Difference between revisions of "Edge template V1b"
(Fixed the continuations after 2nd row ladder.) |
(Handled more cases. Intrusions w and x need more work.) |
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<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| − | Now Red | + | Now Red has two main threats. Via a [[ziggurat]]: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 E *:f4 S f2 g2 f3 e4 area(d6,f4,g4,g6)" | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 E *:f4 S f2 g2 f3 e4 area(d6,f4,g4,g6)" | ||
| + | /> | ||
| + | And via [[edge template IV2b]]: | ||
| + | <hexboard size="6x14" | ||
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 E *:f4 S f2 g2 f3 e4 area(e6,i6,i4,h3,f4)" | ||
/> | /> | ||
| − | + | Blue must play in the overlap: | |
| + | <hexboard size="6x14" | ||
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 S f2 g2 f3 e4 area(e6,f4,g4,g6) | ||
| + | E p:f2 q:g2 r:f3 s:e4 t:f4 u:g4 v:f5 w:g5 x:e6 y:f6 z:g6" | ||
| + | /> | ||
| − | ==== | + | ==== Intrusion at p, q, r ==== |
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
| Line 131: | Line 144: | ||
edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents="R e2 | + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:(f3 f2 g2) R 3:e4 S d6 e5 e6" |
/> | /> | ||
| − | Now Blue must play in one of the 3 shaded cells. | + | Now Blue must play in one of the 3 shaded cells. If Blue plays in the left 2 of those 3, then Red connects via [[Edge_template_IV2b|IV-2-b]]. Otherwise, Red connects via [[Tom's move]]. |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents="R e2 | + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:(f3 f2 g2) R 3:e4 5:e5 7:f5 9:i4 B 2:(f3 f2 g2) 4:e6 6:d6 8:f6" |
/> | /> | ||
| + | ==== Intrusion at s ==== | ||
| + | <hexboard size="6x14" | ||
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:e4 R 3:f2" | ||
| + | /> | ||
| − | + | Red is connected by [[edge template IV1d]]. | |
| − | + | ==== Intrusion at t ==== | |
| − | ==== | + | <hexboard size="6x14" |
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:f4 R 3:e4 B 4:e5 R 5:h2" | ||
| + | /> | ||
| − | + | Now Red is connected by [[Fifth_row_edge_templates#V-2-m|edge template V2m]]. If Blue plays 4 on the first row instead, Red connects by [[Tom's move]]: | |
| + | <hexboard size="6x14" | ||
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:f4 R 3:e4 B 4:e6 R 5:e5 B 6:d6 R 7:f5 B 8:f6 R 9:i4" | ||
| + | /> | ||
| − | ==== | + | ==== Intrusion at u ==== |
| − | + | <hexboard size="6x14" | |
| + | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g4 R 3:f4 B 4:e6 R 5:f5 B 6:f6 R 7:i4" | ||
| + | /> | ||
| + | Red is connected by [[Tom's move]]. | ||
| − | ==== | + | ==== Intrusion at v ==== |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:f5 R 3:f4 E *:e5 *:h4" |
/> | /> | ||
| + | Red is connected by [[double threat]]. | ||
| + | |||
| + | ==== Intrusion at w ==== | ||
| − | + | To do. | |
| − | ==== | + | ==== Intrusion at x ==== |
Red can respond here: | Red can respond here: | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 R 3:f5 B 2:e6" |
/> | /> | ||
| Line 376: | Line 404: | ||
</div> | </div> | ||
| − | ==== | + | ==== Intrusion at y ==== |
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 B e3 R d3 R 1:g3 R d4 B c5 B d5 B 2:f6 R 3:e5 E *:d6 *:e6 B 4:e4 R 5:f2" |
/> | /> | ||
| − | + | Note that the hexes marked "*" are [[captured cell|captured]] by Red 3, so Blue 4 is forced. Then Red is connected by [[edge template IV2e]]. | |
| − | Red | + | |
| − | + | ==== Intrusion at z ==== | |
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 B e3 R d3 R 1:g3 R d4 B c5 B d5 B 2:g6 R 3:e5 E *:d6 *:e6 B 4:e4 R 5:f2" |
/> | /> | ||
| − | + | Note that the hexes marked "*" are [[captured cell|captured]] by Red 3, so Blue 4 is forced. Then Red is connected by [[Fourth_row_edge_templates#IV-2-q|edge template IV2p]]. | |
| − | + | ||
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</div> | </div> | ||
Revision as of 23:46, 24 July 2022
Edge template V1b is a 5th row edge template with 1 stone.
The validity and minimality of this template has been checked by computer. The template was mentioned on 2016-05-19 by the user shalev in this Little Golem thread, but likely predates that post.
Contents
Defense against intrusions
Reduction
Red has 3 main threats. Using the ziggurat:
Using edge template III1b:
And using edge_template_IV1d:
For a blocking attempt, Blue must play in the overlap:
Intrusion at a
If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this
or like this:
Red's continuation will be discussed below.
Intrusion at b
If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:
Red's continuation will be discussed below.
Intrusion at c
If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:
Red's continuation will be discussed below.
Continuation after 3rd row ladder
If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.
Now Red is connected by Tom's move for 3rd and 5th row parallel ladders.
Continuation:
Now Red has two main threats. Via a ziggurat:
And via edge template IV2b:
Blue must play in the overlap:
Intrusion at p, q, r
Now Blue must play in one of the 3 shaded cells. If Blue plays in the left 2 of those 3, then Red connects via IV-2-b. Otherwise, Red connects via Tom's move.
Intrusion at s
Red is connected by edge template IV1d.
Intrusion at t
Now Red is connected by edge template V2m. If Blue plays 4 on the first row instead, Red connects by Tom's move:
Intrusion at u
Red is connected by Tom's move.
Intrusion at v
Red is connected by double threat.
Intrusion at w
To do.
Intrusion at x
Red can respond here:
Continuation:
Now Red has two threats:
and
Blue must play in the overlap:
7. f2
7. g2
7. f3
6 is now connected to the left and to the bottom by Tom's move.
7. e4
4 is again connected to the left and to the bottom by Tom's move.
7. f4
Blue must go on one of the 3 marked fields. However, d6 can't be any better than 35, so it's enough to look at e5 and g6. Let's have a look at g6 first:
4 is now connected to the bottom and to the left in a similar way as in Tom's move. (Just the piece on g3 is connected to the left in a slightly different way.)
The other possible move was e5:
Red 2 is connected to the left by two non-overlapping ways and to the bottom by a 5th row template that has yet to be added to this wiki.
7. g4
Once again 6 is now connected to the bottom and to the left in a similar way as in Tom's move.
7. e5
And Tom's move at the end again.
7. f6
Red 2 is connected to the bottom and to at least one of the red pieces in the middle by Tom's move. Red now has three threats to connect both these pieces to the top:
and
Blue must play in the overlap:
First move:
Second move:
Intrusion at y
Note that the hexes marked "*" are captured by Red 3, so Blue 4 is forced. Then Red is connected by edge template IV2e.
Intrusion at z
Note that the hexes marked "*" are captured by Red 3, so Blue 4 is forced. Then Red is connected by edge template IV2p.
Continuation after 2nd row ladder
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
Now Red connects in essentially the same way as Tom's move.
Continuation:
Red has these threats:
The overlap in which Blue must play is:
Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:
After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.
That leaves only one Blue move to deal with:
Note that Red 4 connects to the bottom with IV-2-b.
