Difference between revisions of "Edge template V1b"

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(Defense against 1. d5: possible responses from Blue)
(Added "see also", and some copy-editing.)
 
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Edge template V1b is a 5th row edge template with 1 stone.
== The template ==
+
  
 
<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 ==
 
== Defense against intrusions ==
  
Red has 3 main threads:
+
=== Reduction ===
 +
 
 +
Red has 3 main threats. Using the [[ziggurat]]:
  
 
<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 +:d3 E +:e3 E *:n3 E *:a4 E *:b4 E +:c4 R 1:d4 E *:a5 E +:b5 E +:c5 E +:d5 E +:a6 E +:b6 E +:c6 E +:d6"
+
  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 the [[ziggurat]],
+
Using [[edge template III1b]]:
  
 
<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 +:d3 E +:e3 E *:n3 E *:a4 E *:b4 E +:c4 R 1:d4 E +:e4 E *:a5 E +:b5 E +:c5 E +:d5 E +:e5 E +:a6 E +:b6 E +:d6 E +:e6"
+
  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"
 
   />
 
   />
 
    
 
    
using [[Defending_against_intrusions_in_template_1-IIIb|III-1-b]] and
+
And using [[edge_template_IV1d]]:
  
 
<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 +:f2 E +:g2 E +:h2 E +:i2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:e3 R 1:f3 E +:g3 E +:h3 E +:i3 E +:j3 E *:n3 E *:a4 E *:b4 E +:e4 E +:f4 E +:g4 E +:h4 E +:i4 E +:j4 E +:k4 E *:a5 E +:d5 E +:e5 E +:f5 E +:g5 E +:h5 E +:i5 E +:j5 E +:k5 E +:c6 E +:d6 E +:e6 E +:f6 E +:g6 E +:h6 E +:i6 E +:j6 E +:k6"
+
  edges="bottom"
 +
  visible="area(f1,a6,n6,n4,l2,h1)"
 +
   contents="R e2 E *:f3 S area(e3,c6,k6,k4,i2,f2)"
 
   />
 
   />
  
using [[Edge_template_IV1d|IV-1-d]].
+
For a blocking attempt, Blue [[mustplay region|must play]] in the overlap:
 
+
For a blocking attempt, Blue has to play on the overlap:
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
   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 +:e3 E *:n3 E *:a4 E *:b4 E *:a5 E +:d5 E +:d6"
+
  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"
 
   />
 
   />
  
=== Defense against 1. e3 ===
+
=== Intrusion at a ===
  
Yet to come ...
+
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"
 +
  />
  
=== Defense against 1. d5 ===
+
Red's continuation will be discussed below.
<div class="toccolours mw-collapsible  mw-collapsed">
+
Red can start like this:
+
  
 +
=== Intrusion at b ===
 +
 +
If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:
 
<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 R 4:g3 E *:n3 E *:a4 E *:b4 R 2:d4 E *:a5 B 3:c5 B 1:d5"
+
  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 has this threat:
+
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"
 
<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 +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 R 1:e4 E +:f4 E +:g4 E *:a5 B c5 B d5 R 3:e5 E +:f5 R 5:g5 B 4:d6 B 2:e6 E +:f6 E +:g6"
+
  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"
 
   />
 
   />
  
So all these fields need to be considered:
+
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"
 
<hexboard size="6x14"
   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 +:f3 R g3 E *:n3 E *:a4 E *:b4 R d4 E +:e4 E +:f4 E +:g4 E *:a5 B c5 B d5 E +:e5 E +:f5 E +:g5 E +:d6 E +:e6 E +:f6 E +:g6"
+
  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"
 
   />
 
   />
  
To be continued ...
+
Now Red is connected by [[Tom's move for 3rd and 5th row parallel ladders]].
</div>
+
  
=== Defense against 1. d6 ===
+
=== Continuation after 2nd row ladder ===
  
Red has this line:
+
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
  
 
<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 R 2:d4 R 8:h4 E *:a5 B 3:c5 R 4:d5 R 6:e5 B 5:c6 B 1:d6 B 7:e6"
+
  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"
 
   />
 
   />
  
Blue 3, 5 and 7 are forced.
+
Now Red connects in essentially the same way as [[Tom's move]].
  
Red has these threats:
+
Specifically, Red has these threats:
  
 
<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 R d4 R h4 E +:i4 E *:a5 B c5 R d5 R e5 R 1:f5 R 3:g5 E +:h5 R 5:i5 B c6 B d6 B e6 B 2:f6 B 4:g6 E +:h6 E +:i6"
+
  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"
 
<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 R d4 E +:g4 R h4 E *:a5 B c5 R d5 R e5 R 1:f5 E +:g5 R 3:h5 B c6 B d6 B e6 B 2:f6 E +:g6 E +:h6"
+
  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"
 
<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 +:f2 E +:g2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 E +:f3 R 1:g3 E +:h3 E *:n3 E *:a4 E *:b4 R d4 E +:f4 E +:g4 R h4 E +:i4 E *:a5 B c5 R d5 R e5 E +:g5 E +:h5 E +:i5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6 E +:i6"
+
  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 has to play is:
+
The overlap in which Blue [[mustplay region|must play]] is:
  
 
<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 R d4 R h4 E *:a5 B c5 R d5 R e5 E +:g5 E +:h5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6"
+
  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 in one line. In the following diagram assume Blue has played 1 on any of the fields marked with +:
+
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"
 
<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 R 6:f2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R 4:g3 E *:n3 E *:a4 E *:b4 R d4 B 5:f4 R h4 E *:a5 B c5 R d5 R e5 B 3:f5 R 2:g5 E +:h5 B c6 B d6 B e6 E +:f6 E +:g6 E +:h6"
+
  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.
+
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:
 
That leaves only one Blue move to deal with:
Line 121: Line 168:
 
<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 B 7:g2 R 6:h2 E *:m2 E *:n2 E *:a3 E *:b3 E *:c3 R 10:f3 R 8:g3 R 4:i3 E *:n3 E *:a4 E *:b4 R d4 B 9:f4 B 5:g4 R h4 E *:a5 B c5 R d5 R e5 R 2:f5 B 1:g5 B c6 B d6 B e6 B 3:f6"
+
  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]].
 
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