Bent four in the corner
Bent four in the corner refers to a position that, if played out, will lead to this bent four shape where the "bend" () is on the 1-1 point. While a normal bent four is a living shape, this shape is unsettled and is the vital point. A white play at will lead to a living group with 3 points of territory. A Black play at leads to a ko favourable to black as described below.
A complication is that bent four in the corner is also used to refer to a group where the defender cannot prevent the attacker from reducing it to a pure bent four in the corner shape (diagram above), and the attacker can postpone the reducing till the end of the game. Such groups are generally dead, but may live because of unremovable ko threats if played out.
A further complication is that some rules decide the status of this group without having the players to play it out. See bent four in the corner is dead.
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Black to play
1. None or one 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.
White responds with an atari at . Black starts the ko at .
White can't play oshitsubushi at a because it would be self-atari; and the fate of the group is decided by a ko fight.
1.1 Finishing the ko one outside liberty
With a single outside liberty, Black finishes the ko by almost filling the eyespace with a bent three. Playing at a would be inferior as it reignites the ko and gives White a second chance.
1.2 Finishing the ko - no outside liberty
With no outside liberties, Black can finish the ko by capturing all the stones. Playing at a would not be as good, as it leaves White a strong ko-threat.
2. Two or more outside liberties
If White has two or more liberties on the outside, however, she can play the atari at , an oshitsubushi: Black cannot form a killing shape at because this would be suicide, which either is forbidden or includes self-capture.
Reducing to a bent four in the corner
Main article: bent four in the corner is dead
A bent four in the corner is also used to refer to a group where the defender cannot prevent the attacker from reducing it to a bent four on the corner shape, and the attacker can postpone the reducing till the end of the game. Such groups are generally dead, but may live because of unremovable ko threats if played out.
The position becomes more complicated when the eye shape is almost filled in the following ways.
This position is also known as bent-four in the corner, satisfying the second definition listed at the top of this page. 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.
Just like the previous position, this shape is also a bent four in the corner even though it has a five point eyespace. Similarly to the previous position, Black can fill up White's outside liberties and then proceed to play at a, followed by b. Like the previous position, this bent four in the corner is also dead as a rule.
Avoiding the bent four shape
at a would be the bent four in the corner. avoids this but at a cost. (Later Black a, White b, and Black has three points.) Although he lives, is a 2-point mistake.
here instead lives with four points, avoiding the bent four altogether.
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:
Some exercises involving bent four in the corner