Shape 6: Bent Four in the Corner
I’ll stop calling these “weeks” now.
Here is the reference shape for “bent four in the corner”.
The reference shape is unsettled
Of course, black can make life:
However, white can start a ko fight:
If white wins the ko fight, black can be captured:
However, white might not want to start the ko fight if the ko situation in unfavorable.
If black has one external liberty, white must end the ko fight differently:
Although black is dead, black may later capture the three white stones (forcing white to play again at 5) as a ko threat should another ko fight arise elsewhere.
Lives with two external liberties
If black has two external liberties, then black does not need to fight a ko to live:
So, there is no urgency for black to play an additional stone inside until white has reduced external liberties to one.
Temporary sekis that can be reduced to bent four in the corner
The basic bent four in the corner shape is unsettled and hence may live or die depending on whether if black plays again to make life or if white can win the ko fight. This pattern also arises as a product of other positions that can be reduced to this shape.
For example, these two (temporary) sekis can be reduced to a bent four in the corner shape:
Above, white could play at A to force black to capture four white stones, in order to yield the bent four in the corner, with white’s turn to play. Similarly, white can play another stone inside in the below shape to do the same:
In these two sekis, black’s stones are usually dead, even if there are other big ko threats remaining on the board.
Under Chinese (and other area-scoring based) rules, white can wait until the end of the game to resolve this position. After other more valuable moves are finished, white can first remove ko threats and then initiate the sequence. The exception is if there are unremovable ko threats (like those that arise from a seki elsewhere). Under that exceptional case, it may turn out that black’s stones in the corner are strategically alive (see Life and Death under Chinese Rules for an example).
Under Japanese rules, white can simply leave the position untouched and then apply the special ko rules of the life and death resolution procedure, which essentially disallows any ko threats besides passing. Even though black’s corner may be uncapturable during normal play (due to large, unremovable ko threats), white can still argue that the stones are dead by not initiating the ko fight during the game.
It should also be noted that under the modern Japanese rules, it is not automatic that bent four in the corner is always dead either. Here is an example where two interacting bent fours in the corner produces a seki: http://warp.povusers.org/go/UndeadBentFours/