturing the two White stones, the position is settled with Black living in the corner. Should White win this ko by connecting at B4. Black captures four stones at a and White sets up a direct ko for life as shown in the next diagram.

[Diagram]
Continuation  

After black+circle (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 shape. 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]
if White is stubborn  

W1 through W5 is copied from the one-outside-liberty main line. 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.

kevinwm: Aside: Even in New Zealand rules where w can play a9, it is not even a ko threat to make a ko for the corner. (That is, a9 does not make ko for the corner, and does not even make ko for the corner if b does not respond. if w a9, b tenuki, w a8, b a9, w b9, and w a7 makes oshitsubushi again.)


4. Endgame

[Diagram]
 

Suppose there are exactly 2 outside liberties.

[Diagram]
External kos after the other liberty is filled  

If external kos are more likely to occur when the corner has no outside liberties than when the corner still has an outside liberty, then White filling one of those liberties directly is better than White starting inside.

After B2, White has no ko threats as long as circle is empty, but will get two ko threats when circle is played.

[Diagram]
External kos before the other liberty is filled  

If external kos are more likely to occur when the corner still has an outside liberty than when the corner has no outside liberties, then White should play like this instead of starting with W5.

W1 and W3 each threaten more than starting with W5 would threaten, and after B4, W5 threatens at least as much as starting with it would've threatened.

After B6, White has one ko threat regardless of whether circle is empty or filled.


5. Weak rectangular six

[Diagram]
Weakness  

If white+circle is in place, the weakness of the connection enables White to create a ko. White takes first with W1.


Addendum

[Diagram]
Black is dead  

In this diagram, Black is dead.

No, this is not a seki. Why?

[Diagram]
Explanation 1  

After W1 and W3 fill up all the outside liberties, the black+circle 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).


See also

Practice


Authors: Scartol, RMDow, unkx80, SAS, Dieter (WME)


Rectangular six in the corner last edited by 70.191.86.10 on April 18, 2020 - 20:23
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