Difference between revisions of "Trapezoid"
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| − | == | + | == Domination and Comparison == |
| + | |||
| + | Although Red is unlikely to begin play in the carrier (since this is a template), | ||
| − | |||
<hexboard size="3x3" | <hexboard size="3x3" | ||
coords="none" | coords="none" | ||
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contents="R a3 b1 c1 c3 E *:a2" | contents="R a3 b1 c1 c3 E *:a2" | ||
/> | /> | ||
| + | |||
| + | if Red does, then Red should play *, because this [[captured cell|captures]] the rest of the carrier. | ||
| + | |||
| + | 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. | To see why, note that Red can play the following pairing strategy. | ||
<hexboard size="3x3" | <hexboard size="3x3" | ||
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contents="R a3 b1 c1 c3 E a:a2 a:b2 b:c2 b:b3" | 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. | + | 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 "*". |
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[[category:interior templates]] | [[category:interior templates]] | ||
[[category:basic Strategy]] | [[category:basic Strategy]] | ||
Revision as of 07:51, 8 December 2020
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.
Common patterns
Gaining Ground
The mouth can be used to steal territory. For example, in the following situation
Red can play as follows:
Ladder Escapes
The mouth 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 "*".
