Difference between revisions of "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 == | ||
| + | |||
| + | <hexboard size="5x9" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a5,i5,i1,h2,g2,g1,f1,c3)" | ||
| + | contents="R A:i1 E B:g1" | ||
| + | /> | ||
| + | |||
| + | 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 play at 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. | ||
| + | |||
| + | <hexboard size="5x9" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a5,i5,i1,h2,g2,g1,f1,c3)" | ||
| + | contents="R A:i1 E B:g1 a:h2 b:i2 c:h3 d:g4 e:h4 f:f5 g:h5" | ||
| + | /> | ||
| + | If Blue plays at a, Red responds with a 3rd row ladder escape fork: | ||
| + | <hexboard size="5x9" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a5,i5,i1,h2,g2,g1,f1,c3)" | ||
| + | contents="R A:i1 E B:g1 B 1:h2 R 2:i2 B 3:h4 R 4:h3 B 5:g4 R 6:f3 B 7:g3 R 8:g1" | ||
| + | /> | ||
| + | If Blue plays at b, Red responds at a and connects outright. | ||
| + | |||
| + | If Blue plays at c, e, or g, Red responds as follows and is connected by [[Fifth_row_edge_templates#V-2-f|edge template V2-f]]. If Blue plays on the left instead of 3, Red responds as if defending template V2-f. | ||
| + | <hexboard size="5x9" | ||
| + | edges="bottom" | ||
| + | coords="none" | ||
| + | visible="area(a5,i5,i1,h2,g2,g1,f1,c3)" | ||
| + | contents="R A:i1 E B:g1 B 1:h3 1:h4 1:h5 R 2:g3 B 3:h2 R 4:g1" | ||
| + | /> | ||
| + | If Blue plays at d or f, 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 [[flank]]s. | ||
| + | |||
| + | [Todo: Add an example.] | ||
| + | |||
| + | == More examples == | ||
| + | |||
| + | <hexboard size="4x6" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(a4,f4,f1,e2,d2,d1)" | ||
| + | contents="R A:d1 E B:f1" | ||
| + | /> | ||
| + | |||
| + | <hexboard size="4x7" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(b2,a4,g4,g2,f1,e1,d2,c1)" | ||
| + | contents="R A:c1 E B:e1" | ||
| + | /> | ||
| + | |||
| + | <hexboard size="3x5" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(c1,a3,d3,e1)-d1" | ||
| + | contents="R A:c1 E B:e1" | ||
| + | /> | ||
| + | |||
| + | <hexboard size="5x10" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(c2,c3,a5,j5,j3,h1,f1,e2)-d2" | ||
| + | contents="R A:c2 E B:e2" | ||
| + | /> | ||
| + | |||
| + | <hexboard size="5x7" | ||
| + | coords="none" | ||
| + | edges="bottom" | ||
| + | visible="area(a5,g5,g1,d1,b3)-f1" | ||
| + | contents="R A:e1 E B:g1" | ||
| + | /> | ||
Revision as of 01:40, 20 June 2021
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
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 play at 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.
If Blue plays at a, Red responds with a 3rd row ladder escape fork:
If Blue plays at b, Red responds at a and connects outright.
If Blue plays at c, e, or g, Red responds as follows and is connected by edge template V2-f. If Blue plays on the left instead of 3, Red responds as if defending template V2-f.
If Blue plays at d or f, 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.]
