Difference between revisions of "Edge template V1b"

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The template:
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Edge template V1b is a 5th row edge template with 1 stone.
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 E *:d1 R e1 E *:i1 E *:j1 E *:k1 E *:l1 E *:m1 E *:n1 E *:a2 E *:b2 E *:c2 E *:d2 R e2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E *:n3 E *:a4 E *:b4 E *:a5"
+
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
   contents="R e2"
 
   />
 
   />
 
    
 
    
(From the [https://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=669 little golem forum])
+
The validity and minimality of this template has been checked by computer. The template was mentioned on 2016-05-19 by the user shalev in this  [https://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=669 Little Golem thread], but likely predates that post.
  
Even though the diagram shows two pieces and one of them on the sixth row, it makes sense to say this is a fifth row template with one stone, as the stone on the sixth row plays no role whatsoever in connecting to the bottom. It could be removed and the stone on the fifth row will still be connected to the bottom. It is only shown so there is a possibility to connect to the top too, as without that it would not be of much use in a practical sense.
 
  
(Note: As I am writing this I have only seen the claim of this being a valid template on the little golem thread. I have not checked it yet and also not if it is minimal. However, as this came from a very competent player I have no reson to doubt it.)
+
 
 +
== Defense against intrusions ==
 +
 
 +
=== Reduction ===
 +
 
 +
Red has 3 main threats. Using the [[ziggurat]]:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 E *:d4 S d4 d3 e3 c4 S b5 c5 d5 a6 b6 c6 d6"
 +
  />
 +
 
 +
Using [[edge template III1b]]:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 E *:d4 S d3 e3 c4 d4 e4 b5 c5 d5 e5 a6 b6 d6 e6"
 +
  />
 +
 
 +
And using [[edge_template_IV1d]]:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 E *:f3 S area(e3,c6,k6,k4,i2,f2)"
 +
  />
 +
 
 +
For a blocking attempt, Blue [[mustplay region|must play]] in the overlap:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 E a:e3 E b:d5 E c:d6 S e3 d5 d6"
 +
  />
 +
 
 +
=== Intrusion at a ===
 +
 
 +
If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B 1:e3 R 2:d3 B 3:c5 R 4:d4 B 5:d5"
 +
  />
 +
or like this:
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B 1:e3 R 2:d3 B 3:d4 R 4:c4 B 5:b6 R 6:c5 B 7:c6 R 8:d5 B 9:d6"
 +
  />
 +
 
 +
Red's continuation will be discussed below.
 +
 
 +
=== Intrusion at b ===
 +
 
 +
If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B 1:d5 R 2:d4 B 3:e3 R 4:d3 B 5:c5"
 +
  />
 +
 
 +
Red's continuation will be discussed below.
 +
 
 +
=== Intrusion at c ===
 +
 
 +
If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B 1:d6 R 2:d4 B 3:e3 R 4:d3 B 5:c5 R 6:d5 B 7:c6"
 +
  />
 +
 
 +
Red's continuation will be discussed below.
 +
 
 +
=== Continuation after 3rd row ladder ===
 +
 
 +
If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3"
 +
  />
 +
 
 +
Now Red is connected by [[Tom's move for 3rd and 5th row parallel ladders]].
 +
 
 +
=== Continuation after 2nd row ladder ===
 +
 
 +
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R 1:e5 B 2:e6 R 3:h4"
 +
  />
 +
 
 +
Now Red connects in essentially the same way as [[Tom's move]].
 +
 
 +
Specifically, Red has these threats:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:g5 B 4:g6 R 5:i5 S area(f5,f6,i6,i4,h4)"
 +
  />
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:h5 S area(f5,f6,h6,h4,g4)"
 +
  />
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:g3 S area(f2,f3,g4,f6,i6,i4,g2)"
 +
  />
 +
 
 +
The overlap in which Blue [[mustplay region|must play]] is:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 S area(f6,h6,h4)"
 +
  />
 +
 
 +
Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 2:g5 B 3:f5 R 4:g3 B 5:f4 R 6:f2 E +:h5 E +:f6 E +:g6 E +:h6"
 +
  />
 +
 
 +
After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.
 +
 
 +
That leaves only one Blue move to deal with:
 +
 
 +
<hexboard size="6x14"
 +
  coords="hide"
 +
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
  contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 10:f3 R 8:g3 R 4:i3 B 9:f4 B 5:g4 R 2:f5 B 1:g5 B 3:f6 R 6:h2 B 7:g2"
 +
  />
 +
 
 +
Note that Red 4 connects to the bottom with [[Edge_template_IV2b|IV-2-b]].
 +
 
 +
== See also ==
 +
 
 +
* [[Tom's move]]
 +
* [[Tom's move for 3rd and 5th row parallel ladders]]
 +
* [[Fourth row edge templates]]
  
 
[[category:edge templates]]
 
[[category:edge templates]]

Latest revision as of 20:44, 26 July 2022

Edge template V1b is a 5th row edge template with 1 stone.

The validity and minimality of this template has been checked by computer. The template was mentioned on 2016-05-19 by the user shalev in this Little Golem thread, but likely predates that post.


Defense against intrusions

Reduction

Red has 3 main threats. Using the ziggurat:

Using edge template III1b:

And using edge_template_IV1d:

For a blocking attempt, Blue must play in the overlap:

abc

Intrusion at a

If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this

21435

or like this:

214368579

Red's continuation will be discussed below.

Intrusion at b

If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:

43251

Red's continuation will be discussed below.

Intrusion at c

If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:

4325671

Red's continuation will be discussed below.

Continuation after 3rd row ladder

If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.

1

Now Red is connected by Tom's move for 3rd and 5th row parallel ladders.

Continuation after 2nd row ladder

If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.

312

Now Red connects in essentially the same way as Tom's move.

Specifically, Red has these threats:

13524
132
1

The overlap in which Blue must play is:

Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:

64532

After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.

That leaves only one Blue move to deal with:

76108495213

Note that Red 4 connects to the bottom with IV-2-b.

See also