Difference between revisions of "Edge template IV2l"

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''This page is about edge template IV2l (four two ell). There is also an [[edge template IV2i]] (four two eye).''
 
''This page is about edge template IV2l (four two ell). There is also an [[edge template IV2i]] (four two eye).''
  
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The template:
+
Template IV2-l is a 4th row [[edge template]] with 2 stones.
  
 
<hexboard size="4x6"
 
<hexboard size="4x6"
 
   coords="hide"
 
   coords="hide"
 +
  edges="bottom"
 +
  visible="area(d1,a4,f4,f1)"
 
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3"
 
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3"
 
   />
 
   />
Line 10: Line 12:
 
(From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk])   
 
(From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk])   
  
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== Choosing which stone to connect ==
+
== Defending the template ==
  
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Red is guaranteed to be able to connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two to connect (see below). But it is easier to analyze the template if we assume Red chooses one of the two stones to connect to the bottom. Here, we assume that Red wants to connect the stone on the right-hand side to the bottom.
+
Red can connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two stones to connect. To show this, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line).
  
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Red has three threats. The first one uses bridges.
+
If Blue plays in any of the cells marked "+", Red can respond at d3.  
  
 
<hexboard size="4x6"
 
<hexboard size="4x6"
−
   coords="hide"
+
   coords="bottom right"
−
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E +:e2 E +:f2 E *:a3 R 1:e3 E +:d4 E +:e4"
+
  edges="bottom"
 +
  visible="area(d1,a4,f4,f1)"
 +
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:e1 +:e2 +:e3 +:e4 +:f2 +:f3 +:f4 R 2:d3"
 
   />
 
   />
  
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The second one uses template [[Defending_against_intrusions_in_template_1-IIIb|II-1-b]].
+
Then d1 is connected by [[edge template IV2d]] and f1 connects via e1 or e2 or [[edge template III2e]]. Since Blue has so far played only one of the cells marked "+", at least two of those three are still available. Also, since d3 [[captured cell|captures]] c4 and d4, the overlap between edge template IV2d and edge template III2e does not matter.
  
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<hexboard size="4x6"
+
If Blue plays d3 or d4, Red can respond at c3.  d1 connects via two bridges, and f1 connects via e1 or e3.  Since Blue has so far played only one of the cells marked "+", two of d3, d4, e4 are still available, which is sufficient to connect e3 to the edge.
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  coords="hide"
+
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E +:d2 R 1:e2 E +:f2 E *:a3 E +:c3 E +:d3 E +:e3 E +:f3 E +:b4 E +:c4 E +:e4 E +:f4"
+
−
  />
+
−
 
+
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The third one uses the [[ziggurat]].
+
  
 
<hexboard size="4x6"
 
<hexboard size="4x6"
−
   coords="hide"
+
   coords="bottom right"
−
   contents="E *:a1 E *:b1 E *:c1 R d1 E +:e1 R f1 E *:a2 E *:b2 E +:c2 R 1:d2 E +:e2 E *:a3 E +:b3 E +:c3 E +:d3 E +:a4 E +:b4 E +:c4 E +:d4"
+
  edges="bottom"
 +
  visible="area(d1,a4,f4,f1)"
 +
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:d3 +:d4 R 2:c3"
 
   />
 
   />
−
 
−
 
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For a blocking attempt, Blue has to play on the only overlapping field:
 
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−
<hexboard size="4x6"
 
−
  coords="hide"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 E +:e1 R f1 E *:a2 E *:b2 B 1:e2 R 2:f2 E *:a3 R 6:c3 E +:d3 R 4:e3 B 5:d4 B 3:e4"
 
−
  />
 
−
 
−
Red 6 is connected to the bottom and can be connected to the top right by one of the fields marked with +.
 
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== Connecting both stones ==
 
−
 
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To show that Red can, in fact, connect both stones to the bottom, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line).
 
−
 
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If Blue plays in any of the cells marked "+", Red responds at d2 and is connected by a [[ziggurat]].
 
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−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:f2 +:f3 +:f4 +:e3 +:e4 R 2:d2"
 
−
  />
 
−
 
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If Blue plays 1.e1, Red responds with 2.d3 and is connected by two copies of [[edge template IV2d]]:
 
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−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e1 R 2:d3"
 
−
  />
 
−
 
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If Blue plays 1.e2, Red responds with 2.f2:
 
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−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e2 R 2:f2"
 
−
  />
 
−
 
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If Blue now plays 3.e4, the game proceeds as shown above. If Blue plays 3.e1, Red responds with 4.c3. In all other cases, Red responds with 4.e1.
 
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If Blue plays 1.d3, Red responds with 2.e1 and is connected via [[edge template IV2a]]:
 
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−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e3 R 2:e1"
 
−
  />
 
−
 
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If Blue plays 1.d4, Red responds with 2.e1:
 
−
 
−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1"
 
−
  />
 
−
 
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Now if Blue plays outside the area marked "+" in the next figure, Red connects with c3:
 
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−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1 E +:b4 +:c2 +:c3 +:c4 +:d2"
 
−
  />
 
−
 
−
If Blue plays outside the area marked "+" in the next figure, Red proceeds as in defending [[edge template IV2a]] (since Blue only has one stone in the template ''and it is Red's turn''):
 
−
 
−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1 E +:c4 +:d2 +:d3 +:e2 +:e3 +:e4 +:f2 +:f3 +:f4"
 
−
  />
 
−
 
−
That leaves only two possible plays for Blue, at d2 and c4. They are easily dealt with:
 
−
 
−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B d4 R e1 B 3:d2 R 4:c3 B 5:c2 R 6:e3"
 
−
  />
 
−
 
−
<hexboard size="4x6"
 
−
  coords="show"
 
−
  contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B d4 R e1 B 3:c4 R 4:b3 B 5:c2 R 6:f3 B 7:f2 R 8:d3"
 
−
  />
 
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== See also ==
 
  
 
[[category:edge templates]]
 
[[category:edge templates]]

Latest revision as of 16:49, 10 December 2020

This page is about edge template IV2l (four two ell). There is also an edge template IV2i (four two eye).

Template IV2-l is a 4th row edge template with 2 stones.

(From: www.drking.org.uk)

Defending the template

Red can connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two stones to connect. To show this, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line).

If Blue plays in any of the cells marked "+", Red can respond at d3.

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Then d1 is connected by edge template IV2d and f1 connects via e1 or e2 or edge template III2e. Since Blue has so far played only one of the cells marked "+", at least two of those three are still available. Also, since d3 captures c4 and d4, the overlap between edge template IV2d and edge template III2e does not matter.

If Blue plays d3 or d4, Red can respond at c3. d1 connects via two bridges, and f1 connects via e1 or e3. Since Blue has so far played only one of the cells marked "+", two of d3, d4, e4 are still available, which is sufficient to connect e3 to the edge.

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