Bent four in the corner is dead
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On this page, we consider a White group (topic diagrams 1 and 2) which is surrounded by a live enemy Black group and whose eyeshape can be reduced to the L-shaped bent four in the corner (reference diagram). Such a surrounded group is also known as bent four in the corner. Note that in the topic diagrams, White cannot play inside the eye, otherwise White will be dead with a three-space dead shape. If White has no unremovable ko threats, then it can be proven that the White group is dead.
Under the Japanese rules, the bent four in the corner is always dead as a rule. This is because the determination of life-and-death at the end of the game effectively assumes that the player of the surrounded group has no unremovable ko threats.
We show that when there are no unremovable ko threats, the bent four in the corner is dead.
When there are no unremovable ko threats, Black can wait until the end of the game, and proceed to fill up all outside liberties and remove all the ko threats that White has (diagram 1). Next, Black turns it into the L-shaped bent four and starts the ko with , , and (diagram 2). Because White has no ko-threats, will capture the entire White group with a, hence White dies.
For the other common kind of bent four in the corner, the illustration is similar.
Note that having an existing stone, or making the mistake of playing the stone before removing all outside liberties, actually allows White to live unconditionally. The reason is because White can capture the Black stones with , and then live via oshitsubushi with and .
The current rule is now that in the determination of life and death at the end of the game, after play has stopped, only a pass for a specific ko will allow that ko to be taken back. Effectively, these rules imply that the player who needs to take back the ko has no unremovable ko threats. Applied to the bent four in the corner, the Japanese rules says that it is dead.
The first written Japanese rules, in 1949, had a special rule that "bent four in the corner is dead". This ruling has been discussed ever since, because of the fact that some games contain unremovable ko threats. Many believed that that made this rule unfair towards the defending side in this position.
Under Chinese rules or under rulesets where life and death questions may be settled by actual play rather than decided by virtual play, the ko should be played. Such rulesets provide means to remove dead stones by playing inside your territory after the game without losing points (e.g. by using area scoring or pass stones). Thus, it costs nothing to remove all ko threats before starting the ko, so the bent four in the corner is still essentially dead. However, unremovable ko threats can make a difference.
- When 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. 
- Japanese rules can be difficult to apply, e.g. in connected Bent-4 situations -- Example at Undead-Bent-4
4. Bent-4 on the Go Servers
Could someone write an overview how Bent-4 is treated on the different Go Servers?
It is one thing to say that one would "apply Japanese Rules" and another to bring them into practice via an electronic medium, most probably without a referee. Which server does actually have this phase where 'only a PASS is allowed as Ko threat'?
My understanding of Japanese rules on go servers is that they are simply not implemented properly, at least on kgs. I have personally lost a game because it was played under japanese rules and my opponent had a shape that would become bent four once played out. The dead shape was disputed by my opponent and I was faced with the choice of either filling in all of my opponent's ko threats and playing it out, or just playing it out and ignoring a threat. Either option would lose the game by about ten points.Under chinese rules, I would have simply removed the ko threats, without losing any points, and then killed the bent four. The worst part about it is that on KGS Japanese scoring is used by default and few people bother to use area scoring, so this situation must be extremely common
zinger: I think that "extremely common" is an exaggeration - I have played over 2000 games of Go and never once had a disputed bent four. Besides that, it sounds like the problem is not that KGS is implementing the rules improperly, but that the opponent did not understand the rules. After all, a dishonest opponent can wrongly dispute life and death under any ruleset.
KGS does implement rules improperly, especially those titled "Japanese Rules" on this server. The programmer has told me: One should occupy all non-seki-dame because KGS makes scoring mistakes otherwise (it is well known that KGS does indeed); where the players cannot agree on scoring, they are supposed to ask a third person to arbitrate; needless to say, implementing and executing complete Japanese rules is theoretically impossible; there are several "Japanese Rules" rulesets, so a server cannot implement them all at the same time under just one title. To describe all this, I speak of "KGS-Japanese Rules". --RobertJasiek.
 Many games in number, but a tiny fraction of all games.
 Well, it can be more complicated than that too, but I think I'll leave that for some other Robert.
Harleqin: I won't say it is complicated. The rule only applies after the end of the game. If the attacker is forced by circumstances to actually remove the "dead" stones before the end of the game, then he will obviously have to fight the ko.
Bass: Interestingly, if the surrounding group has only one four-space big eye, then the same rule works in exactly the opposite direction, and the bent four in the corner is unconditionally alive. See suicidal tendencies for an example.
tywin: I stumbled across a position that is very similar to the bent four in the corner.