Karl Knechtel: 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 being 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 both groups be beneficially saved?
Andre Engels: At least under rules when bent four is dead, there is absolutely no possibility of gaining from playing in this situation. Playing in the left does not gain Black anything: if White does not react, Black has simply lost a point. Playing on the right does not gain anything either - White just captures and has nothing to worry about. This type of position seems to be only interesting in rulesets where dead stones have to be captured.
aLegendWai: I did a trial play based on your above diagram. No matter who begins to kill, the final result is either you can kill your opponent group, or you can save your group. As it is wroth the same in your diagram, no party gains. It is draw in this local match. :P
Any idea is welcome.
Graham: So what is the ruling for this configuration?
I don't think either player will be in a rush to fill the mutual inside liberties, since once these are filled on a group the other player would start the bent four ko and kill the outside group and hence break the whole-board deadlock.
So is this seki even under Japanese rules?
Juha Nieminen: I came up with this position to demonstrate how it's possible to construct a situation where the "bent four in the corner is dead" rule is unfair. Assume no komi and no prisoners.
According to the Japanese rules the black group at the upper left is dead and White does not have to demonstrate this. By this rule White wins by 14 points.
However, there's absolutely no way White can win this game by actually playing it through. There are basicly three things White can try, which I have demonstrated below:
If White plays the bent four by playing at a in the diagram above, Black captures with b and this sequence follows.
Now White has two options: Either ignore black's ko-threat or answer to it.
If White answers the threat by playing at c, Black will capture the ko by playing at 2. Now White has no ko-threats, so must pass, after which Black captures by playing at d. The end result is that Black wins by 2 points.
If White does not answer the threat but captures by playing at d, Black will capture at e and win the game by 5 points.
White could also try to remove the ko-threat with ,
but Black naturally captures with
. Even though now
the black group at the upper left is truly dead, Black
still wins by 5 points.
If we considered the situation at the upper left corner a seki, Black would win by 2 points.
Thus there's absolutely no way White could win this by playing.
The Japanese rules may be anomalous but it's not unfair. It applies to both players and they know about it before they start the game. Isn't the standard way to show it is anomalous just to position a double ko elsewhere on the board?
-- Dieter
aLegendWai: It is because W cannot activate the ko itself. It is the B privilege to activate ko or not. But even that, it is just seki, why say bent 4 in the corner is dead?
The second point is that B can fill up all ko threats and come back to kill W group at anytime. So W group is unconditionally dead. Got it?
So in real game, after a bent 4? is formed in the corner, you don't need to do anything more. And the points are yours :)
Mef: There is some fine print here, and that is if white has an unremovable ko threat. In those rare instances white may be able to save the group.
aLegendWai: I think Bent 4? corner is generally true to be dead. Exceptions exist. How about some cases like Moonshine Life (By the way I feel moonshine life is a beauty. It makes Go more attractive and complex :-P. So I would like to grant a seki to this sophisticated player! "Dead" or "no result" is simply a vote to discourage this marvellous play.!)
TDerz Not only unremovable ko threats as explained above question that Bent4? is unconditionally dead. I am sure that someone on this page will already have mentioned that removing all ko threats will cost points and may thus lose the game!
Chris Hayashida: Not quite. Under Japanese rules, after both players pass, a player needs only to show that the group can be captured to prove its dead status. After that, the points are counted from the original position. So filling all possible ko threats (after both players have passed, and the game has ended) only count as a "what-if" and do not count against the player filling the ko threats.
aLegendWai: That's me again. :P I have highlighted my bits to remind the reader of not doing so.
Who can put a link here to the famous Go Seigen game where he refused to connect a (normal) ko for the reason of having an excess of ko threats (normal, not double ko or so)?