Difference between revisions of "Edge template V1b"
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If Blue plays one of the five upper-right of those cells | If Blue plays one of the five upper-right of those cells | ||
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<hexboard size="6x14" | <hexboard size="6x14" | ||
coords="hide" | coords="hide" | ||
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contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S blue:(f3 f2 g2 g4 f4)" | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S blue:(f3 f2 g2 g4 f4)" | ||
/> | /> | ||
| − | + | then Red still connects via [[Tom's move]], | |
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
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since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group. | since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group. | ||
| − | This leaves only two | + | This leaves only two remaining tries for Blue: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5" | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5" | ||
/> | /> | ||
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If Blue plays the right of those two, | If Blue plays the right of those two, | ||
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Now, it does not matter which of the two shaded cells Blue 2 is at, since | Now, it does not matter which of the two shaded cells Blue 2 is at, since | ||
| − | * if Blue plays the other too then the order in which they were played doesn't matter | + | * if Blue plays the other too then the order in which they were played doesn't matter, and |
| − | + | * if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]]. | |
| − | * if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]] | + | |
| − | + | So this is equivalent to Red having a [[Theorems_about_templates#Corner_clipping|clipped]] version of [[Edge template IV1d]]. | |
In particular, Red is connected down. | In particular, Red is connected down. | ||
Revision as of 12:40, 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:
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 w
Red responds with
Continuation:
We will assume that Red simply defends the pink ziggurat, and therefore we will not need to consider any Blue intrusions there.
Red's main threats are
and
Blue must play in the overlap:
If Blue plays at a, then Red plays 5, after which Red connects via
or
If Blue plays at b, then Red plays 5, after which Red connects via
or
If Blue plays at c, then Red responds with
This forces Blue to defend towards the top, after which
connects directly or via red 1.
If Blue plays at d or e, then Red plays like this:
If Blue plays at f, then Red plays like this:
Now Red threatens to play in one of the cells marked "*", and the only overlap (apart from the two captured cells below 5) is at "+", so Blue must play there. Then Red responds like this:
Now Red is connected left by double threats "*" and right by double threats "+".
Intrusion at x
Red can respond here:
Continuation:
Red's main threat is as follows,
connecting back via one of the cells marked "*".
If Blue plays either of the two of those cells adjacent to the edge, then Red plays the
same move anyway, connecting down via the other of those two cells or Tom's move.
If Blue plays one of the five upper-right of those cells
then Red still connects via Tom's move,
since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group.
This leaves only two remaining tries for Blue:
If Blue plays the right of those two,
then Red connects via double threat.
Thus Blue instead plays the left of those two. Red responds as follows.
Now, it does not matter which of the two shaded cells Blue 2 is at, since
- if Blue plays the other too then the order in which they were played doesn't matter, and
- if instead Red plays the other, then whichever one Blue played will be dead.
So this is equivalent to Red having a clipped version of Edge template IV1d.
In particular, Red is connected down.
Intrusion at v or y or z
If Blue plays one of the three highlighted cells, then Red responds as shown below.
This captures the two cells marked "*", forcing Blue 4, and then Red 5
connects by double threat or edge template IV2e or 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.
