User:Selinger

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Pivoting template

A pivoting template is a kind of edge template that guarantees that the template's owner can either connect the template's stone(s) to the edge, or else can occupy a specified empty hex and connect it to the edge.

Example

AB

This template guarantees that, with Blue to move, Red can either connect A to the edge, or else occupy and connect B to the edge. Its carrier is minimal with this property.

Proof: Red's main threat is to bridge to c and connect to the edge by ziggurat or edge template III1b. Therefore, to prevent Red from connecting to the edge outright, Blue must play in one of the cells a,...,g.

ABabcdefg

If Blue plays at a, Red responds at b and connects outright by edge template IV1a.

If Blue plays at b, Red responds with a 3rd row ladder escape fork:

A82147635

If Blue plays at c, d, or f, Red responds as follows and is connected by edge template V2f. If Blue plays on the right instead of 3, Red responds as if defending template V2f.

A431211

If Blue plays at e or g, Red responds at c and gets a 2nd or 3rd row ladder, which can reach B by ladder escape fork.

Usage

Pivoting templates can be useful in many situations, but are especially useful in connection with flanks.

[Todo: Add an example.]

More examples

AB
AB
AB
AB
AB

See also