TwoSquares/Sandbox

Sub-page of TwoSquares

Seki

Two opposing formations that only share a rectangle, where each side has two stones on one of the longer sides and two corner stones of the rectangle, form a seki; no corner stone may be omitted in this case.

[Diagram]
Sharing a rectangle  


[Diagram]
Not good enough. Fake Seki. Black can make dead inner form  


Two opponent formations that share only two squares also form a seki; again no corner stone may be omitted.

[Diagram]
Sharing two squares  


Two opposing formations, each having only one square, and sharing a square also form a seki; only in the fully owned square may a corner stone be omitted.

[Diagram]
Each owning a square and sharing one  
[Diagram]
Sharing two squares can be repeated in between  


[Diagram]

Fake Seki - Playing W3 on the side of two squares


[Diagram]

Real Seki


[Diagram]
Special Seki with stones in Atari  



Applications

Partial filled squares & rectangles

The square structure can be recognized in many formations that occur in actual play.


Preventing squares

The opponent can prevent the formation of a square in two different ways. Either with a single stone on one of the four sides of the square or with stones in any two corners of the square. You can also prevent squares with more stones or other combinations of two stones, but basically it comes down to the three forms below in the end.

[Diagram]
Preventing squares  


The prevention methods can be recognized in various situations

[Diagram]
Peep, Eye stealing tesuji, Center of 3 stones?  



Three overlapping intersections

This definition can be used to solve life and death problems. Let us start with a simple example.

In this almost completed setup the two squares in Black's collection have three overlapping intersections: one occupied by a black stone at 2-2 black+circle, an empty intersection at 1-2 circle, a ‘virtual’ intersection outside the board adjacent to the 1-2 position (circle). For White to kill this collection of black stones he must use one of the two square preventing methods described earlier. And with a single stone on the 1-2 point circle White can prevent both squares at the same time, since this is a single stone on the side position of each of the two squares. For Black to save his collection of stones he must complete the creation of two fully filled squares. Again by occupying the 1-2 position circle. This makes his collection of stones alive according to the definition above.

[Diagram]
Two squares in corner with 3 overlapping intersections  



Four overlapping intersections

The next example has four overlapping intersections.

One of the corners of each square is the center point of the other, and must therefore be omitted. But this does not mean that a corner stone is missing. It is only covered by the center of the other square.

Black has not completed constructing the two squares, however. A corner stone at 1-2 circle is missing from the square around position 1-1. Moreover, two stones are missing from the square around 2-2, at 1-2 circle and 1-3 square. The latter square can however be completed with the 1-2 position circle only, because one corner intersection may be omitted according to the definition. Since the 1-2 point circle is shared among the two squares, playing here makes the black stones alive.

If White played the 1-2 position circle first then he would prevent both the squares by playing a single stone on a side position of each square.

[Diagram]
Two squares in corner with 4 overlapping intersections  

Preventing rectangles

[Diagram]
Prevent the rectangle with a dagger  
[Diagram]

Prevent the rectangle with two stones on the frame

[Diagram]
Prevent the rectangle with three stones  

Prevent rectangle example

This example uses the three stones technique to prevent White from forming a rectangle. N.B.: The last stone is to be imagined placed outside the board.

[Diagram]
Three stones prevention  
[Diagram]
Reference diagram  

Life and Death examples

The L-group

One of the solutions Black would like to play in the L-group is to make a square and a rectangle with the two 1-2 & 2-1 marked positions circle. So if Black plays one of them then White should prevent Black's square in the corner by playing the other marked position.

[Diagram]
L-group  


Another solution that Black can aim for is to make the rectangle in corner and the square in the bend of the L.

[Diagram]
L-group, alternative solution  


Before we look at the last way Black can try to make two squares, we have to look at how rectangles are prevented.


The J-group

[Diagram]
J-group, Black to play  


If Black plays first in the J-group he can quickly create multiple possibilities for two squares with a stone on any one of the circles. So the question is if Black can survive when White plays first.

[Diagram]
J-group, White to play  


White bends at W1, and Black tries to make two squares with his stone at B2, but White prevent this with W3.

[Diagram]
J-group, White to play, continuation  


Black then tries to make two rectangles with B4 @(3,1) and B6 @(2,2), White W5 and W7 prevent him from completing, because Black has to put his stones in self atari.

[Diagram]
J-group, White to play, alternative  


Another possibility is to create a large rectangle and a square in this way with B4 and B6, but W5 and W7 will again prevent this.


Live & Death analysis

Work in progress

[Diagram]
More complicated position  

My next example is a more complicated one. This will show how to use the second method for preventing squares by placing two stones on the corner positions of a square.


[Diagram]
 

The solution to this problem starts with White W1. This prevents the black square by placing two stones in the corners. Black has to reclaim his square by playing B2.


[Diagram]
 

White plays W3 next. This prevents the black squares in from of the 3 stones


[Diagram]
 

Black answers with B4 to start creating a new square around the white stone.

N.B.: This example is not completed, but I'm currently working on a simpler section above.


[Diagram]
 


TwoSquares/Sandbox last edited by kjp on November 23, 2018 - 12:08
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