Difference between revisions of "Template VI1/Other Intrusion on the 1st row"

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(Defending against VI1 right (other) intrusion on the 1st row)
 
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This article deals with a special case in [[defending against intrusions in template VI1]], namely the right-hand ('other') intrusion on the 1st that is not eliminated by [[sub-templates threat]]s.
+
This article deals with a special case in the defense of [[edge template VI1a]], namely the right-hand ('other') intrusion on the 1st that is not eliminated by [[sub-templates threat]]s.
  
 
== Basic situation ==
 
== Basic situation ==
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R j2 B g7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7
+
</hex>
+
  
 
Red should go here:
 
Red should go here:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R 1:h5 j2 B g7 E +:i3 +:i4"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7  MR Mh5 Pi3 Pi4
+
</hex>
+
 
+
  
 
The Red 1 hex is connected to the bottom, and threatens to connect to the top through
 
The Red 1 hex is connected to the bottom, and threatens to connect to the top through
Line 37: Line 26:
 
If Blue moves to  
 
If Blue moves to  
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 j2 B g7 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i3 +:i4 +:i5 +:i6 +:i7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Pi3 Pi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7
+
</hex>
+
  
 
If not, Red can move to either i3 or i4 and secure a connection.
 
If not, Red can move to either i3 or i4 and secure a connection.
Line 61: Line 45:
 
If we've arrived here, Blue has just taken i3, i4 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i3_addendum|i3 addendum]]).  In this case, Red should first take j3 and force a Blue response at i4:
 
If we've arrived here, Blue has just taken i3, i4 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i3_addendum|i3 addendum]]).  In this case, Red should first take j3 and force a Blue response at i4:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 j2 1:j3 B g7 i3 2:i4 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i5 +:i6 +:i7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi3 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7
+
MV Mj3 Mi4
+
</hex>
+
  
 
CASE #1: Blue has i5.
 
CASE #1: Blue has i5.
 
SOLUTION:  
 
SOLUTION:  
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 7:h6 5:i6 j2 j3 3:j5 1:k4 B g7 6:h7 i3 i4 i5 4:i7 2:k5"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi5 Bi3
+
Rj3 Bi4
+
MV Mk4 Mk5 Mj5 Mi7 Mi6 Mh7 Mh6
+
</hex>
+
  
 
CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +).
 
CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +).
 
SOLUTION:  
 
SOLUTION:  
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 j2 j3 1:j4 3:k5 B g7 i3 i4 2:i5 E +:h6 +:h7 +:i6"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi3
+
Rj3 Bi4
+
MV Mj4 Mi5 Mk5
+
Ph6, Ph7, Pi6
+
</hex>
+
  
 
CASE #3: Blue has i7.
 
CASE #3: Blue has i7.
 
SOLUTION:
 
SOLUTION:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 j2 j3 1:j4 3:j5 B g7 i3 i4 2:i5 i7 E +:j6 +:j7 +:k5 +:k6 +:k7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi7 Bi3
+
Rj3 Bi4
+
MV Mj4 Mi5 Mj5 Pj6 Pj7 Pk5 Pk6 Pk7
+
</hex>
+
  
 
Blue must take one of the + hexes or Red wins.  Now, Red can play i6 and force h7, then play h6 and connect to h5 (which is already securely connected.
 
Blue must take one of the + hexes or Red wins.  Now, Red can play i6 and force h7, then play h6 and connect to h5 (which is already securely connected.
Line 132: Line 88:
 
If we've arrived here, Blue has just taken i4, i3 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i4_addendum|i4 addendum]]).  In this case, Red should first take h3 and force a Blue response at h4:
 
If we've arrived here, Blue has just taken i4, i3 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see [[#i4_addendum|i4 addendum]]).  In this case, Red should first take h3 and force a Blue response at h4:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R 1:h3 h5 j2 B g7 2:h4 i4 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i5 +:i6 +:i7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi4 Pe7 Pf6 Pf7 Pg5 Pg6 Ph6 Ph7 Pi5 Pi6 Pi7
+
MV Mh3 Mh4
+
</hex>
+
  
 
CASE #1: Blue has g5.
 
CASE #1: Blue has g5.
 
SOLUTION:
 
SOLUTION:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R 1:f4 3:f5 5:f6 7:g6 h3 h5 j2 B 2:e5 4:e7 6:f7 g5 g7 h4 i4"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bg5 Bi4 Rh3 Bh4
+
MV Mf4 Me5 Mf5 Me7 Mf6 Mf7 Mg6
+
</hex>
+
  
 
CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +).
 
CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +).
 
SOLUTION:
 
SOLUTION:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R 3:e5 1:g4 h3 h5 j2 B 2:g5 g7 h4 i4 E +:f6 +:f7 +:g6"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi4 Rh3 Bh4
+
MV Mg4 Mg5 Me5
+
Pf6, Pf7, Pg6
+
</hex>
+
  
 
CASE #3: Blue has e7.
 
CASE #3: Blue has e7.
 
SOLUTION:
 
SOLUTION:
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R 3:f5 1:g4 h3 h5 j2 B e7 2:g5 g7 h4 i4 E +:c7 +:d6 +:d7 +:e5 +:e6"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Be7 Bi4 Rh3 Bh4
+
MV Mg4 Mg5 Mf5
+
Pc7 Pd6 Pd7 Pe5 Pe6
+
</hex>
+
  
 
Blue must take one of the + hexes or Red wins.  Now, Red can play f6 and force f7, then play g6 and connect to h5 (which is already securely connected.
 
