Seki is a Japanese
term from the game of Go
). The best English
phrase to describe it is "mutual life."
Ordinarily, a group needs to have two eyes (empty points inside itself) to live (see my writeup on the eye node for an explanation why). However, in relatively rare circumstances (at my very low level, it tends to happen in maybe 1 out of 100 games, but I believe it arises more frequently at higher levels of play), it is possible for two groups of opposite colors, with one, or even zero eyes, to find mutual life.
This is counter-intuitive, because in Go, you kill a group by surrounding it. Logically speaking, it seems like either a group is surrounded, or it isn't. How can two groups surround one another? The answer lies in the fact that Go is a turn-based game. You get to play one stone each turn. In order for a group to be captured, it must be first reduced to one liberty, that is, one empty space beside (or inside) the group. Imagine now that two groups each have only one liberty. Furthermore, imagine that liberty is the same point for both groups. Whoever gets the first opportunity to play on that point will capture the other player's group, and probably make life for his own in the process. Now, imagine that the two groups each have only two liberties and that at least one of those is the same point for both groups. To capture one of the groups, it is first necessary to reduce it to one liberty. To do so, it is necessary to play on the shared liberty. But, as described above, this also reduces the player's own group to one liberty. Since it would now be the opponent's turn, it would be the first, rather than the second player's group that would be captured. Consequently, neither player will ever fill the shared liberty, and both groups "live in seki."
Here is an example of seki with no eyes (edge of the board in these diagrams is marked with ###).
This is, admittedly, a highly artificial situation that you would never see in a real game, but it serves to illustrate the idea. The two internal points marked with commas are empty. If one player plays one, the opponent will play the other, capturing the group and making life for his own.
Here is an example of seki with one eye for each group (note that it is impossible to have seki where one group has one eye and the other has none... in that case, the group with the eye always wins):
Each group has one eye (the hollow points), and there is only one shared liberty, again marked with a comma. If either player fills the shared liberty, the other player will play inside the first player's eye and capture. Note that neither player can play inside the other's eye until the shared liberty is filled (because suicide is forbidden).
It is important to note that sometimes a situation sometimes appears to be seki, but isn't. This occurs when one player capturing the other would result in a dead shape (a shape that cannot make two eyes). In this case, the player who can form the dead shape will fill a common liberty, get captured, and then immediately respond to kill the group that is trying to survive. Here is a before and after example in the corner:
Diagram 1: Seki?
Now, imagine White (o) fills one of the shared liberties and Black (x) captures. We'll choose the top-left one, but the other one achieves the same result.
Diagram 2: Not seki!
After Black captures, he is left with a bulky five big eye. Since White has the next move, she plays at the vital point a. Now Black has no way to split his big eye into two eyes, and he has gone the way of the Monty Python parrot.
In a life-and-death situation, there are four possible results for the defender in a given situation: unconditional life, unconditional death, ko, or seki. Obviously, unconditional life is always the best result for the defender, and unconditional death is the worst. However, the relative desirability of ko or seki depends on how many ko threats each player has, and who would start the ko, since seki is sort of like a tie, whereas ko will result in one player or the other winning, with the result to be determined by the ko fight. In certain situations, one player or the other will have the choice of whether to turn the situation into ko or seki. At this point, careful analysis of the rest of the board is in order, since the death of a large group will generally decide the outcome of the game then and there (usually, ko is more desirable for the attacker, and seki more desireable for the defender, but this is not always the case, if the defender has far more ko threats than the attacker).
It is also worth noting that neither player scores points for shared liberties in a seki. Whether points are scored for the eyes is irrelevant, since if one player has an eye, the other must as well, and one point for each player makes no difference to the outcome of the game, since relative score is all that matters.