Difference between revisions of "Edge template VI2a"

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== The edge template template VI2 ==
+
Edge template IV2a is a 6th row [[edge template]] with two stones.
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R ↑:g1 h1"
 +
/>
 +
 
 +
== Defending the template ==
  
 
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.
 
Let us first see what possibilities [[Red (player)|Red]] has if he moves first.
Line 7: Line 14:
 
There are two obvious options:
 
There are two obvious options:
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vf3 Pa6 Pb5 Pb6 Pc4 Pc5 Pc6 Pd4 Pd5 Pd6 Pe3 Pe4 Pe5 Pe6 Pf2 Pf4 Pf5 Pf6 Pg2 Pg4 Pg5 Pg6</hex>
+
<hexboard size="6x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R f3 g1 h1 E +:a6 +:b5 +:b6 +:c4 +:c5 +:c6 +:d4 +:d5 +:d6 +:e3 +:e4 +:e5 +:e6 +:f2 +:f4 +:f5 +:f6 +:g2 +:g4 +:g5 +:g6"
 +
/>
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Vg3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Ph3 Ph4 Ph5 Ph6 Pi4 Pi5 Pi6 Pg2 Ph2</hex>
+
<hexboard size="6x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R g1 g3 h1 E +:c6 +:d5 +:d6 +:e4 +:e5 +:e6 +:f4 +:f5 +:f6 +:g2 +:g4 +:g5 +:g6 +:h2 +:h3 +:h4 +:h5 +:h6 +:i4 +:i5 +:i6"
 +
/>
  
 
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:
 
In both diagrams the possible [[Template intrusion|intrusion]] points are marked by (+). So we only have to consider the [[Overlapping templates|intersection of the intrusion points]]. They are:
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Pc6 Pd5 Pd6 Pe4 Pe5 Pe6 Pf4 Pf5 Pf6 Pg4 Pg5 Pg6 Pg2</hex>
+
<hexboard size="6x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R g1 h1 E +:c6 +:d5 +:d6 +:e4 +:e5 +:e6 +:f4 +:f5 +:f6 +:g2 +:g4 +:g5 +:g6"
 +
/>
  
−
== Intrusion at E5 and F5 ==
+
=== Intrusion at E5 and F5 ===
  
 
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]
 
If Blue blocks at E5 then Red plays F3, reducing to [[Template IVb]]
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e5 R2f3 Pe3 Pg3 Pc4 Pd4 Pe4 Pf4 Pg4 Ph4 Pb5 Pc5 Pd5 Pf5 Pg5 Ph5 Pa6 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f3 g1 h1 B 1:e5 E +:a6 +:b5 +:b6 +:c4 +:c5 +:c6 +:d4 +:d5 +:d6 +:e3 +:e4 +:e6 +:f4 +:f5 +:f6 +:g3 +:g4 +:g5 +:g6 +:h4 +:h5 +:h6"
 +
/>
  
 
Likewise if blue blocks at F5:
 
Likewise if blue blocks at F5:
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f5 R2g3 Pf3 Ph3 Pd4 Pe4 Pf4 Pg4 Ph4 Pi4 Pc5 Pd5 Pe5 Pg5 Ph5 Pi5 Pb6 Pc6 Pd6 Pe6 Pf6 Pg6 Ph6 Pi6</hex>
 
  
−
== Intrusion at E6 ==
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R g1 2:g3 h1 B 1:f5 E +:b6 +:c5 +:c6 +:d4 +:d5 +:d6 +:e4 +:e5 +:e6 +:f3 +:f4 +:f6 +:g4 +:g5 +:g6 +:h3 +:h4 +:h5 +:h6 +:i4 +:i5 +:i6"
 +
/>
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex>
+
=== Intrusion at E6 ===
  
−
Red threatens to connect via D4. Blue must respond in one of the marked hexs.
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f3 g1 h1 B 1:e6 E +:a6 +:b5 +:b6 +:c4 +:c5 +:c6 +:d4 +:d5 +:d6 +:e3 +:e4"
 +
/>
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4</hex>
+
Red threatens to connect via D4. Blue must respond in one of the marked hexes.
  
