Strong connection - Revision history

Selinger: Added a link

2023-10-01T15:25:40Z

Added a link

Selinger: Fixed a link

2022-03-16T00:45:58Z

Fixed a link

Selinger: Added cross reference to AND and OR rules

2021-12-17T02:44:13Z

Added cross reference to AND and OR rules

Selinger: Added examples.

2020-12-08T01:29:44Z

Added examples.

Selinger at 21:15, 5 July 2020

2020-07-05T21:15:03Z

Selinger: Re-organization and gave a more self-contained definition (previously "strong connection" and "group" were defined in terms of each other).

2020-07-05T21:13:24Z

Re-organization and gave a more self-contained definition (previously "strong connection" and "group" were defined in terms of each other).

Selinger: Editing.

2020-07-05T21:07:10Z

Editing.

Selinger: Punctuation.

2020-07-05T20:27:21Z

Punctuation.

Halladba: typo + added inner link to group + transfered external link to rydh's page to connection types page

2008-01-31T14:54:44Z

typo + added inner link to group + transfered external link to rydh's page to connection types page

Halladba: added cat. connection types

2008-01-31T14:43:49Z

added cat. connection types

@@ Line 1: / Line 1: @@
 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 ''intruding'' on the virtual connection.
+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]].

@@ Line 1: / Line 1: @@
 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 ''intruding'' on the virtual connection.
+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 ''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]].

← Older revision		Revision as of 02:44, 17 December 2021
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	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]].		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]]

← Older revision		Revision as of 01:29, 8 December 2020
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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. A set of virtually connected pieces is also called a [[group]].		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]].
		+

	[[category:connection types]]		[[category:connection types]]

@@ Line 1: / Line 1: @@
 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.
+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 ''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]].
 [[category:connection types]]

← Older revision		Revision as of 21:07, 5 July 2020
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−	Two groups are said to be strongly connected when the opponent cannot prevent a connection between these groups. The [[bridge]] and [[~~group~~]]s ~~in general~~ are strong connections. ~~However strong~~ connections are not always equivalent to [[chain\|actual connections]] ~~in the way that in~~ order to keep their connection the player has to answer ~~their~~ opponent's threats. The opponent can use this to [[stealing territory~~\|steal territory]]. Strong connections are also named [[Virtual connection\| virtual connections~~]].	+	Two groups are said to be ''strongly connected'' or ''virtually connected'' when the opponent cannot prevent a connection between these groups. The [[bridge]] and other [[template]]s are examples of strong connections.
		+
		+	Strong 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]].

	[[category:connection types]]		[[category:connection types]]

← Older revision		Revision as of 20:27, 5 July 2020
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−	Two groups are said to be strongly connected when the opponent cannot prevent a connection between these groups. The [[bridge]] and [[group]]s in general are strong connections. However strong connections are not always equivalent to [[chain\|actual connections]] in the way that in order to keep their connection the player has to answer their opponent's threats. The opponent can use this to [[stealing territory\|steal territory]]. Strong connections are also named [[Virtual connection\| virtual connections]]	+	Two groups are said to be strongly connected when the opponent cannot prevent a connection between these groups. The [[bridge]] and [[group]]s in general are strong connections. However strong connections are not always equivalent to [[chain\|actual connections]] in the way that in order to keep their connection the player has to answer their opponent's threats. The opponent can use this to [[stealing territory\|steal territory]]. Strong connections are also named [[Virtual connection\| virtual connections]].

	[[category:connection types]]		[[category:connection types]]

@@ Line 1: / Line 1: @@
-Two groups are said to be strongly connected we the opponent cannot prevent a connection between these groups. The [[bridge]] is a strong connection. However strong connections are not always equivalent to [[chain|actual connections]] in the way that in order to keep their connection the player has to answer their opponent's threats. The opponent can use this to [[stealing territory|steal territory]]. Strong connections are also named [[Virtual connection| virtual connections]]
+Two groups are said to be strongly connected when the opponent cannot prevent a connection between these groups. The [[bridge]] and [[group]]s in general are strong connections. However strong connections are not always equivalent to [[chain|actual connections]] in the way that in order to keep their connection the player has to answer their opponent's threats. The opponent can use this to [[stealing territory|steal territory]]. Strong connections are also named [[Virtual connection| virtual connections]]
-−
-==External links==
-−
-Jonatan Rydh's [http://www.f.kth.se/~rydh/Hex/strategy.html page] about Hex strategy deals with different types of connection.
 [[category:connection types]]

← Older revision		Revision as of 14:43, 31 January 2008
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	Jonatan Rydh's [http://www.f.kth.se/~rydh/Hex/strategy.html page] about Hex strategy deals with different types of connection.		Jonatan Rydh's [http://www.f.kth.se/~rydh/Hex/strategy.html page] about Hex strategy deals with different types of connection.
		+
		+	[[category:connection types]]