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

To do.

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.