Difference between revisions of "Edge template V1b"
From HexWiki
(→... 5. e6: added e5) |
(Added "see also", and some copy-editing.) |
||
| (34 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
| − | + | Edge template V1b is a 5th row edge template with 1 stone. | |
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2" | ||
/> | /> | ||
| − | + | 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 [https://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=669 Little Golem thread], but likely predates that post. | |
| − | |||
| − | |||
== Defense against intrusions == | == Defense against intrusions == | ||
| − | Red has 3 main | + | === Reduction === |
| + | |||
| + | Red has 3 main threats. Using the [[ziggurat]]: | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 E *:d4 S d4 d3 e3 c4 S b5 c5 d5 a6 b6 c6 d6" | ||
/> | /> | ||
| − | + | Using [[edge template III1b]]: | |
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 E *:d4 S d3 e3 c4 d4 e4 b5 c5 d5 e5 a6 b6 d6 e6" | ||
/> | /> | ||
| − | using [[ | + | And using [[edge_template_IV1d]]: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 E *:f3 S area(e3,c6,k6,k4,i2,f2)" | ||
/> | /> | ||
| − | + | For a blocking attempt, Blue [[mustplay region|must play]] in the overlap: | |
| − | + | ||
| − | For a blocking attempt, Blue | + | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 E a:e3 E b:d5 E c:d6 S e3 d5 d6" | ||
/> | /> | ||
| − | + | === Intrusion at a === | |
| + | If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B 1:e3 R 2:d3 B 3:c5 R 4:d4 B 5:d5" | ||
/> | /> | ||
| − | + | or like this: | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B 1:e3 R 2:d3 B 3:d4 R 4:c4 B 5:b6 R 6:c5 B 7:c6 R 8:d5 B 9:d6" | ||
/> | /> | ||
| − | + | 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: | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B 1:d5 R 2:d4 B 3:e3 R 4:d3 B 5:c5" | ||
/> | /> | ||
| − | + | 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: | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B 1:d6 R 2:d4 B 3:e3 R 4:d3 B 5:c5 R 6:d5 B 7:c6" | ||
/> | /> | ||
| − | + | 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. | |
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3" | ||
/> | /> | ||
| − | ' | + | Now Red is connected by [[Tom's move for 3rd and 5th row parallel ladders]]. |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| + | === Continuation after 2nd row ladder === | ||
| − | + | If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows. | |
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R 1:e5 B 2:e6 R 3:h4" | ||
/> | /> | ||
| − | |||
| − | ' | + | Now Red connects in essentially the same way as [[Tom's move]]. |
| − | + | Specifically, Red has these threats: | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:g5 B 4:g6 R 5:i5 S area(f5,f6,i6,i4,h4)" | ||
/> | /> | ||
| − | |||
| − | |||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:f5 B 2:f6 R 3:h5 S area(f5,f6,h6,h4,g4)" | ||
/> | /> | ||
| − | |||
| − | |||
| − | |||
| − | |||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 1:g3 S area(f2,f3,g4,f6,i6,i4,g2)" | ||
/> | /> | ||
| − | + | The overlap in which Blue [[mustplay region|must play]] is: | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 S area(f6,h6,h4)" | ||
/> | /> | ||
| − | + | 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 +: | |
| − | + | ||
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 2:g5 B 3:f5 R 4:g3 B 5:f4 R 6:f2 E +:h5 E +:f6 E +:g6 E +:h6" | ||
/> | /> | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | + | 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: | |
<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
| − | contents=" | + | edges="bottom" |
| + | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| + | contents="R e2 B e3 R d3 B d4 R c4 B b6 R c5 B c6 R d5 B d6 R e5 B e6 R h4 R 10:f3 R 8:g3 R 4:i3 B 9:f4 B 5:g4 R 2:f5 B 1:g5 B 3:f6 R 6:h2 B 7:g2" | ||
/> | /> | ||
| − | + | Note that Red 4 connects to the bottom with [[Edge_template_IV2b|IV-2-b]]. | |
| − | + | == See also == | |
| − | + | * [[Tom's move]] | |
| − | + | * [[Tom's move for 3rd and 5th row parallel ladders]] | |
| − | + | * [[Fourth row edge templates]] | |
| − | + | ||
| − | |||
| − | |||
[[category:edge templates]] | [[category:edge templates]] | ||
Latest revision as of 20:44, 26 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 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.
Specifically, 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.
