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Bent four in the corner is dead
Path: SecondCourseOnKo · Prev: NoResult · Next: EternalLife
Keywords: Life & Death, Ko, Rules
This page discusses the fact that under Japanese rules, a group whose eyeshape can be reduced to bent four in the corner, is unconditionally dead.
Let's take over this position from bent four in the corner. 1. Japanese rulesBy Japanese rules the white group in the above diagram is considered dead and is removed without playing any ko. The reasoning for this is as follows. Since White can never play a nor b, Black can fill all outside liberties at the end of the game, and then play a to create the ko explained in bent four in the corner and shown in the following diagram:
The assumption is now that at the end of the game, there are no ko-threats. So White can't recapture and Black wins the ko. This rule has been discussed ever since its existence, because the fact that some (even many) games contain unremovable ko threats, makes this rule unfair towards the defending side in this position. KarlKnechtel: How about a double bent-four situation like this?
It seems to me that when one side starts a sequence (by extending to either a, forcing a play at the corresponding b, and replacing the circled stone), that the other corner can provide ko threats for the first fight. If the response to a is the other a (applying mutual damage), then the first player has the choice of capturing four stones and starting a sequence, or capturing a large group and having his captured in return (in which case there is nothing more to dispute). What asymmetries can be introduced here? The Japanese rules suggest to me that both "sandwiched" groups die leaving an even result, but is there a way that the first player can do better than that? (obviously there is no way the second player can do better, because of passing - the same reason that the proper value of komi must be nonnegative.) Suppose one of the "sandwiched" groups contains some extra stones; if the player with the large group is to move, can he play to save both groups (which would benefit him)? (Should this go on a separate page?) 2. Other rulesetsUnder Chinese rules or under rulesets where life and death have to be proven rather than simply decided, the ko should be played, because unremovable ko threats can make a difference. 3. CautionWhen the surrounding group of a group which is supposed to be dead by this rule, is not alive with two eyes itself, the rule doesn't apply: in that case the aforementioned ko will be played out. [1] Authors
[1] Well, it can be more complicated than that too but I think I'll leave that for some other Robert. Path: SecondCourseOnKo · Prev: NoResult · Next: EternalLife This is a copy of the living page "Bent four in the corner is dead" at Sensei's Library. ![]() |