Difference between revisions of "Edge template V1b"

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m (Intrusion at v or y or z: small typo)
m (Intrusion at x: minor copy-edits)
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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
 
 
<hexboard size="6x14"
 
<hexboard size="6x14"
 
   coords="hide"
 
   coords="hide"
Line 375: Line 374:
 
   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]],
, ​ then Red still connects via [[Tom's move]],
+
  
 
<hexboard size="6x14"
 
<hexboard size="6x14"
Line 387: Line 385:
 
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"
Line 395: Line 393:
 
   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"
 
   />
 
   />
 
remaining tries for Blue.
 
  
 
If Blue plays the right of those two,
 
If Blue plays the right of those two,
Line 420: Line 416:
 
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
* 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]].
+
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.


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:

abc

Intrusion at a

If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this

21435

or like this:

214368579

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:

43251

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:

4325671

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.

1

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:

1

And via edge template IV2b:

1

Blue must play in the overlap:

pqr1stuvwxyz


Intrusion at p, q, r

22213

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.

22213957648

Intrusion at s

312

Red is connected by edge template IV1d.

Intrusion at t

51324

Now Red is connected by edge template V2m. If Blue plays 4 on the first row instead, Red connects by Tom's move:

132957648

Intrusion at u

1327546

Red is connected by Tom's move.

Intrusion at w

Red responds with

132

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

1532

and

5132

Blue must play in the overlap:

a1debf32c

If Blue plays at a, then Red plays 5, after which Red connects via

41573626

or

4111537928610

If Blue plays at b, then Red plays 5, after which Red connects via

7185493626

or

1115437928610

If Blue plays at c, then Red responds with

15324

This forces Blue to defend towards the top, after which

666157324

connects directly or via red 1.

666157839112104

If Blue plays at d or e, then Red plays like this:

7144689352

If Blue plays at f, then Red plays like this:

14352

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:

7164352

Now Red is connected left by double threats "*" and right by double threats "+".

Intrusion at x

Red can respond here:

132

Continuation:

Red's main threat is as follows,

1352

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

1352

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

132

then Red still connects via Tom's move,

15937628

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:

132

If Blue plays the right of those two,

15342

then Red connects via double threat.

Thus Blue instead plays the left of those two. ​ Red responds as follows.

5671432

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.

13

This captures the two cells marked "*", forcing Blue 4, and then Red 5

5143

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.

312

Now Red connects in essentially the same way as Tom's move.

Continuation:

Red has these threats:

13524
132
1

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 +:

64532

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:

76108495213

Note that Red 4 connects to the bottom with IV-2-b.