Difference between revisions of "Edge template V1a"

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m (Selinger moved page Template Va to Edge template V1a: The page should be named like other template pages.)
(Merged "Defending against intrusions in template 1-Va" into this page.)
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Template V1-a is a 5th row [[edge template]] with 1 stone.
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<hexboard size="5x10"
 
<hexboard size="5x10"
 
   visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
 
   visible="area(a5,c3,d3,f1,h1,h2,i2,i3,j3,j5)"
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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 [[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]].
  
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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 &mdash; the entire edge on the 10x10 board!
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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.
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== Defending the template ==
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=== Red's threats ===
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Reduction to [[defending against intrusions in template 1-IIIb|template III-1-b]]:
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<hex>R5 C10 Q0
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1:SSSSS_R_SS
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2:SSSS_PP__S
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3:SS__PRP__
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4:S__PPPP
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5:__PP_PP</hex>
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Reductions to [[template IVa]]:
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<hex>R5 C10 Q0
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1:SSSSS_R_SS
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2:SSSSPR___S
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3:SSPPPPP
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4:SPPPPPP
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5:PPPPPPP</hex>
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<hex>R5 C10 Q0
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1:SSSSS_RPSS
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2:SSSS__PRPS
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3:SS___PPPPP
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4:S___PPPPPP
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5:___PPPPPPP</hex>
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Reductions to [[template IVb]]:
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<hex>R5 C10 Q0
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1:SSSSS_R_SS
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2:SSSSPRP__S
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3:SSPPPPPP
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4:SPPP_PPP
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5:PPPPPPPP</hex>
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<hex>R5 C10 Q0
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1:SSSSS_R_SS
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2:SSSS_PRP_S
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3:SS_PPPPPP
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4:S_PPP_PPP
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5:_PPPPPPPP</hex>
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=== Blue's options ===
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These threats only overlap in 3 hexes, so to attempt blocking the template, Blue must move in one of these.
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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+f3 +d5 +f5</hex>
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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.
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=== If Blue moves at f3: ===
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The key move is the response d4. Yielding
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MH Mf3 Md4 +e2</hex>
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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
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MH Mf3 Md4 Me2 Mh2 Mh3</hex>
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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
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MH Mf3 Md4 Me2 Mh2 Mh3 Mg3 Mf5 Mf4 Me5 Me4</hex>
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=== If Blue moves at d5: ===
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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
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MB Md5 Mh2 Mh3 Mf4 Mg2 Mf2 Mf3 Me3</hex>
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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
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MB Md5 Mh2 Mg2 Mh1 Mh3 Mf4 Mg3 Mf2 Mf3 Me3</hex>
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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.
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=== If Blue moves at f5: ===
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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.
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MB Mf5 Me4 Pf2 Pf3</hex>
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The move f2 is defeated by the forcing sequence g2, f3, g3 yielding
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MB Mf5 Me4 Mf2 Mg2 Mf3 Mg3</hex>
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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
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<hex>R5 C10 Q1
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1:SSSSS_R_SS
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2:SSSS_____S
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3:SS
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4:S
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MB Mf5 Me4 Mf3 Me2 Md5 Me5 Me3 Md3</hex>
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Red is threatening to connect to the bottom in two non-overlapping ways, by playing at d4 or c4.
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[[category:edge templates]]
  
 
[[Defending against intrusions in template 1-Va|Proof]] of the template.
 
[[Defending against intrusions in template 1-Va|Proof]] of the template.

Revision as of 18:50, 11 December 2020

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

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.

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!

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.

abcdefghij12345

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

abcdefghij1234512

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

abcdefghij1234534152

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

abcdefghij1234534165210897

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

abcdefghij1234565287341

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

abcdefghij1234548321097561

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.

If Blue moves at f5:

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.

abcdefghij1234521

The move f2 is defeated by the forcing sequence g2, f3, g3 yielding

abcdefghij12345345621

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

abcdefghij1234548732561

Red is threatening to connect to the bottom in two non-overlapping ways, by playing at d4 or c4.Proof of the template.

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