Blue must take one of the + hexes or Red wins.  Now, Red can play f6 and force f7, then play g6 and connect to h5 (which is already securely connected.
Line 201: Line 131:
 
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge.  But in this case Red definitely can acquire i6.
 
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge.  But in this case Red definitely can acquire i6.
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R h5 h6 i6 j2 B f6 g7 i3 i5 E +:e7 +:f7 +:g5 +:g6 +:h7 +:i7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6
+
Pe7 Pf7 Pg5 Pg6 Ph7 Pi7
+
</hex>
+
  
 
In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:
 
In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:
  
 
+
<hexboard size="7x14"
<hex>
+
  coords="full bottom right"
R7 C14 Q1
+
  edges="bottom"
1:BBBBBBBBBRBBBBB
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  contents="R h5 h6 i6 j2 1:j3 3:k4 5:l5 B f6 g7 i3 2:i4 i5 4:j5"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
/>
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi3 Rh6 Bi5 Ri6 Bf6
+
MV Mj3 Mi4 Mk4 Mj5 Ml5
+
</hex>
+
  
 
== i4 addendum ==
 
== i4 addendum ==
Line 234: Line 151:
 
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge.  But in this case Red definitely can acquire f6.
 
I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge.  But in this case Red definitely can acquire f6.
  
<hex>
+
<hexboard size="7x14"
R7 C14 Q1
+
  coords="full bottom right"
1:BBBBBBBBBRBBBBB
+
  edges="bottom"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
  contents="R f6 g6 h5 j2 B g5 g7 i4 i6 E +:e7 +:f7 +:h6 +:h7 +:i5 +:i7"
Sa4 Sb4 Sc4 Sd4 Sn4
+
/>
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6
+
Pe7 Pf7 Ph6 Ph7 Pi5 Pi7
+
</hex>
+
  
 
In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:
 
In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:
  
 
+
<hexboard size="7x14"
<hex>
+
  coords="full bottom right"
R7 C14 Q1
+
  edges="bottom"
1:BBBBBBBBBRBBBBB
+
  visible="area(a7,n7,n5,k2,i2,c5)"
Sa2 Sb2 Sc2 Sd2 Se2 Sf2 Sg2 Sh2 Rj2 Sl2 Sm2 Sn2
+
  contents="R 5:d5 3:f4 f6 g6 1:h3 h5 j2 B 4:f5 g5 g7 2:h4 i4 i6"
Sa3 Sb3 Sc3 Sd3 Se3 Sf3 Sm3 Sn3
+
/>
Sa4 Sb4 Sc4 Sd4 Sn4
+
Sa5 Sb5
+
Sa6
+
 
+
Bg7 Rh5 Bi4 Bg5 Rg6 Rf6 Bi6
+
MV Mh3 Mh4 Mf4 Mf5 Md5
+
</hex>
+
 
+
 
+
  
 
[[category:edge templates]]
 
[[category:edge templates]]

Latest revision as of 21:56, 20 June 2021

This article deals with a special case in the defense of edge template VI1a, namely the right-hand ('other') intrusion on the 1st that is not eliminated by sub-templates threats.

Basic situation

abcdefghijklmn234567

Red should go here:

abcdefghijklmn2345671

The Red 1 hex is connected to the bottom, and threatens to connect to the top through either one of the "+" hexes. It is now Blue's move.

Claim #1: Blue must move in one of the following + squares below

If Blue moves to

abcdefghijklmn234567

If not, Red can move to either i3 or i4 and secure a connection.

Proposed first Red response

If Blue moves to {e7, f6, f7, g5, g6}, Red should take i6 and force a Blue response in either i3 or i4. If Blue moves to {h6, h7, i5, i6, i7}, Red should take f6 and force a Blue response in either i3 or i4. If Blue takes i3 or i4 direcly, proceed with Response to i3 or Response to i4 instructions below.

Response to i3

If we've arrived here, Blue has just taken i3, i4 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see i3 addendum). In this case, Red should first take j3 and force a Blue response at i4:

abcdefghijklmn23456712

CASE #1: Blue has i5. SOLUTION:

abcdefghijklmn2345671327564

CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +). SOLUTION:

abcdefghijklmn234567123

CASE #3: Blue has i7. SOLUTION:

abcdefghijklmn234567123

Blue must take one of the + hexes or Red wins. Now, Red can play i6 and force h7, then play h6 and connect to h5 (which is already securely connected.

Response to i4

If we've arrived here, Blue has just taken i4, i3 is free, h5 is securely connected to the bottom and Blue has at most one of the "+" squares below (with one exception; see i4 addendum). In this case, Red should first take h3 and force a Blue response at h4:

abcdefghijklmn23456712

CASE #1: Blue has g5. SOLUTION:

abcdefghijklmn2345671235746

CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +). SOLUTION:

abcdefghijklmn234567132

CASE #3: Blue has e7. SOLUTION:

abcdefghijklmn234567132

Blue must take one of the + hexes or Red wins. Now, Red can play f6 and force f7, then play g6 and connect to h5 (which is already securely connected.

i3 addendum

I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire i6.

abcdefghijklmn234567

In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:

abcdefghijklmn23456712345

i4 addendum

I claimed that Blue can have only one of the + hexes but this is not quite true if Blue first "plays out" the secured bridge. But in this case Red definitely can acquire f6.

abcdefghijklmn234567

In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:

abcdefghijklmn23456713254