−
The H4 piece is connected to the bottom with [[defending against intrusions in template 1-IIIa|template III-1-a]], and is connected to the top in two non-overlapping ways:
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f3 g1 h1 4:h4 B 3:e4 1:e6"
 +
/>
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex>
+
The H4 piece is connected to the bottom with [[ziggurat|template III-1a]], and is connected to the top in two non-overlapping ways:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f3 g1 h1 4:h4 i2 B 3:e4 1:e6 E +:h2 +:h3 +:i1 +:i3"
 +
/>
  
 
and
 
and
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1e6 R2f3 B3e4 R4h4 Pf2 Pg2 Pg3 Pf4 Rg4</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f3 g1 g4 h1 4:h4 B 3:e4 1:e6 E +:f2 +:f4 +:g2 +:g3"
 +
/>
  
−
== Intrusion at F4 ==
+
=== Intrusion at F4 ===
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1f4 R2d4</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:d4 g1 h1 B 1:f4"
 +
/>
  
 
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:
 
The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:
  
−
=== Block at F2 ===
+
==== Block at F2 ====
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1f2 R2g3 B3f3 R4h4</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R d4 g1 2:g3 h1 4:h4 B 1:f2 3:f3 f4"
 +
/>
  
−
Red is now connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.
+
Red is now connected to the bottom via [[ziggurat|template III-1a]]. Note that neither of Red's threats overlapped.
  
−
=== Block at E3 ===
+
==== Block at E3 ====
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 B1e3 R2f3 B3e4 R4h3</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R d4 2:f3 g1 4:g4 h1 10:h4 6:i2 8:i3 B 1:e3 3:e4 f4 5:g3 7:h3 9:h5"
 +
/>
  
−
The Red piece at H3 is connected to the top and threatening to connect. Blue has one defense:
+
And now Red can escape the ladder:
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bf4 Rd4 Be3 Rf3 Be4 Rh3 B1h4 R2g4 B3f6 R4f5 B5e6 R6e5 B7d6 R8d5 B9c6</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R d4 6:d5 4:e5 f3 2:f5 g1 g4 h1 h4 i2 i3 B 5:d6 e3 e4 3:e6 f4 1:f6 g3 h3 h5"
 +
/>
  
−
Attempts by blue to block the use of the D4 piece as a ladder escape can be shown to not work
+
And now Red has connected.
 +
Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.
  
−
And now Red can connect via B5.
+
=== Intrusion at G2 ===
  
−
== Intrusion at G2 ==
+
<hexboard size="6x9"
−
 
+
  coords="bottom right"
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 B1g2 R2f2</hex>
+
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f2 g1 h1 B 1:g2"
 +
/>
  
 
Blue has four options that don't immediately reduce to another edge template:
 
Blue has four options that don't immediately reduce to another edge template:
−
=== Block at E4 ===
+
==== Block at E4 ====
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e4 R2g3</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R f2 g1 2:g3 h1 B 1:e4 g2"
 +
/>
  
 
Red's G3 piece is connected to the top via F3 or H2.
 
Red's G3 piece is connected to the top via F3 or H2.
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be4 Rg3 B1g4 R2f4 B3e6 R4c5</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 4:c5 f2 2:f4 g1 g3 h1 B e4 3:e6 g2 1:g4"
 +
/>
  
−
Here Red has created a [[Ladder escape fork]]. If blue blocks the ladder Red plays at D3.
+
Here Red has created a [[Ladder escape fork]]. If Blue blocks the ladder Red plays at D3.
  
−
=== Block at D5 ===
+
==== Block at D5 ====
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1d5 R2e4 B3e5 R4g4 B5f4 R6h2</hex>
+
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:e4 f2 g1 4:g4 h1 6:h2 B 1:d5 3:e5 5:f4 g2"
 +
/>
  
 
And Red has connected. If blue choose to play at E6 instead of E5:
 
And Red has connected. If blue choose to play at E6 instead of E5:
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Bd5 Re4 B1e6 R2e5 B3d6 R4g5 B5f5 R6g4 B7f4 R8h2</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R e4 2:e5 f2 g1 6:g4 4:g5 h1 8:h2 B d5 3:d6 1:e6 7:f4 5:f5 g2"
 +
/>
  
−
=== Block at C6 ===
+
==== Block at C6 ====
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1c6 R2e4 B3e5 R4g4 B5f4 R6h2</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:e4 f2 g1 4:g4 h1 6:h2 B 1:c6 3:e5 5:f4 g2"
 +
/>
  
−
=== Block at E6 ===
+
==== Block at E6 ====
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 B1e6 R2e4 B3d5 R4e5 B5d6 R6g5</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:e4 4:e5 f2 g1 6:g5 h1 B 3:d5 5:d6 1:e6 g2"
 +
/>
  
 
Play continues...
 
Play continues...
  
