Difference between revisions of "Template VI1/Intrusion on the 3rd row"

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<hex>
+
This article deals with a special case in the defense of [[edge template VI1a]], namely the intrusion on the 3rd that is not eliminated by [[sub-templates threat]]s.
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
  
Bh5
+
== Basic situation ==
</hex>
+
  
Red should go here:
+
<hexboard size="6x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(i1,c4,a6,o6,o4,k1)"
 +
  contents="R j1 B h4 E a:h2 b:k2 c:l3"
 +
  />
  
<hex>
+
In this situation, there are only 3 possible winning moves for Red, and they are "a", "b", and "c". Of these, "a" is the easiest to verify, so we will assume Red plays there.
R7 C14 Q0
+
<hexboard size="6x14"
1:BBBBBBBBBRBBBBB
+
   coords="none"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  edges="bottom"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  visible="area(i1,c4,a6,o6,o4,k1)"
Sa4 Sb4 Sc4 Sd4 Sn4
+
  contents="R j1 B h4 R h2"
Sa5 Sb5
+
  />
Sa6
+
 
+
Bh5  MR Mi5 Pi4 Pj3
+
</hex>
+
 
+
The Red 1 hex is connected to the bottom, and threatens to connect to the top through
+
either one of the "+" hexes. Thus these are the only important incursions.  An incursion to the right of the
+
number 1 hex is important only in connection with the two indicated here, and will be seen in the treatement
+
below transposed into the sequel.
+
 
+
== Third-row followup: i4 ==
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  MR Mi5 Mi4 Mk3
+
Pj4    Pl4
+
Pj5
+
</hex>
+
 
+
=== Figuring out the [[Must-play region]]===
+
Red threatens to play at "+" points above, with these templates:
+
 
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
Rj5
+
Pk4 Pj4
+
Pk5
+
Ph6    Pj6 Pk6
+
Pg7 Ph7  Pj7 Pk7
+
</hex>
+
 
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
Rj5
+
Pk4 Pj4
+
Ph6 Pi6 Pj6
+
Pg7 Ph7 Pi7
+
</hex>
+
 
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
Rj4
+
Pj5
+
Ph6 Pi6 Pj6
+
Pg7 Ph7 Pi7 Pj7
+
</hex>
+
 
+
 
+
[[Edge template IV1a]]
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
Rl4
+
                         
+
                  Pl3
+
              Pk4            Pm4
+
          Pj5    Pk5    Pl5    Pm5    Pn5
+
      Pi6    Pj6    Pk6    Pl6    Pm6    Pn6
+
  Ph7    Pi7    Pj7    Pk7      Pl7    Pm7    Pn7
+
</hex>
+
 
+
We need only consider the intersection of these templates.
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
Pj5
+
   Pj6
+
Ph7
+
</hex>
+
 
+
=== Incursion at j5 ===
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
MB Mj5 Mj4 Mh7 Mi6 Mi7 Mk6
+
Pj6 Pl4
+
</hex>
+
 
+
=== Incursion at j6 ===
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
MB Mj6 Mk4
+
Ph7 Pl5
+
</hex>
+
 
+
=== Incursion at h7 ===
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  Ri5 Bi4 Rk3
+
MB Mh7 Mj6 Mj5 Ml4 Mk5 Ml5
+
Pm5
+
Pk6 Pl6 Pm6
+
Pj7 Pk7 Pl7 Pm7
+
</hex>
+
 
+
== Third-row followup: j3 (stub) ==
+
<hex>
+
R7 C14 Q0
+
1:BBBBBBBBBRBBBBB
+
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bh5  MR Mi5 Mj3
+
</hex>
+
  
 +
Before continuing the analysis, we first note that Red can escape all 2nd row ladders coming from the left, as follows:
 +
<hexboard size="6x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(i1,c4,a6,o6,o4,k1)"
 +
  contents="R j1 B h4 R h2
 +
            R 1:g5 B 2:g6 R 3:h5 B 4:h6 R 5:j5 B 6:i5 R 7:j4 B 8:i4 R 9:k2"
 +
  />
 +
Apart from attacking the bridge, which Red defends, Blue's next move must be in the shaded blue area, or else Red plays at d and connects.
 +
<hexboard size="6x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(i1,c4,a6,o6,o4,k1)"
 +
  contents="R j1 B h4 R h2
 +
            S blue:area(g3,d6,g6,g4,h3)
 +
            E a:g3 b:h3 c:f4 d:g4 e:e5 f:f5 g:g5 h:d6 i:e6 j:f6 k:g6 x:f3"
 +
  />
 +
If Blue plays at c, e, h, or j, Red responds at d and gets a 2nd row ladder, which connects.
 +
If Blue plays at b, Red plays at x and connects by [[edge template IV1a]].
 +
If Blue plays at d, Red plays at x and gets a 2nd row ladder, which connects.
 +
This leaves a, f, i, g, k. To be continued.
 
{{stub}}
 
{{stub}}
 
[[category:edge templates]]
 
[[category:edge templates]]

Revision as of 21:55, 20 June 2021

This article deals with a special case in the defense of edge template VI1a, namely the intrusion on the 3rd that is not eliminated by sub-templates threats.

Basic situation

abc

In this situation, there are only 3 possible winning moves for Red, and they are "a", "b", and "c". Of these, "a" is the easiest to verify, so we will assume Red plays there.

Before continuing the analysis, we first note that Red can escape all 2nd row ladders coming from the left, as follows:

987136524

Apart from attacking the bridge, which Red defends, Blue's next move must be in the shaded blue area, or else Red plays at d and connects.

xabcdefghijk

If Blue plays at c, e, h, or j, Red responds at d and gets a 2nd row ladder, which connects. If Blue plays at b, Red plays at x and connects by edge template IV1a. If Blue plays at d, Red plays at x and gets a 2nd row ladder, which connects. This leaves a, f, i, g, k. To be continued.