Difference between revisions of "Trapezoid"

Revision as of 00:44, 8 January 2023

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 "*".