Trapezoid - Revision history

Selinger: mouth -> trapezoid

2023-01-08T00:46:54Z

mouth -> trapezoid

Selinger: Selinger moved page Mouth to Trapezoid over redirect: The name "mouth" doesn't seem to have caught on.

2023-01-08T00:44:49Z

Selinger moved page Mouth to Trapezoid over redirect: The name "mouth" doesn't seem to have caught on.

Selinger: /* Domination and Comparison */ link

2022-02-14T15:20:44Z

‎Domination and Comparison: link

Selinger: minor copy-edit

2020-12-08T13:08:39Z

minor copy-edit

Demer: fixed last section

2020-12-08T07:51:17Z

fixed last section

Selinger: /* Dominated cells */ Added a caveat.

2020-12-07T06:37:32Z

‎Dominated cells: Added a caveat.

Selinger: /* Dominated cells */ Updated the argument about dominated cells. The new one might still be wrong.

2020-12-07T06:21:49Z

‎Dominated cells: Updated the argument about dominated cells. The new one might still be wrong.

Selinger: Converted to new hexboard diagrams, and added missing material on dominated moves in the trapezoid

2020-12-07T04:37:36Z

Converted to new hexboard diagrams, and added missing material on dominated moves in the trapezoid

Selinger: Minor formatting; added "trapezoid" as alternate name for this template.

2020-08-16T13:12:43Z

Minor formatting; added "trapezoid" as alternate name for this template.

Graue: add stars to make it clear which cells are included in the mouth

2009-03-11T03:58:29Z

add stars to make it clear which cells are included in the mouth

@@ Line 1: / Line 1: @@
-The '''mouth''' or '''trapezoid''' is an [[interior template]] with a wide base. It is one of the most common interior templates after the [[bridge]]. The [[carrier]] of the template, i.e., the set of cells that must be empty for the template to be valid, is shown in the following diagram.
+The '''trapezoid''' is an [[interior template]] with a wide base. It is one of the most common interior templates after the [[bridge]]. The [[carrier]] of the template, i.e., the set of cells that must be empty for the template to be valid, is shown in the following diagram.
 <hexboard size="3x3"
@@ Line 7: / Line 7: @@
    contents="R a3 b1 c1 c3"
    />
 == Common patterns ==
 === Gaining Ground ===
-The mouth can be used to steal [[territory]]. For example, in the following situation
+The trapezoid can be used to steal [[territory]]. For example, in the following situation
 <hexboard size="6x7"
    coords="none"
@@ Line 26: / Line 28: @@
    />
 === Ladder Escapes ===
-The mouth also allows some [[ladder escape]] constructions.
+The trapezoid also allows some [[ladder escape]] constructions.
 <hexboard size="6x11"
    coords="none"

@@ Line 53: / Line 53: @@
    />
-To see why, note that Red can play the following pairing strategy.
+To see why, note that Red can play the following [[pairing strategy]].
 <hexboard size="3x3"
    coords="none"

@@ Line 37: / Line 37: @@
 Although Red is unlikely to begin play in the carrier (since this is a template),
+if Red does, then Red should play *, because this [[captured cell|captures]] the rest of the carrier.
 <hexboard size="3x3"
    coords="none"
@@ Line 44: / Line 44: @@
    contents="R a3 b1 c1 c3 E *:a2"
    />
 With the carrier empty, the region is no worse for Red than the following.

@@ Line 34: / Line 34: @@
    />
-== Dominated cells ==
+== Domination and Comparison ==
 <hexboard size="3x3"
    coords="none"
@@ Line 43: / Line 44: @@
    contents="R a3 b1 c1 c3 E *:a2"
    />
 To see why, note that Red can play the following pairing strategy.
 <hexboard size="3x3"
@@ Line 50: / Line 62: @@
    contents="R a3 b1 c1 c3 E a:a2 a:b2 b:c2 b:b3"
    />
-If Blue plays in one of the cells marked "a", then Red plays in the other one. Similarly, if Blue plays in one of the cells marked "b", Red plays in the other one. The end result is that all of Red's pieces are connected, and any Blue pieces other than in "*" are dead. Since Blue cannot achieve anything better than to get "*", playing at "*" immediately is at least as good as playing anywhere else in the template. In other words, from Blue's point of view, "*" [[dominated cell|dominates]] all other possible moves in the trapezoid's carrier.
+If Blue plays in one of the cells marked "a", then Red plays in the other one. Similarly, if Blue plays in one of the cells marked "b", Red plays in the other one. The end result is that all of Red's pieces are connected, and any Blue pieces other than in "*" are dead. Thus Blue cannot achieve anything better than getting "*".
-−
-The same holds from Red's point of view as well. If Red is to play anywhere in the trapezoid's carrier, the only sensible move is at "*", because this [[captured cell|captures]] the rest of the carrier.
 [[category:interior templates]]
 [[category:basic Strategy]]

@@ Line 36: / Line 36: @@
 == Dominated cells ==
-If Blue wants to intrude into the trapezoid, the only possible intrusion point is the hex marked "*".
+If Blue wants to intrude into the trapezoid, and assuming that Red wants to defend it, the only possible intrusion point is the hex marked "*".
 <hexboard size="3x3"
    coords="none"

← Older revision	Revision as of 00:44, 8 January 2023
(No difference)

@@ Line 1: / Line 1: @@
-The '''mouth''' is a [[group]] with a wide base.
+The '''mouth''' or '''trapezoid''' is a [[template]] with a wide base. It is one of the most common [[interior template]]s after the [[bridge]]. The [[carrier]] of the template, i.e., the set of cells that must be empty for the template to be valid, has been marked "*".
 <hex>R5 C5
-Sa1 Sb1 Sc1 Sd1 Se1
- Sa2 Sb2 Vc2 Vd2 Se2
+         Vc2 Vd2
-  Sa3             Se3
+      Sb3 Sc3 Sd3
-   Sa4 Vb4     Vd4 Se4
+       Vb4 Sc4 Vd4
-    Sa5 Sb5 Sc5 Sd5 Se5</hex>
 == Common patterns ==
 === Gaining Ground ===
-The mouth can be used to [[Stealing territory|steal territory]].
+The mouth can be used to steal [[territory]]. For example, in the following situation
 <hex>R6 C7 Ve2 Vf2 Hc4 Hd5</hex>
-<hex>R6 C7 Ve2 Vf2 Hc4 Hd5   Vd4 Hc5 Vf4</hex>
+Red can play as follows:
 === Ladder Escapes ===
-It can also allow some [[ladder escape]] constructions.
+The mouth also allows some [[ladder escape]] constructions.
-<hex>R6 C10 Ve2 Vf2 Vd4 Vf4 Vg4 Vh4 He5 Hf5 Hg5 Hh5</hex>
+<hex>R6 C10 Ve2 Vf2 Vh4 Hg5 Hh5 N:on Vg4 Hf5 Vf4 He5 Vd4</hex>
 == Dominated cells ==