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Connection is the linking and its degree of safety between a player's stones.
There are different concepts of connection; each concept tries to classify or characterise different kinds of connection. These are some possible concepts:
- Classification: solid connection (string connection) — tactical connection (direct connection) — strategic connection (indirect connection)
- Generalization: n-connection
This page just gives a quick overview of the difference between these types of connections. For more details on them, see the pages for the specific usage in question.
- Strategic connection
- Stones are connected if they are part of the same group. Although they might still be separated, they currently function as a single unit for strategic purposes like attack, defense and living. This is known as a strategic connection.
These Black stones are not connected. White can cut at the marked point. But depending on the surrounding situation, White might not be able to enforce the cut ("make it stick", not die in the process). Thus diagonally adjacent stones may be tenuously (weakly) connected.
More generally, stones are connected if the opponent can't cut them apart--that is, if it is impossible to prevent the solid connection, assuming alternating play (see ko threat). Stones can even be considered "connected" if the opponent can cut them, but not without serious damage to his own position.
Depending on how far the stones are located from each other and the amount of thinking required to assess their connectivity, we speak of tactical connection (close range, little thinking) or strategic connection (wide range, higher thinking).
With , black has strategically connected his marked stones to his corner.
There are many different kinds of connections with with ranging implications. Some connections are strong, but move across the board slowly (not gaining much territory), while the faster connections are weaker.
In mathematical theory, the term connection may be used in a different context and with a different meaning. In particular, the phrase a set of connected intersections do not refer to stones of any colour, but the intersections themselves.
More specifically, a set of non-empty connected intersections can be constructed as follows:
- A set consisting of a single intersection is a set of connected intersections.
- Given a set of connected intersections, we can add to this set an intersection that is outside this set and is adjacent to some intersection in the set. The resultant set is also a set of connected intersections.
A set of connected intersections is also known as a region.