Second order template - Revision history

Demer: /* Examples */ added fifth row template

2025-08-30T23:57:13Z

‎Examples: added fifth row template

Selinger: Added a second order ladder creation template.

2022-05-29T13:22:28Z

Added a second order ladder creation template.

Selinger: Added common phrases used to describe 2nd order templates.

2022-04-27T13:10:54Z

Added common phrases used to describe 2nd order templates.

Demer: fixed a typo, and chose singular in a conflict between that and plural

2022-04-27T03:10:13Z

fixed a typo, and chose singular in a conflict between that and plural

Selinger: Added another second order template.

2022-04-26T22:40:07Z

Added another second order template.

Selinger: Indicate the moves corresponding to Red's threats.

2022-04-26T22:36:29Z

Indicate the moves corresponding to Red's threats.

Demer: /* Third row */ simplified reasoning for one 2nd-order template

2022-04-26T18:07:07Z

‎Third row: simplified reasoning for one 2nd-order template

Selinger: Expanded second order templates.

2022-04-26T01:18:48Z

Expanded second order templates.

Selinger: Converted to new hexboard diagrams. Some copy-editing.

2020-12-24T05:01:16Z

Converted to new hexboard diagrams. Some copy-editing.

Halladba: concept + examples + usage

2010-06-20T12:40:47Z

concept + examples + usage

New page

A '''second order [[template]]''', is a pattern which guarantees a connection even if the opponent is given a free move at the beginning. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[edge template|first order template]].

== Examples ==
<hex> R2 C3
Sa1 Vb1 Vc1
</hex>
=== Third row ===
<hex> R3 C6
Sa1 Sb1 Vd1 Ve1
Sa2</hex>

This pattern can be reduced to [[ziggurat]]s:

<hex> R3 C6
Sa1 Sb1 Pc1 Vd1 Ve1
Sa2 Pb2 Pc2
Pa3 Pb3
</hex>

<hex> R3 C6
Sa1 Sb1 Vd1 Ve1 Pf1
Sa2 Pe2 Pf2
Pe3 Pf3
</hex>

Therefore the only forcing moves must lie in the overlapping area. However, the overlapping is alson non-forcing thanks to Vertical's (1) moves.
<hex> R3 C6
Sa1 Sb1 Vd1 Ve1
Sa2 V1b2 Pd2 V1f2
Pc3 Pd3
</hex>

== Usage ==

A first order edge template prove that a group is connected to the edge provided the player answer threats made to the connection. If the player wants to preserve the connection, the opponent can throw stones in the carrier that will later serve as [[ladder escape]]s, such moves belong to the category of [[double threat]]s. Recognizing second order edge templates helps to know whether an area is safe or might be subject to such double threats.

[[category:templates]]
[[category:connection types]]
[[category:advanced Strategy]]

@@ Line 60: / Line 60: @@
    contents="R d1 e1 f1"
    />
 == Usage ==

← Older revision		Revision as of 13:10, 27 April 2022
Line 1:		Line 1:
	A '''second order template''' is a [[template]] that guarantees a connection even if the opponent starts with two moves in the template. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[template\|first order template]]. To qualify as a second order template, the pattern should also be minimal.		A '''second order template''' is a [[template]] that guarantees a connection even if the opponent starts with two moves in the template. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[template\|first order template]]. To qualify as a second order template, the pattern should also be minimal.
		+
		+	Phrases such as "Blue cannot even threaten to disconnect Red" and "if Blue moves in this area, Red can just ignore it" are often used to indicate that Red has a second order template.

