An overview of life and death
Life and death is an extremely wide topic in Go, yet it is a central tenet in the oriental game whose age is in the thousands. The article attempts to give a general overview to life and death and its techniques, but it is by no means comprehensive.
Locally speaking, a group of stones is said to be alive if it cannot be captured starting with the opponent's turn, assuming both players make perfect play. Similarly, a group of stones is said to be dead if it will always be captured starting from the player's turn. Otherwise, the life and death status of this group is unsettled, depending on which player is playing first, or possibly hinging on the result of a ko fight. The life and death of stones is a central concept in Go, since determining the winning player largely depends on the amount of territory surrounded by the groups that are alive. A particularly significant fact is that almost always captured groups become territory of the capturer, especially when the captured group is large. Also, the life and death status of one chain can affect the status of other chains of either player, such as the stones involved in a cross-cut. Hence, much of the discussion in Go on Sensei's Library and elsewhere pertains to issues related to life and death. In particular, techniques for making life? and killing are among the most discussed topics. Problems on life and death of stones are often called tsumego in Japanese.
Life and death techniques can be discussed on two levels. At one level, we can talk about the art of surrounding opponent's stones, conversely the opponent would want to find means of escape. At this level, we often refer to target groups that are single chains with relatively fewer liberties, but it is also possible to talk about larger groups with more liberties instead. Here we usually discuss capturing techniques, such as double atari, snapback, net, ladder, and connect-and-die. Many of the capturing techniques involve some form of sacrifice and deal with the fact that the target chains suffer from a shortage of liberties, and hence having more liberties is often advantageous. On the other hand, the perused would want to find holes in the opponent's surrounding stones and exploit them to break through the network of surrounding stones. Thus, one important related concept is on connection and cutting, as connected groups tend to be stronger, while stones cut into disconnected groups are much weaker since each has to be managed separately. Put another way, stones that are cut off sometimes fail to escape and get captured, hence divide and conquer is a very useful strategy in Go. Many connecting techniques exist, such as tiger's mouth, bamboo joint, and bridge under. Many cutting techniques exist as well, these include wedge, angle wedge, and curiously, techniques that cause shortage of liberties.
At another level, we can discuss life and death when the group in question is completely sealed in. The central concept here is the eye, with the key observation that to capture a group having an eye, the opponent must start filling liberties from the outside before he can remove this group off the board by playing inside the eye. The corollary of this key observation is that a group with two or more eyes is unconditionally alive even when totally surrounded. Therefore much of the literature in life and death techniques revolve around making eyes and destroying eyes. At the simplest level there is the concept of real eyes versus false eyes, with eyes being equated to real eyes, while shapes surrounding a empty point but not being an eye equated to false eyes. Then there is the idea of eye space, which is how much maneuvering space there is for the surrounded group to make eyes. Part of this also leads to the concept of big eyes and placement inside an eye, which is about whether the empty points surrounding by a group can be split into two separate eyes. A generalization of such placement techniques is the concept on vital points. As having larger eye space give better chances of living, a common theme in life and death problems is to enlarge the eye space, while a common technique for killing is to reduce the eye space, hence the proverb there is death in the hane.
It should be emphasized that these two levels are not necessarily independent. For example, one can make use of weakness such as shortage of liberties in the surrounding group to help the surrounded group make eyes, or one can attempt to connect two groups with one eye each to form a single living group with two eyes, or one can simply capture opponent's chains to make life. In more extreme cases, part of a Black group surrounding a White group may also be surrounded by other White stones, and neither surrounded group can make life individually. This situation is called a capturing race, and typically the group with more liberties wins the capturing race. When there both surrounded groups share mutual liberties, a possible result is seki in which both surrounded groups are simultaneously alive because neither player can approach the other group. In capturing races, there are many techniques, mainly to increase the liberties of a chain or to decrease the liberties of the opponent's chain, to enable or disable approach moves. The number of liberties in a solidly connected chain cannot be altered except by approach moves, but groups with cutting points may contain weaknesses that allow their liberties to be reduced, through moves such as throw-in and squeeze. On the other hand, a surrounded group having a big eye has more liberties than the number of intersections surrounded by the eye, hence big eyes do play an important role in capturing races.
On both levels, there are many different techniques for capturing or saving stones, and some of these techniques go under the name tesuji. However, getting sealed in early in the game often has negative connotations, because even when the surrounded group lives, it is often at a price of allowing the opponent getting superior external influence while the surrounded group makes small life? in an inefficient manner. In any case, as life and death issues impact almost any aspect in Go, it will always be an important and active area in the study of the game. The ability to read out difficult life and death problems is a sign of the strength of the player.