View source for Edge template IV2l

''This page is about edge template IV2l (four two ell). There is also an [[edge template IV2i]] (four two eye).''

The template:

<hexboard size="4x6"
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3"
   />

(From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk])   

== Choosing which stone to connect ==

Red is guaranteed to be able to connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two to connect (see below). But it is easier to analyze the template if we assume Red chooses one of the two stones to connect to the bottom. Here, we assume that Red wants to connect the stone on the right-hand side to the bottom.

Red has three threats. The first one uses bridges.

<hexboard size="4x6"
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E +:e2 E +:f2 E *:a3 R 1:e3 E +:d4 E +:e4"
   />

The second one uses template [[Defending_against_intrusions_in_template_1-IIIb|II-1-b]].

<hexboard size="4x6"
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E +:d2 R 1:e2 E +:f2 E *:a3 E +:c3 E +:d3 E +:e3 E +:f3 E +:b4 E +:c4 E +:e4 E +:f4"
   />

The third one uses the [[ziggurat]].

<hexboard size="4x6"
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 R d1 E +:e1 R f1 E *:a2 E *:b2 E +:c2 R 1:d2 E +:e2 E *:a3 E +:b3 E +:c3 E +:d3 E +:a4 E +:b4 E +:c4 E +:d4"
   />


For a blocking attempt, Blue has to play on the only overlapping field:

<hexboard size="4x6"
   coords="hide"
   contents="E *:a1 E *:b1 E *:c1 R d1 E +:e1 R f1 E *:a2 E *:b2 B 1:e2 R 2:f2 E *:a3 R 6:c3 E +:d3 R 4:e3 B 5:d4 B 3:e4"
   />

Red 6 is connected to the bottom and can be connected to the top right by one of the fields marked with +. 

== Connecting both stones ==

To show that Red can, in fact, connect both stones to the bottom, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line).

If Blue plays in any of the cells marked "+", Red responds at d2 and is connected by a [[ziggurat]].

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:f2 +:f3 +:f4 +:e3 +:e4 R 2:d2"
   />

If Blue plays 1.e1, Red responds with 2.d3 and is connected by two copies of [[edge template IV2d]]:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e1 R 2:d3"
   />

If Blue plays 1.e2, Red responds with 2.f2:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e2 R 2:f2"
   />

If Blue now plays 3.e4, the game proceeds as shown above. If Blue plays 3.e1, Red responds with 4.c3. In all other cases, Red responds with 4.e1.

If Blue plays 1.d3, Red responds with 2.e1 and is connected via [[edge template IV2a]]:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:e3 R 2:e1"
   />

If Blue plays 1.d4, Red responds with 2.e1:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1"
   />

Now if Blue plays outside the area marked "+" in the next figure, Red connects with c3:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1 E +:b4 +:c2 +:c3 +:c4 +:d2"
   />

If Blue plays outside the area marked "+" in the next figure, Red proceeds as in defending [[edge template IV2a]] (since Blue only has one stone in the template ''and it is Red's turn''):

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B 1:d4 R 2:e1 E +:c4 +:d2 +:d3 +:e2 +:e3 +:e4 +:f2 +:f3 +:f4"
   />

That leaves only two possible plays for Blue, at d2 and c4. They are easily dealt with:

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B d4 R e1 B 3:d2 R 4:c3 B 5:c2 R 6:e3"
   />

<hexboard size="4x6"
   coords="show"
   contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 B d4 R e1 B 3:c4 R 4:b3 B 5:c2 R 6:f3 B 7:f2 R 8:d3"
   />

== See also ==

[[category:edge templates]]