Defending against intrusions in template 1-Va - Revision history

Selinger: Merged this page into "Edge template V1a"

2020-12-11T18:51:11Z

Merged this page into "Edge template V1a"

Show changes

Halladba: link back to template Va

2008-10-26T11:16:30Z

link back to template Va

Halladba: minor board rewriting

2008-10-26T11:07:10Z

minor board rewriting

Halladba: copied and completed what was in advanced guide

2007-12-10T01:40:50Z

copied and completed what was in advanced guide

New page

<hex>R5 C10 Q0
1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S</hex>

== Red's threats ==
=== Reduction to [[defending against intrusions in template 1-IIIb|template III-1-b]]===
<hex>R5 C10 Q0
1:SSSSS_R_SS
2:SSSS_PP__S
3:SS__PRP__
4:S__PPPP
5:__PP_PP</hex>
=== Reduction to [[template IVa]]===
<hex>R5 C10 Q0
1:SSSSS_R_SS
2:SSSSPR___S
3:SSPPPPP
4:SPPPPPP
5:PPPPPPP</hex>

<hex>R5 C10 Q0
1:SSSSS_RPSS
2:SSSS__PRPS
3:SS___PPPPP
4:S___PPPPPP
5:___PPPPPPP</hex>
=== Reduction to [[template IVb]]===
<hex>R5 C10 Q0
1:SSSSS_R_SS
2:SSSSPRP__S
3:SSPPPPPP
4:SPPP_PPP
5:PPPPPPPP</hex>

<hex>R5 C10 Q0
1:SSSSS_R_SS
2:SSSS_PRP_S
3:SS_PPPPPP
4:S_PPP_PPP
5:_PPPPPPPP</hex>

== Blue's choice==
There are only 3 ways for blue not to fall into one of the previous reduction, we can see it if we consider the intersection of every relevant move in previous diagrams.
<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S +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.

=== Solution to the intrusion 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>

=== Solution to the intrusion 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 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

<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S MB Md5 Mh2 Mg2 Mh1 Mh3 Mf4 Mg3 Mf2 Mf3 Me3</hex>

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.

=== Solution to the intrusion 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.

<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S MB Mf5 Me4 Pf2 Pf3</hex>

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

<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S 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

<hex>R5 C10 Q1 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.

Note that template Va 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, template area surrounds the 5th row piece on both "shoulders" so that non-overlapping plays from the 5th row piece can occur in only two directions.

[[category:edge templates]]

← Older revision		Revision as of 11:16, 26 October 2008
Line 1:		Line 1:
		+	Here is the proof of [[Template Va\|Template 1-Va]].
		+
	<hex>R5 C10 Q0		<hex>R5 C10 Q0
	1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S</hex>		1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S</hex>

@@ Line 41: / Line 41: @@
 == Blue's choice==
 There are only 3 ways for blue not to fall into one of the previous reduction, we can see it if we consider the intersection of every relevant move in previous diagrams.
-<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   +f3 +d5 +f5</hex>
+<hex>R5 C10 Q1
 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.
@@ Line 48: / Line 53: @@
 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>
+<hex>R5 C10 Q1
 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>
+<hex>R5 C10 Q1
 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>
+<hex>R5 C10 Q1
 === Solution to the intrusion at d5 ===
@@ Line 62: / Line 82: @@
 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 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   MB Md5 Mh2 Mh3 Mf4 Mg2 Mf2 Mf3 Me3</hex>
+<hex>R5 C10 Q1
 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
-<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   MB Md5 Mh2 Mg2 Mh1 Mh3 Mf4 Mg3 Mf2 Mf3 Me3</hex>
+<hex>R5 C10 Q1
 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.
@@ Line 74: / Line 104: @@
 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.
-<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   MB Mf5 Me4 Pf2 Pf3</hex>
+<hex>R5 C10 Q1
 The move f2 is defeated by the forcing sequence g2, f3, g3 yielding
-<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   MB Mf5 Me4 Mf2 Mg2 Mf3 Mg3</hex>
+<hex>R5 C10 Q1
 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
-<hex>R5 C10 Q1 1:SSSSS_R_SS 2:SSSS_____S 3:SS 4:S   MB Mf5 Me4 Mf3 Me2 Md5 Me5 Me3 Md3</hex>
+<hex>R5 C10 Q1
 Red is threatening to connect to the bottom in two non-overlapping ways, by playing at d4 or c4.