Difference between revisions of "Template VI1/Other Intrusion on the 1st row"
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| − | This article deals with a special case in [[ | + | 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 == | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R j2 B g7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
Red should go here: | Red should go here: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | 1: | + | edges="bottom" |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R 1:h5 j2 B g7 E +:i3 +:i4" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
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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 | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 j2 B g7 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i3 +:i4 +:i5 +:i6 +:i7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 j2 1:j3 B g7 i3 2:i4 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i5 +:i6 +:i7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
CASE #1: Blue has i5. | CASE #1: Blue has i5. | ||
SOLUTION: | SOLUTION: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | 1: | + | edges="bottom" |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 7:h6 5:i6 j2 j3 3:j5 1:k4 B g7 6:h7 i3 i4 i5 4:i7 2:k5" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 j2 j3 1:j4 3:k5 B g7 i3 i4 2:i5 E +:h6 +:h7 +:i6" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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CASE #3: Blue has i7. | CASE #3: Blue has i7. | ||
SOLUTION: | SOLUTION: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 j2 j3 1:j4 3:j5 B g7 i3 i4 2:i5 i7 E +:j6 +:j7 +:k5 +:k6 +:k7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R 1:h3 h5 j2 B g7 2:h4 i4 E +:e7 +:f6 +:f7 +:g5 +:g6 +:h6 +:h7 +:i5 +:i6 +:i7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
CASE #1: Blue has g5. | CASE #1: Blue has g5. | ||
SOLUTION: | SOLUTION: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R 1:f4 3:f5 5:f6 7:g6 h3 h5 j2 B 2:e5 4:e7 6:f7 g5 g7 h4 i4" | |
| − | + | /> | |
| − | + | ||
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| − | + | ||
| − | + | ||
| − | + | ||
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: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R 3:e5 1:g4 h3 h5 j2 B 2:g5 g7 h4 i4 E +:f6 +:f7 +:g6" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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| − | + | ||
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CASE #3: Blue has e7. | CASE #3: Blue has e7. | ||
SOLUTION: | SOLUTION: | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R 3:f5 1:g4 h3 h5 j2 B e7 2:g5 g7 h4 i4 E +:c7 +:d6 +:d7 +:e5 +:e6" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
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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. | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R h5 h6 i6 j2 B f6 g7 i3 i5 E +:e7 +:f7 +:g5 +:g6 +:h7 +:i7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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" | |
| − | < | + | coords="full bottom right" |
| − | + | edges="bottom" | |
| − | 1: | + | visible="area(a7,n7,n5,k2,i2,c5)" |
| − | + | contents="R h5 h6 i6 j2 1:j3 3:k4 5:l5 B f6 g7 i3 2:i4 i5 4:j5" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
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| − | + | ||
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== 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. | ||
| − | < | + | <hexboard size="7x14" |
| − | + | coords="full bottom right" | |
| − | + | edges="bottom" | |
| − | + | visible="area(a7,n7,n5,k2,i2,c5)" | |
| − | + | contents="R f6 g6 h5 j2 B g5 g7 i4 i6 E +:e7 +:f7 +:h6 +:h7 +:i5 +:i7" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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" | |
| − | < | + | coords="full bottom right" |
| − | + | edges="bottom" | |
| − | 1: | + | visible="area(a7,n7,n5,k2,i2,c5)" |
| − | + | contents="R 5:d5 3:f4 f6 g6 1:h3 h5 j2 B 4:f5 g5 g7 2:h4 i4 i6" | |
| − | + | /> | |
| − | + | ||
| − | + | ||
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[[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.
Contents
Basic situation
Red should go here:
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
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:
CASE #1: Blue has i5. SOLUTION:
CASE #2: Blue has no tiles in {h6, h7, i5, i6, i7}, or has either {h6, h7, i6} (indicated by +). SOLUTION:
CASE #3: Blue has i7. SOLUTION:
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:
CASE #1: Blue has g5. SOLUTION:
CASE #2: Blue has no tiles in {e7, f6, f7, g5, g6}, or has either {f6, f7, g6} (indicated by +). SOLUTION:
CASE #3: Blue has e7. SOLUTION:
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.
In this case, Red can still play j3 to force i4, then k4 to force j5, then l5 wins:
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.
In this case, Red can still play h3 to force h4, then f4 to force f5, then d5 wins:
