Difference between revisions of "Edge template V1a"

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(Merged "Defending against intrusions in template 1-Va" into this page.)
(Converted to new hexboard diagrams. Some copy-editing.)
Line 8: Line 8:
 
   />
 
   />
  
−
This [[edge template]] appears often as a third move, for instance in the [[a3 opening]], because the played piece is guaranteed to link to one edge and is not too far from the other one. Thus it follows the principle of the [[weakest link]].
+
This template often appears as a third move, for instance in the [[a3 opening]], because the played piece is guaranteed to link to one edge and is not too far from the other one. Thus it follows the principle of the [[weakest link]].
  
−
Note that template V1-a also occurs in a mirror-image form (in the mirror image form, the three hexes on the 5th row (from the bottom) are shifted over 1 hex to the G, H, and I columns). It may seem that this template is very strong because it reaches 5 rows into the board, but it rarely occurs because of the huge size of the template; the template requires 31 empty hexes and 10 hexes along an edge — the entire edge on the 10x10 board!
+
Note that there is also a mirror image form of this template.  
 +
 
 +
It may seem that this template is very strong because it reaches 5 rows into the board, but it rarely occurs outside of the opening, because of the huge size of the template; the template requires 31 empty hexes and 10 hexes along an edge — the entire edge on the 10x10 board!
  
 
Furthermore, the large perimeter makes it more vulnerable to encroaching adjacent plays and forcing moves. Additionally, the [[carrier]] surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.
 
Furthermore, the large perimeter makes it more vulnerable to encroaching adjacent plays and forcing moves. Additionally, the [[carrier]] surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.
Line 19: Line 21:
  
 
Reduction to [[defending against intrusions in template 1-IIIb|template III-1-b]]:
 
Reduction to [[defending against intrusions in template 1-IIIb|template III-1-b]]:
−
<hex>R5 C10 Q0
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSS_PP__S
+
  edges="bottom"
−
3:SS__PRP__
+
  coords="none"
−
4:S__PPPP
+
  contents="R g1 R f3 S area(f2,c5,g5,g2)-e5"
−
5:__PP_PP</hex>
+
  />
 +
 
 
Reductions to [[template IVa]]:
 
Reductions to [[template IVa]]:
−
<hex>R5 C10 Q0
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSSPR___S
+
  edges="bottom"
−
3:SSPPPPP
+
  coords="none"
−
4:SPPPPPP
+
  contents="R g1 R f2 S area(e2,c3,a5,g5,g3,f2)"
−
5:PPPPPPP</hex>
+
  />
 +
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 R h2 S area(h1,d5,j5,j3)"
 +
  />
  
−
<hex>R5 C10 Q0
 
−
1:SSSSS_RPSS
 
−
2:SSSS__PRPS
 
−
3:SS___PPPPP
 
−
4:S___PPPPPP
 
−
5:___PPPPPPP</hex>
 
 
Reductions to [[template IVb]]:
 
Reductions to [[template IVb]]:
−
<hex>R5 C10 Q0
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSSPRP__S
+
  edges="bottom"
−
3:SSPPPPPP
+
  coords="none"
−
4:SPPP_PPP
+
  contents="R g1 R f2 S area(e2,c3,a5,h5,h3,g2)-e4"
−
5:PPPPPPPP</hex>
+
  />
−
 
+
<hexboard size="5x10"
−
<hex>R5 C10 Q0
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
1:SSSSS_R_SS
+
  edges="bottom"
−
2:SSSS_PRP_S
+
  coords="none"
−
3:SS_PPPPPP
+
  contents="R g1 R g2 S area(f2,d3,b5,i5,i3,h2)-f4"
−
4:S_PPP_PPP
+
  />
−
5:_PPPPPPPP</hex>
+
  
 
=== Blue's options ===
 
=== Blue's options ===
  
 
These threats only overlap in 3 hexes, so to attempt blocking the template, Blue must move in one of these.  
 
These threats only overlap in 3 hexes, so to attempt blocking the template, Blue must move in one of these.  
−
<hex>R5 C10 Q1
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSS_____S
+
  edges="bottom"
−
3:SS
+
  coords="none"
−
4:S
+
  contents="R g1 E x:f3 y:d5 z:f5"
−
+f3 +d5 +f5</hex>
+
  />
−
If Blue intrudes in the template at any hex besides the three marked '+', Red makes a move that reduces the situation to a closer template.
+
−
 
+
−
=== If Blue moves at f3: ===
+
−
 
+
−
The key move is the response d4. Yielding
+
−
 
+
−
<hex>R5 C10 Q1
+
−
1:SSSSS_R_SS
+
−
2:SSSS_____S
+
−
3:SS
+
−
4:S
+
−
MH Mf3 Md4 +e2</hex>
+
−
 
+
−
Red is threatening to play at the marked hex which would complete the connection of the g1 piece to the bottom. Blue must block by a playing at some hex between Red's two pieces. Red then plays h2 forcing Blue to block at h3 yielding
+
−
 
+
−
<hex>R5 C10 Q1
+
−
1:SSSSS_R_SS
+
−
2:SSSS_____S
+
−
3:SS
+
−
4:S
+
−
MH Mf3 Md4 Me2 Mh2 Mh3</hex>
+
−
 
+
−
Red has forced the most common pre-ladder formation. Red can get a second row ladder by squeezing through at g3 (Blue blocks at f5). Red's initial key d4 piece acts as a ladder escape which completes the connection. The final position is
+
−
 
+
−
<hex>R5 C10 Q1
+
−
1:SSSSS_R_SS
+
−
2:SSSS_____S
+
−
3:SS
+
−
4:S
+
−
MH Mf3 Md4 Me2 Mh2 Mh3 Mg3 Mf5 Mf4 Me5 Me4</hex>
+
−
 
+
−
=== If Blue moves at d5: ===
+
−
 
+
−
Red's best response is to two-chain to h2. To stop the threatened immediate connection, Blue must block at h3 or play the forcing move g2 in the two-chain.  The first play is defeated by the forcing sequence f4, g2, f2, f3, e3 yielding
+
  
−
<hex>R5 C10 Q1
+
=== If Blue moves at x: ===
−
1:SSSSS_R_SS
+
−
2:SSSS_____S
+
−
3:SS
+
−
4:S
+
−
MB Md5 Mh2 Mh3 Mf4 Mg2 Mf2 Mf3 Me3</hex>
+
  
−
Red is now threatening to connect to the bottom in two non-overlapping ways, by playing e4 or by two-chaining to c4. Blue cannot stop both threats with a single move. The other play, g2 (after Red's h2) is defeated by the forcing sequence h1, h3, f4, g3, f2, f3, e3 yielding
+
Red responds as follows.
 +
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 B 1:f3 R 2:d4 E +:e2"
 +
  />
 +
Red is threatening to connect at "+". Blue must block by playing somewhere between Red's two pieces. Red then continues as follows:
  
−
<hex>R5 C10 Q1
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSS_____S
+
  edges="bottom"
−
3:SS
+
  coords="none"
−
4:S
+
  contents="R g1 B 1:f3 R 2:d4 B 3:e2 R 4:h2 B 5:h3 R 6:g3 B 7:f5"
−
MB Md5 Mh2 Mg2 Mh1 Mh3 Mf4 Mg3 Mf2 Mf3 Me3</hex>
+
  />
 +
Red has forced a [[bottleneck]], resulting in a 2nd row [[ladder]]. Red's 2 acts as a [[ladder escape]]. The final position is
  
−
Red is again threatening to connect to the bottom in the same two non-overlapping ways: by playing at e4 or two-chaining to c4. Blue cannot stop both threats with a single move.
+
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 B 1:f3 R 2:d4 B 3:e2 R 4:h2 B 5:h3 R 6:g3 B 7:f5 R 8:f4 B 9:e5 R 10:e4"
 +
  />
  
−
=== If Blue moves at f5: ===
+
=== If Blue moves at y: ===
  
−
Red's best response is play e4 which is connected to the bottom and forms a loose connection with the g1 piece. To stop the immediate connection, Blue must play in the middle of the loose connection at one of the hexes marked "+" in the following diagram.
+
Red's best response is to [[bridge]] to 2. To stop the threatened immediate connection, Blue must block at 3 or intrude on the bridge. If Blue plays at 3, Red plays the following sequence of forcing moves:
  
−
<hex>R5 C10 Q1
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSS_____S
+
  edges="bottom"
−
3:SS
+
  coords="none"
−
4:S
+
  contents="R g1 B 1:d5 R 2:h2 B 3:h3 R 4:f4 B 5:g2 R 6:f2 B 7:f3 R 8:e3 E +:(c4 e4)"
−
MB Mf5 Me4 Pf2 Pf3</hex>
+
  />
  
−
The move f2 is defeated by the forcing sequence g2, f3, g3 yielding
+
Red is now connected to the edge by [[double threat]] at the cells marked "+".
 +
If Blue intrudes on the bridge instead, play proceeds similarly:
  
−
<hex>R5 C10 Q1
+
<hexboard size="5x10"
−
1:SSSSS_R_SS
+
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
−
2:SSSS_____S
+
  edges="bottom"
−
3:SS
+
  coords="none"
−
4:S
+
  contents="R g1 B 1:d5 R 2:h2 B 3:g2 R 4:h1 B 5:h3 R 6:f4 B 7:g3 R 8:f2 B 9:f3 R 10:e3 E +:(c4 e4)"
−
MB Mf5 Me4 Mf2 Mg2 Mf3 Mg3</hex>
+
  />
  
−
Red is threatening to connect to the bottom in two non-overlapping ways: by playing at f4 or two-chaining to h4. The alternative response, f3, is defeated by the forcing sequence e2, d5, e5, e3, d3 yielding
+
Again, Red is connected by double threat at "+".
  
−
<hex>R5 C10 Q1
+
=== If Blue moves at z: ===
−
1:SSSSS_R_SS
+
−
2:SSSS_____S
+
−
3:SS
+
−
4:S
+
−
MB Mf5 Me4 Mf3 Me2 Md5 Me5 Me3 Md3</hex>
+
  
−
Red is threatening to connect to the bottom in two non-overlapping ways, by playing at d4 or c4.
+
Red's best response is 2, which is connected to the bottom and forms a loose connection with the Red's piece on the 5th row. To stop the immediate connection, Blue must play at a or b.
  
−
[[category:edge templates]]
+
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 B 1:f5 R 2:e4 E a:f2 b:f3"
 +
  />
  
−
[[Defending against intrusions in template 1-Va|Proof]] of the template.
+
If Blue moves at a, Red plays the following forcing sequence, connecting by double threat at "+".
 +
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 B 1:f5 R 2:e4 B 3:f2 R 4:g2 B 5:f3 R 6:g3 E +:(f4 h4)"
 +
  />
 +
If Blue moves at b, Red plays the following forcing sequence, again connecting by double threat.  
 +
<hexboard size="5x10"
 +
  visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 +
  edges="bottom"
 +
  coords="none"
 +
  contents="R g1 B 1:f5 R 2:e4 B 3:f3 R 4:e2 B 5:d5 R 6:e5 B 7:e3 R 8:d3 E +:(c4 d4)"
 +
  />
  
 
[[Category: Advanced Strategy]]
 
[[Category: Advanced Strategy]]
 
[[Category: Edge templates]]
 
[[Category: Edge templates]]

Revision as of 04:32, 12 December 2020

Template V1-a is a 5th row edge template with 1 stone.

This template often appears as a third move, for instance in the a3 opening, because the played piece is guaranteed to link to one edge and is not too far from the other one. Thus it follows the principle of the weakest link.

Note that there is also a mirror image form of this template.

It may seem that this template is very strong because it reaches 5 rows into the board, but it rarely occurs outside of the opening, because of the huge size of the template; the template requires 31 empty hexes and 10 hexes along an edge — the entire edge on the 10x10 board!

Furthermore, the large perimeter makes it more vulnerable to encroaching adjacent plays and forcing moves. Additionally, the carrier surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.

Defending the template

Red's threats

Reduction to template III-1-b:

Reductions to template IVa:

Reductions to template IVb:

Blue's options

These threats only overlap in 3 hexes, so to attempt blocking the template, Blue must move in one of these.

xyz

If Blue moves at x:

Red responds as follows.

12

Red is threatening to connect at "+". Blue must block by playing somewhere between Red's two pieces. Red then continues as follows:

3416527

Red has forced a bottleneck, resulting in a 2nd row ladder. Red's 2 acts as a ladder escape. The final position is

34165210897

If Blue moves at y:

Red's best response is to bridge to 2. To stop the threatened immediate connection, Blue must block at 3 or intrude on the bridge. If Blue plays at 3, Red plays the following sequence of forcing moves:

65287341

Red is now connected to the edge by double threat at the cells marked "+". If Blue intrudes on the bridge instead, play proceeds similarly:

48321097561

Again, Red is connected by double threat at "+".

If Blue moves at z:

Red's best response is 2, which is connected to the bottom and forms a loose connection with the Red's piece on the 5th row. To stop the immediate connection, Blue must play at a or b.

ab21

If Blue moves at a, Red plays the following forcing sequence, connecting by double threat at "+".

345621

If Blue moves at b, Red plays the following forcing sequence, again connecting by double threat.

48732561
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