Difference between revisions of "Connection"
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| − | + | Two or more pieces (and/or edges) of the same color are said to be ''connected'' to each other if they either belong to a [[chain]] or they are [[virtual connection|virtually connected]]. | |
| − | + | A [[chain]] is the strongest kind of connection. In a chain, any two pieces are connected by an unbroken sequence of adjacent pieces of the same color. In order to win the game of Hex, a player must construct a chain connecting her two edges. | |
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| + | A [[virtual connection]] between two (or more) pieces consists of a set of cells that are either empty or occupied by pieces of the same color (the "carrier" of the virtual connection), such that whatever moves the opponent makes in the carrier, it is always possible for the player to respond in the carrier in such a way that the pieces remain connected. | ||
| − | + | Playing in the carrier of an opponent's virtual connection is called ''invading'' the virtual connection. While it is not possible to disconnect the opponent's pieces, there can nevertheless be benefits to invading a virtual connection, such as gaining [[territory]]. | |
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| + | Every chain is trivially a virtual connection. Virtual connections are often formed by connecting several chains via [[template]]s and [[double threat]]s. | ||
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| + | A set of virtually connected pieces is also called a [[group]]. | ||
[[category:interior templates]] | [[category:interior templates]] | ||
[[category:connection types]] | [[category:connection types]] | ||
Revision as of 21:02, 5 July 2020
Two or more pieces (and/or edges) of the same color are said to be connected to each other if they either belong to a chain or they are virtually connected.
A chain is the strongest kind of connection. In a chain, any two pieces are connected by an unbroken sequence of adjacent pieces of the same color. In order to win the game of Hex, a player must construct a chain connecting her two edges.
A virtual connection between two (or more) pieces consists of a set of cells that are either empty or occupied by pieces of the same color (the "carrier" of the virtual connection), such that whatever moves the opponent makes in the carrier, it is always possible for the player to respond in the carrier in such a way that the pieces remain connected.
Playing in the carrier of an opponent's virtual connection is called invading the virtual connection. While it is not possible to disconnect the opponent's pieces, there can nevertheless be benefits to invading a virtual connection, such as gaining territory.
Every chain is trivially a virtual connection. Virtual connections are often formed by connecting several chains via templates and double threats.
A set of virtually connected pieces is also called a group.