−
<hex>R6 C10 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Sj1 Sj2 Sj3 Bg2 Rf2 Be6 Re4 Bd5 Re5 Bd6 Rg5 B1f5 R2g4 B3f4 R4h2</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R e4 e5 f2 g1 2:g4 g5 h1 4:h2 B d5 d6 e6 3:f4 1:f5 g2"
 +
/>
 +
 
 +
=== Intrusion at D6 or F6 ===
 +
 
 +
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f5 g1 h1 B 1:d6 E +:f4 +:g2 +:g3 +:g4 +:h2"
 +
/>
 +
 
 +
Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.
 +
 
 +
==== Block at F4 ====
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 8:c5 6:e4 4:f3 f5 g1 2:g4 h1 B d6 7:e5 1:f4 5:g3 3:h2"
 +
/>
 +
 
 +
Or, if for move three Blue played G3:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R f5 g1 g4 10:g5 h1 8:h5 2:i2 4:i3 6:i4 B d6 f4 1:g3 9:g6 3:h3 5:h4 7:h6"
 +
/>
 +
 
 +
And Red is connected. This method can be used by Red in the symmetrical case of Blue intruding at F6.
 +
 
 +
==== Block at G2 ====
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 8:c5 6:e4 4:f3 f5 g1 h1 2:h2 B d6 7:e5 5:f4 1:g2 3:g4 E +:f2 +:g3"
 +
/>
 +
 
 +
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R f5 g1 h1 2:h2 4:h3 6:h4 B d6 1:g2 3:g3 5:g4"
 +
/>
 +
 
 +
And Red connects via [[ziggurat|template III-1a]].
 +
 
 +
==== Block at H2, G3, or G4 ====
 +
 
 +
Red's responses are similar in all three cases:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 6:c5 4:e4 2:f3 f5 g1 h1 B d6 5:e5 3:f4 1:h2"
 +
/>
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 6:c5 4:e4 2:f3 f5 g1 h1 B d6 5:e5 3:f4 1:g3"
 +
/>
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 6:c5 4:e4 2:f3 f5 g1 h1 B d6 5:e5 3:f4 1:g4"
 +
/>
 +
 
 +
=== Intrusion at C6 or G6 ===
 +
 
 +
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 2:f4 g1 h1 B 1:g6 E +:c6 +:d5 +:d6 +:e4 +:e5 +:e6 +:f5 +:f6"
 +
/>
 +
 
 +
Red's F4 piece is connected to the bottom via [[ziggurat|template III-1a]]. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.
 +
 
 +
==== Block at G2 ====
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R f4 g1 h1 2:h2 4:h3 6:h4 B 1:g2 3:g3 5:g4 g6"
 +
/>
 +
 
 +
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 8:d5 f4 g1 6:g4 h1 2:h2 4:h3 B 5:e6 7:f6 1:g2 3:g3 g6"
 +
/>
 +
 
 +
And if Blue had played F5 for move five:
 +
 
 +
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R 6:e4 f4 g1 h1 2:h2 4:h3 B 5:f5 1:g2 3:g3 g6 E +:e3 +:f2 +:f3 +:g4"
 +
/>
 +
 
 +
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[ziggurat|template III-1a]].
  
 
[[Category:Edge templates]]
 
[[Category:Edge templates]]
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Latest revision as of 14:36, 11 May 2023

Edge template IV2a is a 6th row edge template with two stones.

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Defending the template

Let us first see what possibilities Red has if he moves first.

There are two obvious options:

In both diagrams the possible intrusion points are marked by (+). So we only have to consider the intersection of the intrusion points. They are:

Intrusion at E5 and F5

If Blue blocks at E5 then Red plays F3, reducing to Template IVb

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Likewise if blue blocks at F5:

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Intrusion at E6

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Red threatens to connect via D4. Blue must respond in one of the marked hexes.

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The H4 piece is connected to the bottom with template III-1a, and is connected to the top in two non-overlapping ways:

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and

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Intrusion at F4

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The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:

Block at F2

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Red is now connected to the bottom via template III-1a. Note that neither of Red's threats overlapped.

Block at E3

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And now Red can escape the ladder:

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And now Red has connected. Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.

Intrusion at G2

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Blue has four options that don't immediately reduce to another edge template:

Block at E4

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Red's G3 piece is connected to the top via F3 or H2.

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Here Red has created a Ladder escape fork. If Blue blocks the ladder Red plays at D3.

Block at D5

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And Red has connected. If blue choose to play at E6 instead of E5:

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Block at C6

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Block at E6

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Play continues...

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Intrusion at D6 or F6

The D6 case is shown here, but Red's responses work symmetrically for the F6 case.

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Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.

Block at F4

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Or, if for move three Blue played G3:

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And Red is connected. This method can be used by Red in the symmetrical case of Blue intruding at F6.

Block at G2

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Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:

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And Red connects via template III-1a.

Block at H2, G3, or G4

Red's responses are similar in all three cases:

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Intrusion at C6 or G6

The G6 case is shown here, but Red's responses work symmetrically for the C6 case.

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Red's F4 piece is connected to the bottom via template III-1a. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.

Block at G2

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And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:

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And if Blue had played F5 for move five:

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Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with template III-1a.

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