semeai

A semeai arises when two weak groups of opposite colours are both enclosed by the other player's stones, but part of that enclosure comes from the other weak group. That is, Black has a strong group A and a weak group B. White has a strong group C and a weak group D. A and B enclose D, and C and D enclose B. Consider this diagram, for instance (edge of the goban marked with ###):

.........
..xxooo..
.xxoxxxo.
.xooa..o.
.x.o...o.
#########

(No stone at a: see below)

The six Black (x) and White (o) stones on the outside are strong. They are difficult or impossible to kill (depending on the surroundings), but the four White and three Black stones inside are weak. Note that neither weak group can connect to its friendly strong group, because of the existence of the enemy weak group.

In a semeai, the two weak groups are locked in a life-and-death struggle from which there is no escape. Killing the other weak group guarantees life, and this, or seki (mutual life) are the only ways to live. Therefore, unless seki is possible (and it rarely is), one must die, and neither player wants it to be his or her group, hence the term capturing race.

If neither weak group has an eye, the result of a semeai generally comes down to the number of outside liberties each group has. An outside liberty is one that is not shared between the two groups. They are generally the first to be filled in a semeai, because filling an inside (shared) liberty also deprives one's own group of a liberty as well. In the diagram above, the point marked "a" is a shared liberty and will probably be filled last under most circumstances (although in this case it doesn't make much difference). In the simplest situations, whichever group has more outside liberties will kill the other and make life for itself. In the case of a tie with only one inside liberty (like this one, where each group has two outside and one inside liberty), the player whose turn it is to play will win. With more than one inside liberty, seki (mutual life) can result. Using the above example:

.........
..xxooo..
.xxoxxxo.
.xoo431o.
.x2o5..o.
#########

Imagine White can play first. White plays 1, Black plays 2, White plays 3, and Black's three stones are dead. If Black plays 4, he is still in atari, and White simply captures at 5. Note that if Black had the initiative, the move at 4 (or 5) would come before the White move at 3, and Black could capture White before being captured himself.

Semeai can be more complicated than this, though. Sometimes approach moves are required before filling an opponent's outside liberty (that is, playing on the liberty immediately would let him capture that stone and save himself, so another supporting move is required first), in which case approach moves are counted as if they were outside liberties. If one group has an eye, inside liberties must be filled before the eye, so they are counted as outside liberties for that group only (unless the other group also has an eye). This is a big advantage, hence the proverb "Eyes win semeai." Here is an example:

..........
.....xxx..
.oooox..x.
.oxxxoo.x.
..x.xa..x.
##########

At first glance, this looks good for White; three outside liberties vs. two (one on the left, plus the eye). But White must fill the inside liberty "a" before playing in the eye, so Black essentially has three outside liberties as well.

..........
.....xxx..
.oooox1.x.
.oxxxoo3x.
.2x.x456x.
##########

If Black plays first: Black 1, White 2, Black 3, White 4, Black 5 captures (if White 5, Black 6, and White then can't play 4... White is still dead).

Of course, one can go on to create more and more complex semeai, with oodles of liberties, potential to create eyes, cutting points, approach moves, etc., etc. In fact, many tsumego (kind of the Go equivalent to the chess problems you see in the newspaper) involve semeai.