Unremovable Ko Threat
Unremovable ko threat
An unremovable ko threat is a ko threat which cannot be removed without also executing the threat.
Unremovable ko threats typically occur in seki positions; here is an example. White has a ko threat here at a, which Black can never remove. Removing the ko-threat would mean Black playing at a himself, which of course leads to instant capture.
Sometimes dead groups contain unremovable ko threats for unremovable kos.
One-sided unremovable ko threat without loss
chewtonic: If Black answers White's move at a by playing at b (diagram above), White loses points. There is a class of positions which could be called 'one-sided unremovable ko threats' where one player loses nothing with their threat. See diagram on left.
Black can play any of the internal points as a threat that loses nothing (leaving a position similar to the first diagram if White answers), whereas White cannot threaten anything. If a bent four in the corner happens in another corner, Black would feel cheated, under Japanese rules. Note that if you reversed the colours in the bent four in the corner diagram, you would need to reverse the colours in this diagram too, to create a similar situation for White.
cliftut; notice, though, that whoever plays first in this diagram can gain sente. If white plays one of the points first, black has to pick which is more important to him, filling in ko, or getting 10 points in the corner:
- If black fills in ko, then white can create seki in the corner(this would be pointless, of course, if winning ko gave black 10 points or more). This is also assuming white can take no further action to save points after losing ko(ko for life).
- If black prevents seki by playing in the corner, white can take back ko and the fight continues. This loses 10 points for white, though, so it could only be played if winning ko kept white from losing over ten points, and if there were no more ko threats(at least no large ones, depending on how much winning ko is worth.)
I hope I made sense. If not, say so and I'll try to make a diagram. As far as I can tell, though, my comment is valid, if only in very paticular situations(depending on who gains or loses more by winning ko, and exactly how much ko is worth to each player). I just wanted to show that this may not be completely 'one-sided'. If anyone can see a flaw in my logic, please point it out.
yong?: cliftut, you dont make sense, it is seki without white playing.
Jake: He means that black can play this as a ko threat, and white cannot play anything to negate that. Black plays, forcing white to play or black lives, while white can never play here first - assuming white responds to a play (ie threat) move by black, it does become/stay seki.
chewtonic: It is conceivable that Black's best play is to ignore a white move in the seki. For example if Black has no ko threats and the ko is worth more than 10 points. So Black wins the ko and white then plays a second stone in the seki. If stone counting is being used, this extra white stone could win the game. Of course if 2 dame exist elsewhere on the board, white could play there instead and the result would be the same.
Infinite unremovable ko threats without loss
A double ko seki has the interesting property that it contains infinitely many unremovable ko threats for both sides. This means that if a game deciding ko occurs elsewhere, then a triple ko is created. One of the oldest rules disputes also includes the double ko seki, since the infinite unremovable ko threats seem to create life even where there is none.