Edge template V1b

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:

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

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 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 b, then Red

to be completed

Intrusion at x

Red can respond here:

Continuation:

Red has several threats. Via double threats:

Via double threat and edge template III2b:

Via bridges and Tom's move:

Via a wheel and Tom's move:

Via a double threat and Tom's move:

Via a different double threat and Tom's move:

Blue must play in the overlap:

If Blue plays at r:

And then, depending on Blue's next move, either a crescent

or Tom's move:

If Blue plays at t:

If Blue plays at b or c, Red plays at a and connects via Tom's move. If Blue plays at a:

Now Red is connected left by double threat, and right by a clipped version of edge template V2m.

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.