Bent four in the corner

  Difficulty: Advanced   Keywords: Life & Death, Rules

Bent four in the corner is an expression referring to two things.

  1. The eye shape of a group in the corner being bent four, which we will discuss here.
  2. The fact that under Japanese rules, a group which is surrounded by a live group and whose eye shape can be reduced to this shape, is --as a rule-- dead. Discussion at Bent four in the corner is dead.

Table of contents Table of diagrams
Fewer than two outside liberties
Main line
Finishing the ko - a
Finishing the ko - b
Bent four in the corner
Bent four in corner
Situation 1 with a potential bent four
Situation 2 with a potential bent four
Mistake
Correct
Not Corner Bent Four
Not Corner Bent Four
Not Corner Bent Four


1. Fewer than two outside liberties

[Diagram]

Fewer than two outside liberties

If the defending shape has fewer than two liberties on the outside, Black can prevent unconditional life for White's group and make a ko by playing at a.

[Diagram]

Main line

White responds with an atari at W2. Black starts the ko at B3.

White can't play oshitsubushi at a, because of shortage of liberties; and the fate of the group is decided by a ko fight.



1.1 Finishing the ko

[Diagram]

Finishing the ko - a

With a single outside liberty, Black finishes the ko by almost filling the eyespace with a bent three. Playing B1 at a reignites the ko and gives White a second chance.

[Diagram]

Finishing the ko - b

With no outside liberties, Black can finish the ko by capturing all the stones. Playing B1 at a leaves White a strong ko-threat.


2. At least two outside liberties

[Diagram]

Bent four in the corner

If White has an extra liberty on the outside, however, she can play the atari at W4, an oshitsubushi: Black cannot form a killing shape at W2 because this would be suicide, which either is forbidden or includes self-capture.

[Diagram]

Bent four in corner

So, if B5 takes away a liberty, White plays W6 (capturing two stones) and makes life with two eyes.


3. Making bent four in the corner

The position becomes more complicated when the eye shape is almost filled in the following ways.

[Diagram]

Situation 1 with a potential bent four

White can play at neither a nor b because having her eyespace almost filled with straight three means death. Therefore Black can fill the marked outside liberties at any time, before playing a. As we now know this starts a ko. We now refer to the page bent four in the corner is dead to explain why this is dead as a rule.

[Diagram]

Situation 2 with a potential bent four

Black cannot play either at a or b, because White will play c to almost fill the eye space with bent three, which kills. Therefore White can fill the marked outside liberties at any time, before playing c then a or b. Again, as we now know this starts a ko and we refer to the page bent four in the corner is dead to explain why this is dead as a rule.


4. Avoiding The Bent Four

[Diagram]

Mistake

B3 at a would be the bent four in the corner. B3 avoids this but at a cost. (Later Black a, White b, and Black has three points.) Although he lives, B1 is a mistake.

[Diagram]

Correct

B1 here instead lives with four points, avoiding the bent four altogether.


5. Corner Non-Bent Four

The following are Bent Four and are in the corner but are not examples of what is meant by Bent Four in the Corner. In each, 'a' and 'b' are miai for life:

[Diagram]

Not Corner Bent Four

[Diagram]

Not Corner Bent Four

[Diagram]

Not Corner Bent Four


6. Links

Some exercises involving bent four in the corner

See also


Authors


This is a copy of the living page "Bent four in the corner" at Sensei's Library.
(OC) 2005 the Authors, published under the OpenContent License V1.0.
[Welcome to Sensei's Library!]
StartingPoints
ReferenceSection
About