	== Examples ==		== Examples ==

@@ Line 40: / Line 40: @@
    />
-So no matter where Blue plays in the template, Red will still have at least two non-overlapping threats, and therefore a first-order template, remaining. Or to put it another way: If Blue makes two moves in the template, Blue can disable at most two of Red's threat, so Red can still use the third one to reconnect.
+So no matter where Blue plays in the template, Red will still have at least two non-overlapping threats, and therefore a first-order template, remaining. Or to put it another way: If Blue makes two moves in the template, Blue can disable at most two of Red's threats, so Red can still use the third one to reconnect.
 Here is another second order template on the third row:
@@ Line 63: / Line 63: @@
 === In play ===
-It is usually not a good idea to create a second order templates on purpose, as this tends to waste a move that would be better spent elsewhere. However, it is still useful to recognize second order templates in case they form accidentally.
+It is usually not a good idea to create a second order template on purpose, as this tends to waste a move that would be better spent elsewhere. However, it is still useful to recognize second order templates in case they form accidentally.
 When the opponent intrudes into a first order template, it is usually necessary to defend the template to preserve the connection. The opponent can take advantage of this by playing template intrusions that will later be useful to the opponent, for example as [[ladder escape]]s or to gain [[territory]]. Such moves belong to the category of [[double threat]]s.

← Older revision		Revision as of 22:40, 26 April 2022
Line 42:		Line 42:
	So no matter where Blue plays in the template, Red will still have at least two non-overlapping threats, and therefore a first-order template, remaining. Or to put it another way: If Blue makes two moves in the template, Blue can disable at most two of Red's threat, so Red can still use the third one to reconnect.		So no matter where Blue plays in the template, Red will still have at least two non-overlapping threats, and therefore a first-order template, remaining. Or to put it another way: If Blue makes two moves in the template, Blue can disable at most two of Red's threat, so Red can still use the third one to reconnect.

		+	Here is another second order template on the third row:
		+	<hexboard size="3x4"
		+	coords="none"
		+	edges="bottom"
		+	visible="-a1 a2 b1"
		+	contents="R c1 b2"
		+	/>

	=== Fourth row ===		=== Fourth row ===

@@ Line 23: / Line 23: @@
    edges="bottom"
    visible="-a1 b1 a2"
-   contents="R d1 e1 S a3 b3 b2 c2 c1"
+   contents="R d1 e1 S a3 b3 b2 c2 c1 E *:b2"
    />
@@ Line 30: / Line 30: @@
    edges="bottom"
    visible="-a1 b1 a2"
-   contents="R d1 e1 S c3 d2 d3"
+   contents="R d1 e1 S c3 d2 d3 E *:d2"
    />
@@ Line 37: / Line 37: @@
    edges="bottom"
    visible="-a1 b1 a2"
-   contents="R d1 e1 S f1 e2 f2 e3 f3"
+   contents="R d1 e1 S f1 e2 f2 e3 f3 E *:f2"
    />
 === Fourth row ===
@@ Line 57: / Line 60: @@
 When the opponent intrudes into a first order template, it is usually necessary to defend the template to preserve the connection. The opponent can take advantage of this by playing template intrusions that will later be useful to the opponent, for example as [[ladder escape]]s or to gain [[territory]]. Such moves belong to the category of [[double threat]]s.
-On the other hand, when the opponent intrudes into a second order template, no immediate response is necessary; the template's owner can simply ignore the intrusion and is free to move elsewhere, thereby gaining the [[initiative]]. Recognizing second order edge templates helps to know whether an area is safe or might be subject to threats.
+On the other hand, when the opponent intrudes into a second order template, no immediate response is necessary; the template's owner can simply ignore the intrusion and is free to move elsewhere, thereby gaining the [[initiative]]. Recognizing second order templates helps to know whether an area is safe or might be subject to threats.
 === In mustplay analysis ===

@@ Line 88: / Line 88: @@
    />
 Since Blue has at most one stone in this template, the result is still a first-order template, so that Red is connected to the edge. Therefore, the only intrusions we need to consider are a, b, and c. This greatly simplifies the analysis, as we must now only consider 3 possible intrusions, rather than all 22 of them. (The intrusions at a or c are easily dealt with, since Red can simply respond at b to connect via [[edge template IV2a]]. The final intrusion at b has a few further cases to consider, but is relatively straighforward).
 [[category:templates]]
 [[category:connection types]]
 [[category:advanced Strategy]]

