Pivoting template - Revision history

Bobson8: Fix the flawed statement. Also extend some statement to the weak version.

2026-06-27T02:51:52Z

Fix the flawed statement. Also extend some statement to the weak version.

Mason: Add new pivoting template

2024-03-01T08:02:03Z

Add new pivoting template

Selinger: /* If A and B are semi-connected */ Copy-editing.

2023-03-18T21:24:48Z

‎If A and B are semi-connected: Copy-editing.

Mason: remove redundant information and link to the page where it is, and currently belongs

2023-03-11T02:27:00Z

remove redundant information and link to the page where it is, and currently belongs

Mason: /* If A and B semi-connected */

2023-03-10T19:59:36Z

‎If A and B semi-connected

Mason: Add clarification/correction

2023-03-10T01:08:33Z

Add clarification/correction

Mason: Add some properties of pivoting templates, as well as some important missing templates.

2023-03-09T22:31:19Z

Add some properties of pivoting templates, as well as some important missing templates.

Selinger: /* Pivoting ladder creation templates */ typo

2022-10-28T00:19:00Z

‎Pivoting ladder creation templates: typo

Selinger: /* 6th row */ Added a 6th row pivoting template.

2022-10-22T18:27:06Z

‎6th row: Added a 6th row pivoting template.

Selinger: /* 5th row */ Added two new pivoting templates.

2022-09-16T18:56:08Z

‎5th row: Added two new pivoting templates.

@@ Line 179: / Line 179: @@
    contents="R A:h1 E B:j1 R h3"
    />
 == Weak pivoting templates ==
@@ Line 247: / Line 214: @@
              S area(b9,h9,h5,e5,c7)-g5"
    />
 == Pivoting ladder creation templates ==

@@ Line 171: / Line 171: @@
    visible="area(a6,f1,i1,i2,g6)-h1"
    contents="R A:g1 E B:i1 R g3"
    />

@@ Line 194: / Line 194: @@
 These templates make up a subset of a larger group of [https://www.hexwiki.net/index.php/Flank#Edge_templates_from_capped_flanks edge templates formed with capped flanks].
-== If A and B are [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==
+== If A and B are semi-connected ==
-The following arguments only apply when the semi-connection does not overlap with the template. However, if there is an overlap, these properties may still hold.
+The following arguments only apply when the [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connection] does not overlap with the template. If there is an overlap, these properties may or may not hold.
 === Connecting B with sente ===
-If A and B are semi-connected and blue decides to block red from connecting A, red not only gets to connect B, but also gets [https://www.hexwiki.net/index.php/Initiative sente]. This is because once red connects B, blue will have to spend a move blocking B from connecting back to A.
+If A and B are semi-connected and Blue decides to block Red from connecting A, Red not only gets to connect B, but also gets [https://www.hexwiki.net/index.php/Initiative sente]. This is because once Red connects B, Blue will have to spend a move blocking B from connecting back to A.
 === Deriving normal templates ===
-A normal template for connecting A can be derived from a pivoting template by placing a red stone in B, and adding sufficient space for A and B to be semi-connected. This is because, by definition, if blue tries to block A from the edge, red can connect B. However, if red already has a stone at B, they can spend that move connecting back to A.
+A normal template for connecting A can be derived from a pivoting template by placing a red stone in B, and adding sufficient space for A and B to be semi-connected. This is because, by definition, if Blue tries to block A from the edge, Red can connect B. However, if Red already has a stone at B, they can spend that move connecting back to A.
 == Weak pivoting templates ==

@@ Line 54: / Line 54: @@
 === 3rd row ===
 <hexboard size="3x5"
@@ Line 77: / Line 70: @@
 === 4th row ===
 <hexboard size="4x6"
@@ Line 205: / Line 191: @@
    />
 This guarantees that Red can connect A to the edge, because either A will connect outright, or else B connects to the edge and also to A via the flank.
 == If A and B are [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==

@@ Line 206: / Line 206: @@
 This guarantees that Red can connect A to the edge, because either A will connect outright, or else B connects to the edge and also to A via the flank.
-== If A and B [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==
+== If A and B are [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==
 The following arguments only apply when the semi-connection does not overlap with the template. However, if there is an overlap, these properties may still hold.

← Older revision		Revision as of 01:08, 10 March 2023
Line 207:		Line 207:

	== If A and B [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==		== If A and B [https://www.hexwiki.net/index.php/AND_and_OR_rules#Connections_and_semi-connections semi-connected] ==
		+
		+	The following arguments only apply when the semi-connection does not overlap with the template. However, if there is an overlap, these properties may still hold.

	=== Connecting B with sente ===		=== Connecting B with sente ===

@@ Line 229: / Line 229: @@
 == Pivoting ladder creation templates ==
-Sometimes, the pivoting property can be combined with other properties of templates. For example, [[ladder creation template]] guarantees that Red can get at least a specified ladder. A ''pivoting ladder creation template'' is a template with a red stone A and an empty hex B, such that Red can continuously threaten to get a ladder from A, until the point where Red either gets the ladder or occupies and connects B to a ladder. When combined with an appropriate ladder escape, a pivoting ladder creation template becomes a pivoting template.
+Sometimes, the pivoting property can be combined with other properties of templates. For example, a [[ladder creation template]] guarantees that Red can get at least a specified ladder. A ''pivoting ladder creation template'' is a template with a red stone A and an empty hex B, such that Red can continuously threaten to get a ladder from A, until the point where Red either gets the ladder or occupies and connects B to a ladder. When combined with an appropriate ladder escape, a pivoting ladder creation template becomes a pivoting template.
 For example, the following is a pivoting 3rd-row-ladder creation template.

@@ Line 164: / Line 164: @@
    visible="area(e1,e2,a6,h6,h2,g1)-f1"
    contents="R A:e1 E B:g1 R f3"
    />

@@ Line 106: / Line 106: @@
    visible="area(a5,i5,i3,h1,e1)-f1"
    contents="R A:e1 E B:g1"
    />