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

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This article deals with a special case in [[defending against intrusions in template VI1]], namely the intrusion on the 3rd that is not eliminated by [[sub-templates threat]]s.
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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.
  
 
== Basic situation ==
 
== Basic situation ==
  
<hex>
+
<hexboard size="6x14"
R7 C14 Q0
+
  coords="none"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(i1,c4,a6,o6,o4,k1)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R j1 B h4 E a:h2 b:k2 c:l3"
Sa4 Sb4 Sc4 Sd4 Sn4
+
  />
Sa5 Sb5
+
Sa6
+
  
Bh5
+
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.
</hex>
+
<hexboard size="6x14"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(i1,c4,a6,o6,o4,k1)"
 +
  contents="R j1 B h4 R h2"
 +
  />
  
Red should go here:
+
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, j or k, 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, g, i.
  
<hex>
+
<hexboard size="6x14"
R7 C14 Q0
+
  coords="none"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(i1,c4,a6,o6,o4,k1)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R j1 B h4 R h2 R 1:h3
Sa4 Sb4 Sc4 Sd4 Sn4
+
            E a:g3 d:g4 f:f5 g:g5 k:g6 y:i4"
Sa5 Sb5
+
  />
Sa6
+
If Blue plays at a, f or g, then Red plays at b.
 +
Note that Red connect down from the left by playing d, and connect down from the right by playing y.
 +
The only way for Blue to block both is to play k, but Red with the same strategy on the left would at worst produce a 2nd row ladder toward the right.
  
Bh5  MR Mi5 [[#Third-row_followup:_i4|Pi4]] [[#Third-row_followup:_j3_(stub)|Pj3]]
+
<hexboard size="6x14"
</hex>
+
  coords="none"
 +
  edges="bottom"
 +
  visible="area(i1,c4,a6,o6,o4,k1)"
 +
  contents="R j1 B h4 R h2 B e6 R 1:g4
 +
            E a:g3 b:h3 y:i4 g:g5 j:f6 z:d5"
 +
  />
  
The Red 1 hex is connected to the bottom, and threatens to connect to the top through
+
Finally if Blue plays at i, then Red plays at d. Apart from the bridges, Blue is forced to play g, and then Red plays b, forcing Blue to block on the right part (against Red y), and then Red wins with z.
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 ==
+
If Blue intrudes at a, then Red responds at b, forcing Blue to block on the right part, and then Red wins with j.
<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
+
If Blue intrudes at b, then Red responds at a. Blue is still forced to play g, and then Red wins with z.
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>
 
 
{{stub}}
 
 
[[category:edge templates]]
 
[[category:edge templates]]

Latest revision as of 05:02, 17 May 2024

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, j or k, 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, g, i.

a1dyfgk

If Blue plays at a, f or g, then Red plays at b. Note that Red connect down from the left by playing d, and connect down from the right by playing y. The only way for Blue to block both is to play k, but Red with the same strategy on the left would at worst produce a 2nd row ladder toward the right.

ab1yzgj

Finally if Blue plays at i, then Red plays at d. Apart from the bridges, Blue is forced to play g, and then Red plays b, forcing Blue to block on the right part (against Red y), and then Red wins with z.

If Blue intrudes at a, then Red responds at b, forcing Blue to block on the right part, and then Red wins with j.

If Blue intrudes at b, then Red responds at a. Blue is still forced to play g, and then Red wins with z.