Difference between revisions of "Edge template VI2a"

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(After checking with benezene, the template was not minimal. I've replaced it with the minimal version, and updated one of the lines to use the reduced space.)
(Converted to new hexboard diagrams)
Line 1: Line 1:
 
== The edge template template VI2 ==
 
== The edge template template VI2 ==
  
−
<hexboard size="6x9" edges="bottom" coords="bottom right" contents="R ↑:g1 h1" visible="area(a6,f1,i1,i6)"/>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  edges="bottom"
 +
  visible="area(a6,f1,i1,i6)"
 +
  contents="R ↑:g1 h1"
 +
/>
  
 
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 12:
 
There are two obvious options:
 
There are two obvious options:
  
−
<hex>R6 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 ==
Line 19: Line 39:
 
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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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>
+
 
 +
<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"
 +
/>
  
 
== Intrusion at E6 ==
 
== Intrusion at E6 ==
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 Pe3 Pc4 Pd4 Pe4 Pb5 Pc5 Pd5 Pa6 Pb6 Pc6 Pd6</hex>
+
<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"
 +
/>
  
 
Red threatens to connect via D4. Blue must respond in one of the marked hexes.
 
Red threatens to connect via D4. Blue must respond in one of the marked hexes.
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 B3e4 R4h4</hex>
+
<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"
 +
/>
  
 
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:
 
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:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1e6 R2f3 B3e4 R4h4 Pi1 Ph2 Ri2 Ph3 Pi3</hex>
+
<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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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:
Line 48: Line 104:
 
=== Block at F2 ===
 
=== Block at F2 ===
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 [[defending against intrusions in template 1-IIIa|template III-1-a]]. Note that neither of Red's threats overlapped.
Line 54: Line 115:
 
=== Block at E3 ===
 
=== Block at E3 ===
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bf4 Rd4 B1e3 R2f3 B3e4 R4g4 B5g3 R6i2 B7h3 R8i3 B9h5 R10h4</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"
 +
/>
  
 
And now Red can escape the ladder:
 
And now Red can escape the ladder:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bf4 Rd4 Be3 Rf3 Be4 Rg4 Bg3 Ri2 Bh3 Ri3 Bh5 Rh4 B1f6 R2f5 B3e6 R4e5 B5d6 R6d5</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"
 +
/>
  
 
And now Red has connected.
 
And now Red has connected.
Line 65: Line 136:
 
== Intrusion at G2 ==
 
== Intrusion at G2 ==
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1g2 R2f2</hex>
+
<hexboard size="6x9"
 +
  coords="bottom right"
 +
  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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 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 ==
 
== Intrusion at D6 or F6 ==
Line 101: Line 213:
 
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.
 
The D6 case is shown here, but Red's responses work symmetrically for the F6 case.
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1d6 R2f5 Pf4 Pg4 Pg3 Pg2 Ph2</hex>
+
<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.
 
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.
Line 107: Line 224:
 
=== Block at F4 ===
 
=== Block at F4 ===
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1f4 R2g4 B3h2 R4f3 B5g3 R6e4 B7e5 R8c5</hex>
+
<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:
 
Or, if for move three Blue played G3:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 Bf4 Rg4 B1g3 R2i2 B3h3 R4i3 B5h4 R6i4 B7h6 R8h5 B9g6 R10g5</hex>
+
<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.
 
And Red is connected. This method can be used by Red in the symmetrical case of Blue intruding at F6.
Line 117: Line 244:
 
=== Block at G2 ===
 
=== Block at G2 ===
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g2 R2h2 B3g4 R4f3 B5f4 R6e4 B7e5 R8c5 Pg3 Pf2</hex>
+
<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:
 
Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex>
+
<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 [[defending against intrusions in template 1-IIIa|template III-1-a]].
 
And Red connects via [[defending against intrusions in template 1-IIIa|template III-1-a]].
Line 129: Line 266:
 
Red's responses are similar in all three cases:
 
Red's responses are similar in all three cases:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1h2 R2f3 B3f4 R4e4 B5e5 R6c5</hex>
+
<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"
 +
/>
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g3 R2f3 B3f4 R4e4 B5e5 R6c5</hex>
+
<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"
 +
/>
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bd6 Rf5 B1g4 R2f3 B3f4 R4e4 B5e5 R6c5</hex>
+
<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 ==
 
== Intrusion at C6 or G6 ==
Line 139: Line 291:
 
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.
 
The G6 case is shown here, but Red's responses work symmetrically for the C6 case.
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 B1g6 R2f4 Pe4 Pf5 Pe5 Pd5 Pf6 Pe6 Pd6 Pc6</hex>
+
<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 [[defending against intrusions in template 1-IIIa|template III-1-a]]. 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.  
 
Red's F4 piece is connected to the bottom via [[defending against intrusions in template 1-IIIa|template III-1-a]]. 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 ===
 
=== Block at G2 ===
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5g4 R6h4</hex>
+
 
 +
<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:
 
And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5e6 R6g4 B7f6 R8d5</hex>
+
<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:
 
And if Blue had played F5 for move five:
  
−
<hex>R6 C9 Q1 Vg1 Vh1 Sa1 Sa2 Sa3 Sa4 Sa5 Sb1 Sb2 Sb3 Sb4 Sc1 Sc2 Sc3 Sd1 Sd2 Se1 Bg6 Rf4 B1g2 R2h2 B3g3 R4h3 B5f5 R6e4 Pe3 Pf3 Pf2 Pg4</hex>
+
<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 [[defending against intrusions in template 1-IIIa|template III-1-a]].
 
Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with [[defending against intrusions in template 1-IIIa|template III-1-a]].
−
 
−
 
−
 
  
 
[[Category:Edge templates]]
 
[[Category:Edge templates]]
 
{{stub}}
 
{{stub}}

Revision as of 02:58, 9 March 2021

The edge template template VI2

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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-1-a, 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-1-a. 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

abcdefghi12345634561287

Or, if for move three Blue played G3:

abcdefghi12345621345610897

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-1-a.

Block at H2, G3, or G4

Red's responses are similar in all three cases:

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abcdefghi123456214365
abcdefghi123456243165

Intrusion at C6 or G6

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

abcdefghi12345621

Red's F4 piece is connected to the bottom via template III-1-a. 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

abcdefghi123456123456

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-1-a.

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