Seki, a Japanese go term adopted into English, it means mutual life. In its simplest form, it is a sort of symbiosis where two live groups share liberties which neither of them can fill without dying.
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The simplest form of a seki is shown in this diagram: the and groups have no eyes, and share two liberties at a and b. If either player plays on one of these points, the opponent will play the other and capture. So neither player will.
If Black plays anyway at , White can capture the bulky five shape with , It is then useless for Black to play because White can respond with and connect to her group below.
It is clear that and both locally work out badly for the players, but sometimes and can be used as big (but point-losing) ko threats.
A slightly more complex variant is formed by the marked black and white groups. Both groups have one eye, and they share a liberty. Again if either player plays at a, the other one will capture.
The two white groups both have one eye. The black group has none, but shares a liberty with both of the white groups. Again no player can capture any stones of the other player, and the position is seki.
Here is a similar position without depending on the status of the outside white group:
The only play for either side which doesn't immediately lose the corner, is White at a. However that costs 1 point in gote, as Black captures at b and White must recreate the original position by recapturing at . This is an example of sending two returning one.
In this Diagram b is a real eye, Now it is not a seki: White would be able to capture Black and she would be alive.
a and b are (false) eyes, which would count in Chinese (and de facto Internet) rules, but not in Japanese scoring.
Note: that again in some rulesets this may not be seki under rare circumstances, depending upon the superko rule.
Another type of a seki. Black can capture the three white stones, but if he does, White will then come back at the point where the marked stone is. Black will then be left with a dead shape, so Black will not do so. Likewise, if White were to try to capture Black, she would at some point need to play another stone inside Black's eyespace. However, Black would then happily capture the four stones and be left with a live 'straight four' eyespace. Therefore, neither side wants to play here and this position will remain until the end, with the three white stones and the black group surrounding them alive through seki.
When scored, the black group gets zero points.
Example of a seki with double ko
This is an interesting seki, but involving double ko. If White captures at a, then Black will capture at b; later, if White recaptures at , then Black can recapture at , returning to the original position. The same comment applies to Black as well.
Seki with strings in atari
Both sides have a string in atari, but for either side, capturing starts a capturing race that the other side can win. Best play is to leave this, therefore it's seki.
To see why this is so, see hanezeki.
The Japanese Rules say that "eyes in seki" are not counted as territory.
This may sound like a stupid question, but what does that refer to? Are all eyes of the groups living in seki ignored, or just the shared eyes?
Are the circled points counted as territory for White?
- According to Japanese rules they are not, but according to Chinese rules they are.
A group living in Seki should have no more than one eye. --Confused
Benjamin Geiger: If I understand correctly, each group living in seki can have one eye.
Annodomini: Under Chinese Rules, and other area-scoring rulesets (AGA, New Zealand, Ing I believe), points in Seki do count. This is something to watch out for, because the results differ in Japanese rules and area-scoring rules.
Sending Two Returning One with an eye for each side
In the 4-move (3-move?) cycle Black plays 2 stones, White only one. With territory rules, this costs Black one point. After some (finite) number of cycles have been played, White could simply admit Black's claim that the white group is dead, and still have enough points to win. So Black does not start the cycle. (Why would Black initiate at all if costs one pt per cycle?)
Chris L After one cycle the board position will have been recreated. Is this not prohibited by some form of ko rule?
chrisg I'd be interested if someone could add a reference to a page explaining if this isn't a seki, and under what rules.
El Draco With the positional superko rule, it would be prohibited to complete a cycle, but with situational superko, after one cycle it's white's move instead of black's. If he plays somewhere else, black can try playing there again, with the same result.
If, at some point, white passes and black tries playing again, he may not move again at a1 if white passes again, since that would be prohibited by either superko rule.
There is one devious way black could play however, which is playing a ko threat right after white captures the two stones. After this, white can't pass, lest black plays a1 again and white may not capture the two stones without repeating a previous position with same player to move. This way, black could win if he has more ko threats than white has moves to play. If white plays in black's territory just to not-pass, black must pass and it wouldn't have cost either player a point. If white has no legal (or plain dumb) moves left however at some point, and black has at least one ko threat, black can win.
Correct me if I'm wrong, since I just thought this up. ;)
But you are not alone. I think Frank Janssen was the first to have that idea in the '90s. See Rules Beast 1.
Sekis can get very complex. Here is an example containing 2 Black and 3 White strings.
In my opinion: Sekis exist for 2 reasons:
- One player cannot put his opponent in atari without putting himself in atari as well (auto atari)
- A player can capture the opponents stones but if he does this group is left with only one eye. and dies because he has only one.
the first reason is the most common one, in all sekis it applies (or will later apply) to at least one of the players.
This is just my first impression can there be other reasons
All the examples on this page fit this description. sometimes both players fall under the atari case, sometimes it is for one the atari case and the other the eye case.
Different Japanese rules describe seki differently. The Japanese 1989 Rules do not define seki but define stones to be in seki if they have dame (where, informally, dame are points that aren't inside eyes). It is possible for players not to fill dame points before passing. However, a pedantic player is pefectly within his rights to demand that any group of his opponent's (even if it has 15 eyes) is in seki if it is touching dame, and therefore its territory isn't to be counted. 
However, this isn't really important as there is another Japanese rule that says if one player asks that the game be resumed - the other player MUST oblige but the other player plays first (of course they can pass). So if your opponent tells you (rightly) that one of your groups is in seki, you can just resume play.
Bill: While Charles has a point, the usual assumption that outer stones in a diagram are alive applies. Also, there is a slight inaccuracy. White's outer group does not need two eyes to preserve the seki.
isd: Whether this request would be accepted by a referee has not yet been tested.
RobertJasiek: I could tell something about how it has been tested, etc., but this is off-topic.
isd: If it has been tested in Japan I would be interested in hearing about it, if it has not been tested in Japan I would be disinterested.
RobertJasiek: According to the official J1989 commentary, dame adjacent to ordinary groups create in-seki.
isd: What I am asking is has a Japanese referee ever had to make a ruling on this situation. I am not asking about the content of these rules.
RobertJasiek: IIRC, yes, but I do not recall details by heart. Besides, Sakai Takeshi (the major J1989 author) has confirmed this interpretation clearly. He regrets to have created rules with that side-effect but confirms that such are the current rules.
- All you ever wanted to know about sekis
- Seki unambiguous definition discussion
- Seki in the corner
- A pathological seki
- Seki Examples from real life play
- False seki
- Temporary seki
- Seki collapse
- Butterfly seven
- One stone alive in seki
- Odd eyed seki
- Nine point Eye - Possible Seki
- Ten point Eye - Possible Seki
- Maximum number of live groups
- Strange Sekis
- Whole board seki