Difference between revisions of "Trapezoid"
(Copied/adapted page from http://hexwiki.tk) |
(mouth -> trapezoid) |
||
| (11 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | The ''' | + | 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" |
| + | coords="none" | ||
| + | edges="none" | ||
| + | visible="-a1" | ||
| + | contents="R a3 b1 c1 c3" | ||
| + | /> | ||
| + | |||
| + | An older version of this page called the trapezoid the "mouth", but that name does not seem to be widely used. | ||
== Common patterns == | == Common patterns == | ||
=== Gaining Ground === | === Gaining Ground === | ||
| + | The trapezoid can be used to steal [[territory]]. For example, in the following situation | ||
| + | <hexboard size="6x7" | ||
| + | coords="none" | ||
| + | edges="bottom right" | ||
| + | visible="area(a5,a6,g6,g1,e1)" | ||
| + | contents="R e2 f2 B c4 d5" | ||
| + | /> | ||
| + | Red can play as follows: | ||
| + | <hexboard size="6x7" | ||
| + | coords="none" | ||
| + | edges="bottom right" | ||
| + | visible="area(a5,a6,g6,g1,e1)" | ||
| + | contents="R e2 f2 B c4 d5 R 1:d4 B 2:c5 R 3:f4" | ||
| + | /> | ||
| + | === Ladder Escapes === | ||
| + | The trapezoid also allows some [[ladder escape]] constructions. | ||
| + | <hexboard size="6x11" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(e1,c3,a6,g6,h5,j1)" | ||
| + | contents="R e2 f2 h4 B h5 g5 R 1:g4 B 2:f5 R 3:f4 B 4:e5 R 5:d4" | ||
| + | /> | ||
| − | + | == Domination and Comparison == | |
| − | + | ||
| − | === | + | 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" | ||
| + | edges="none" | ||
| + | visible="-a1" | ||
| + | contents="R a3 b1 c1 c3 E *:a2" | ||
| + | /> | ||
| + | |||
| + | With the carrier empty, the region is no worse for Red than the following. | ||
| + | <hexboard size="3x3" | ||
| + | coords="none" | ||
| + | edges="none" | ||
| + | visible="-a1" | ||
| + | contents="R a3 b1 b2 b3 c1 c2 c3 B a2" | ||
| + | /> | ||
| + | |||
| + | To see why, note that Red can play the following [[pairing strategy]]. | ||
| + | <hexboard size="3x3" | ||
| + | coords="none" | ||
| + | edges="none" | ||
| + | visible="-a1" | ||
| + | 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. Thus Blue cannot achieve anything better than getting "*". | ||
| − | + | [[category:interior templates]] | |
| + | [[category:basic Strategy]] | ||
Latest revision as of 00:46, 8 January 2023
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.
An older version of this page called the trapezoid the "mouth", but that name does not seem to be widely used.
Common patterns
Gaining Ground
The trapezoid can be used to steal territory. For example, in the following situation
Red can play as follows:
Ladder Escapes
The trapezoid also allows some ladder escape constructions.
Domination and Comparison
Although Red is unlikely to begin play in the carrier (since this is a template), if Red does, then Red should play *, because this captures the rest of the carrier.
With the carrier empty, the region is no worse for Red than the following.
To see why, note that Red can play the following pairing strategy.
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 "*".