@@ Line 1: / Line 1: @@
-A '''second order template''' is a [[template]] that guarantees a connection even if the opponent is given a free move at the beginning. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[template|first order template]].
+A '''second order template''' is a [[template]] that guarantees a connection even if the opponent starts with two moves in the template. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[template|first order template]]. To qualify as a second order template, the pattern should also be minimal.
 == Examples ==
@@ Line 39: / Line 39: @@
    visible="-a1 b1 a2"
    contents="R d1 e1 S area(c1,a3,f3,f1)-c3,d2,d3 R A:b2 B:f2"
    />
 == Usage ==
-A first order edge template proves that a group is connected, provided the player answers threats made to the connection. If the player wants to preserve the connection, the opponent can intrude into the template's [[carrier]] and play stones that will later serve as [[ladder escape]]s. Such moves belong to the category of [[double threat]]s. Recognizing second order edge templates helps to know whether an area is safe or might be subject to such double threats.
+=== In play ===
 [[category:templates]]
 [[category:connection types]]
 [[category:advanced Strategy]]

@@ Line 1: / Line 1: @@
-A '''second order [[template]]''', is a pattern which guarantees a connection even if the opponent is given a free move at the beginning. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[edge template|first order template]].
+A '''second order template''' is a [[template]] that guarantees a connection even if the opponent is given a free move at the beginning. Put another way, a second order template is a pattern in which an intrusion is not a [[forcing move]]. A pattern can be proved to be a second order template by showing that every possible intrusion preserves at least one [[template|first order template]].
 == Examples ==
-<hex> R2 C3
+=== Second row ===
-Sa1 Vb1 Vc1
+<hexboard size="2x3"
- </hex>
+  coords="none"
 === Third row ===
-<hex> R3 C6
+<hexboard size="3x6"
-Sa1 Sb1    Vd1 Ve1
+  coords="none"
- Sa2</hex>
+  edges="bottom"
 This pattern can be reduced to [[ziggurat]]s:
-<hex> R3 C6
+<hexboard size="3x6"
-Sa1 Sb1 Pc1 Vd1 Ve1
+  coords="none"
- Sa2 Pb2 Pc2
+  edges="bottom"
-   Pa3 Pb3
+   visible="-a1 b1 a2"
-</hex>
+  contents="R d1 e1 S area(e1,c3,f3,f1)"
-<hex> R3 C6
+<hexboard size="3x6"
-Sa1 Sb1    Vd1 Ve1 Pf1
+  coords="none"
- Sa2            Pe2 Pf2
+  edges="bottom"
-                 Pe3 Pf3
+  visible="-a1 b1 a2"
-</hex>
+  contents="R d1 e1 S area(c1,a3,d3,d1)"
-Therefore the only forcing moves must lie in the overlapping area. However, the overlapping is alson non-forcing thanks to Vertical's (1) moves.
+Therefore, any potential forcing moves must lie in the overlapping area. However, the overlap is also non-forcing, thanks to Red's moves A and B.
-<hex> R3 C6
+<hexboard size="3x6"
-Sa1 Sb1    Vd1 Ve1
+  coords="none"
- Sa2 V1b2   Pd2     V1f2
+   edges="bottom"
-         Pc3 Pd3
+  visible="-a1 b1 a2"
-</hex>
+  contents="R d1 e1 S area(c1,a3,f3,f1)-c3,d2,d3 R A:b2 B:f2"
 == Usage ==
-A first order edge template prove that a group is connected to the edge provided the player answer threats made to the connection. If the player wants to preserve the connection, the opponent can throw stones in the carrier that will later serve as [[ladder escape]]s, such moves belong to the category of [[double threat]]s. Recognizing second order edge templates helps to know whether an area is safe or might be subject to such double threats.
+A first order edge template proves that a group is connected, provided the player answers threats made to the connection. If the player wants to preserve the connection, the opponent can intrude into the template's [[carrier]] and play stones that will later serve as [[ladder escape]]s. Such moves belong to the category of [[double threat]]s. Recognizing second order edge templates helps to know whether an area is safe or might be subject to such double threats.