Life and death

Life and death is a fundamental concept in the game of Go, where the status of a distinct "group" of "stones" is determined as either being "alive", and may remain on the board, or "dead," where the group will be lost as "captured". The basic idea can be simply but slightly inaccurately put in the form that:

:"A group must have two eyes (meaning secured internal liberties) to live (meaning to survive through to the end of the game)."

Importance

"Life and death" situations and issues occur when an area with a group of stones surrounds a small area (<7 points) so that it may not be possible to form two separate independent "eyes". As the board fills up during the course of the game, certain groups will survive, and others may not. A group with a "single eye" can normally be captured, in the end, by filling first round the outside. The purpose of making "two eyes" is to prevent this. Novices sometimes interpret "making two eyes" in a narrow way, and form 'explicit' eyes one by one. This is often the wrong approach, and it is better to play generally to make a territory inside a group out of which "two eyes can surely be made", if and when the opponent attacks it. Groups with seven or more points of territory will be able to form two eyes easily when attacked, unless there are some serious structural weaknesses.

Because the loss of a group can mean the loss of the game, and because the efficient use of each move is important, knowing the "life and death" status of one's own groups (as well as one's opponent's) is an important skill to cultivate, if one is to become a strong player. The correct, accurate plays with which to make a group secure, or to kill the opponent's group, are studied deeply by all strong players.

tatus of a group

The concept of 'status' is discussed in "Life and Death" by James Davies. Groups of stones are divided into those that are "alive", "dead" or "unsettled". Here "alive", for example, is an unconditional judgement made, that with best play from both players, the group can survive to the end of the game. That assumes the "opponent" starts: the alive status means that, whatever the attack made, there is an adequate defensive answer.

The "unsettled" status is therefore most worthy of attention. By playing first, the attacking player can kill such a group. By playing first, the defending player can save such a group. There is an enormous range of formations that are unsettled.

A group can be considered "alive", "dead", or "unsettled" based on whether two eyes can be made regardless of how the opponent plays. Naturally, one space is insufficient. Two adjacent spaces are insufficient to make two eyes as well, since putting a stone in will create one eye only. The opponent can simply fill in one of the two spots, threatening to fill in the other, forcing the player to capture that one by playing in the second one. Then, the opponent simply plays there again, killing the group. Usually this will not be done during the game, but at the end, during calculation, the group will be labeled "dead" and removed as prisoners. The only way to actually remove a group from the board is to fill its "eye space" with all but one, forcing it to capture the filling-in group by putting a stone in the last space. If the created group is not alive, then continuing this process will eventually kill the entire group.

There are two possible groups of three, an "r" shape and three in a line. Both of these are unsettled, as whoever plays obtains the desirable result. The person trying to create two eyes can play in the middle spot (the one connected to the other two) and the other two are now eyes. If the opponent plays, he will play in the same spot, followed by an adjacent spot, leaving only one empty spot left. This forces the first player to capture, leaving the dead two shape.

With four blank spots, there are four unique shapes. Two are alive, one is unsettled, and one is dead. The two alive ones are the straight line and the L shape. If the opponent plays in any spot, the first player can live by playing in the adjacent spot in the center two. (in the straight line, for example, if the first player goes in either center, threatening to put an unsettled three-space line in, putting one in the other center one will do the trick). The unsettled shape is the four-stone pyramid. Whoever plays in the center spot gets the desired result, so whoever's move it is wins. A two by two four square space is dead. If the player plays in it, the opponet plays in the opposite diagonal point.

There are no dead shapes with more than four empty points, though there are a couple unsettled ones. A five stone plus sign and a "bulky five" (a square and one point off it, similar shape to a fist with the thumb extended") are the two unsettled ones. Playing in the point that touches the most others (four in the plus sign - center point, three in the "bulky five" - the one point in the square touching the outside point) will give the desired result to whoever does so.

There is only one unsettled six shape, and the rest are all alive. This one shape is the square, plus adding the two points touching any one of the corners. (Similar to the plus sign five, but add any of the four taken corner points to get the unsettled six). The opponent playing in the center point threatens to fill all but one spot with a bulky five shape, and there is no defense.

Any group surrounding more than six points is alive, but it may be necessary to respond correctly if the opponent attacks.

Caveats

Because of the possibility of "seki" positions, the basic doctrine on "two eyes" is not to be applied absolutely literally. It is not precisely the case that the necessity of two eyes is a "derived rule" of the basic rules. That being said, mastery of the principle of two eyes is completely fundamental for go players.

Groups that are "alive" may yet die. One reason is that they may be sacrificed, in the course of a ko fight.

Another way in which the "ko" rule enters the discussion is through the complications "ko" adds to the classification by status. It is quite possible for a group to be alive in "ko": that is, the group is "conditionally alive", the condition being to be able to win a particular "ko" fight relating to the control of a key intersection.

Dead stones

Virtually all games will have at least a few dead stones, which remain on the board at the end of the game, when both players pass. Those dead stones are then removed, in an operation often called 'cleaning', which is a separate phase of the game. The stones removed are treated exactly like other captured stones. Under Chinese rules, which use area counting, stones removed during the cleaning phase are returned to their bowls.

It is a novice mistake to carry out the capture of dead stones before it is of tactical importance to do so. Such plays, during the game, waste a turn, and may also cost points.

Single stones and small groups are often sacrificed. In cases where a group is more than of sacrificial value, that group typically must "make life" in order for one to have a chance at winning the overall game.

Generally each side will have at most 4-5 living groups on the board at the end of the game. There is a go proverb that says that "Five groups may live, but the sixth will die" [http://senseis.xmp.net/?path=GoProverbs&page=FiveGroupsMightLiveButTheSixthWillDie] which in a nutshell describes the need to emphasise connection between developing groups. The struggle for life can be solved by connection. Since each group needs two eyes, (and eyes are sometimes hard to come by) the alternative is to connect out to another group, thereby sharing both liberties and eyes.

"Aji"

Even if a group is lost, one can still use one's own dead stones for aji (potential). Ko threats are just one way in which apparently dead stones are put to good use. Expert players use a variety of 'squeezing' tactics, of which "semedori", an advanced endgame technique, and "shibori" are two that have recognised Japanese-language names.

ee also

* Tsumego

References

* James Davies, "Life and Death: Elementary Go Series, Vol. 4", The Ishi Press, Inc., Tokyo, Japan, 1975.

External links

* [http://www.goproblems.com Goproblems.com site] has over 3000 life and death and other Go puzzles, in an interactive applet. (Requires [http://java.sun.com Java] )

* [http://lie.math.brocku.ca/GoTools/applet.html GoTools] , free (but a password will be required) Java applet for solving life-and-death problems, of professional level. Note that the applet is buggy: it often freezes, gives up, or returns the wrong result.

* [http://senseis.xmp.net/?LifeAndDeath Sensei's Library: Life and death]