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Territory  in  Go

Concept of a territory is one of the central in Go — after all the entire game is a struggle for it.  Definition of a territory is deceptively simple — it is an empty space surrounded by an uninterrupted line of stones of the same color (only horizontal and vertical holes are considered to be interruptions).  It is important, however, that stones surrounding the territory are "alive" — empty space surrounded by the "dead" stones is not a territory — such stones are removed from the board upon the game completion and are added to the "prisoner" stones (Basic rule 10).

In the process of struggle for the territory stones of both players intertwine on the board in complex combinations, and it is extremely important to be able to tell the "live" stones from the "dead".  The decision might be complicated by the presence of the opponent's stones within a potential territory.

To formulate the generalized concepts of "live" and "dead" stones it is helpful to review a series of characteristic positions.  Reviewing of each position amounts to analysis of all possible moves for each player in a given position.

Position 1
  • White move into point A is prohibited (Basic rule 7).
  • Black move into point A captures white stones (Basic rule 6).
  • Consequently, white stones in this position are unconditionally "dead", and can be left as-is till the end of the game.

Position 2
  • White move into one of the points A or B transforms position into the previous one (entirely surrounded group with only one internal "liberty" left).
  • Black move into one of the points A or B deprives White of the one before the last point of "liberty" threatening by the capture (puts White in the Atari).
  • If White doesn't reply to this move, Black can make the move into the remaining point of "liberty" capturing white stones (Basic rule 6).
  • If White captures the black stone (Basic rule 6), position is transformed into the previous one (entirely surrounded group with only one internal "liberty" left).
  • Consequently, white stones in this position are unconditionally "dead", and can be left as-is till the end of the game.

Position 3
  • White move into one of the points A or C transforms position into the previous one (entirely surrounded group with only two internal "liberties" left).
  • White move into point B forms the group with two separated free spaces — "eyes" (points A and C).  This group can not be captured (black move into any of the "eyes" is prohibited (Basic rule 7) because of the presence of another "eye" that keeps the white group "alive").
  • Black move into point B ensures the capture of the white group, because White reply (or another Black move and a "forced" White reply) transform position into the previous one (entirely surrounded group with only two internal "liberties" left).  If White doesn't reply to the second black move, then the third black move into remaining point of "liberty" captures the white group (Basic rule 6).
  • Black move into any of the points A or C is absolutely senseless, since after such move White gets its turn and a possibility to save his group by making a move into point B, and to capture one black stone.
  • Point B that separates white group into two free spaces (two "eyes") is "critical" from the point of view of the white group survival.  White move into the "critical" point ensures group's "life"; Black move into the "critical" point makes white group "dead".
  • Consequently, "life" or "death" of the white stones in this position depends on whose turn is to make a move.

Position 4
  • White group has two "critical" points B and C (by making a move into any of these points White can get a group with two "eyes").
  • Consequently, white stones in this position are unconditionally "alive" (i.e., regardless of the move turn).  Indeed, if Black attacks by a move into one of the "critical" points, White can always occupy another "critical" point in reply, thus getting a group with two "eyes", which is unconditionally "alive".
  • It is obvious that black moves into any of the points A or D are senseless since they only add a Black "prisoner" without imposing any treat for White.  These moves can be simply ignored by White.

Position 5
  • If White attempts to capture 3 black stones by making an approach move into one of the points A or B, Black will be able to capture all white stones by making his move into the remaining free point (Basic rule 6).  Consequently, White won't try to capture Black in this position.
    If Black attempts to capture all white stones by making an approach move into one of the points A or B, White will be able to capture 3 black stones by making his move into the remaining free point (Basic rule 6) and get a group with two "critical" points which is unconditionally "alive".  Consequently, Black won't try to capture White in this position.
  • Thus, an attacking move of any of the players leads to his loss in this local position, which means that generally none of the players will make a move here, and position will remain as-is until the end of the game (determined by (Basic rule 9), unless used by one of the sides as a Ko-threat during a Ko-fight.
  • Both white and black stones in this position are considered to be "alive" while points A and B are considered to be "neutral" (Dame).
  • This sort of position is called Seki.  Technique of building a Seki permits to get "live" groups within opponent's territory when it's impossible to build a group with with two "eyes".

   It is possible to make the following conclusions basing on the above analysis of characteristic positions:

        Note: 
Groups of types 3, 4 and 5 are "alive" (conditionally or unconditionally) only with the provisions of the right moves of the player in reply to the opponent's attack.  These groups might also "die" as a result of a Ko-fight, which is discussed separately.  If a possibility of a Ko-fight is to be taken in consideration (and in the real game it should always be), then the only absolutely "alive" groups are those having at least two "eyes" — anything less formidable than that can be captured.  It's not practical, however, to waste moves on making the actual "eyes" in the positions with more than one "critical" points, since each move is valuable, and presents an opportunity to the player.  The proper balance of the opportunities might be a protection almost as strong as two "eyes".

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