Difference between revisions of "Strong connection"
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| − | + | A ''strong connection'' or ''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. | |
| − | + | Virtual connections are not always equivalent to [[chain|actual connections]]. In order to keep their connection, the player has to answer the opponent's threats. The opponent can use this to their advantage, for example by stealing [[territory]]. Playing in the carrier of an opponent's virtual connection is called ''[[intrusion|intruding]]'' on the virtual connection. | |
| + | |||
| + | Every [[chain]] is trivially a virtual connection. Virtual connections are often formed by connecting several chains via [[template]]s and [[double threat]]s. A set of virtually connected pieces is also called a [[group]]. | ||
| + | |||
| + | == Examples == | ||
| + | |||
| + | The simplest and most common example of a virtual connection is the [[bridge]]. | ||
| + | <hexboard size="2x2" | ||
| + | coords="none" | ||
| + | edges="none" | ||
| + | contents="R A:a1 B:b2" | ||
| + | /> | ||
| + | If Blue plays in one of the empty hexes, Red can respond in the other one. Therefore, Red can guarantee that pieces A and B stay connected. | ||
| + | |||
| + | More complex virtual connections can be formed by a combination of [[template]]s and [[double threat]]s. For example, consider the following position: | ||
| + | <hexboard size="11x11" | ||
| + | coords="none" | ||
| + | edges="all" | ||
| + | contents="R b3 b7 b8 c3 c9 c10 d3 e7 f4 f5 f10 g7 g8 g9 h4 h8 i5 i6 j3 | ||
| + | B c2 c5 c7 d8 e4 e5 e10 f7 f8 f9 g4 g6 h3 h6 h9 i3 i7 j2" | ||
| + | /> | ||
| + | As shown in the next diagram, Blue's stones A and B are connected to the right edge by [[edge template II]] and a [[ziggurat]], respectively. C is connected to either A or B by [[double threat]] at x and y. C is connected to D, E, and F by a [[crescent]], [[bridge]], and [[trapezoid]], and finally F is connected to the left edge by another [[ziggurat]]. Therefore, Blue has a virtual connection between their two edges, and has won the game. The carrier of the virtual connection is shown in gray. | ||
| + | <hexboard size="11x11" | ||
| + | coords="none" | ||
| + | edges="all" | ||
| + | contents="R b3 b7 b8 c3 c9 c10 d3 e7 f4 f5 f10 g7 g8 g9 h4 h8 i5 i6 j3 | ||
| + | B c2 F:c5 E:c7 D:d8 e4 e5 e10 f7 f8 f9 g4 C:g6 h3 h6 h9 i3 B:i7 A:j2 | ||
| + | E x:g5 y:h7 | ||
| + | S area(j2,k2,k1) area(i7,i8,k8,k5) g5 h7 area(d8,d10,e10,f9,f8) area(c7,c8,d8,d7) | ||
| + | area(c5,c7,e5,e4,d4) area(c5,c4,a4,a7) i3 h3 g4 g6 h6 f7" | ||
| + | /> | ||
| + | Red can either [[resigning|resign]], or continue playing in the carrier and forcing Blue to defend the virtual connection. If Red plays outside of the carrier, Blue could just ignore Red's move and move anywhere or even [[passing|pass]]. | ||
| + | |||
| + | == See also == | ||
| + | |||
| + | * [[AND and OR rules]] | ||
[[category:connection types]] | [[category:connection types]] | ||
Latest revision as of 15:25, 1 October 2023
A strong connection or 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.
Virtual connections are not always equivalent to actual connections. In order to keep their connection, the player has to answer the opponent's threats. The opponent can use this to their advantage, for example by stealing territory. Playing in the carrier of an opponent's virtual connection is called intruding on the virtual connection.
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.
Examples
The simplest and most common example of a virtual connection is the bridge.
If Blue plays in one of the empty hexes, Red can respond in the other one. Therefore, Red can guarantee that pieces A and B stay connected.
More complex virtual connections can be formed by a combination of templates and double threats. For example, consider the following position:
As shown in the next diagram, Blue's stones A and B are connected to the right edge by edge template II and a ziggurat, respectively. C is connected to either A or B by double threat at x and y. C is connected to D, E, and F by a crescent, bridge, and trapezoid, and finally F is connected to the left edge by another ziggurat. Therefore, Blue has a virtual connection between their two edges, and has won the game. The carrier of the virtual connection is shown in gray.
Red can either resign, or continue playing in the carrier and forcing Blue to defend the virtual connection. If Red plays outside of the carrier, Blue could just ignore Red's move and move anywhere or even pass.
