Defending against intrusions in template VI2

From HexWiki
Jump to: navigation, search

The edge template template VI2


abcdefghij123456

Let us first see what possibilities Red has if he moves first.

There are two obvious options:



In both diagrams the possible intrusion points are marked by (+). So we only have to consider the intersection of the intrusion points. They are:


Intrusion at E5 and F5

If Blue blocks at E5 then Red plays F3, reducing to Template IVb


abcdefghij12345621

Likewise if blue blocks at F5:


abcdefghij12345621

Intrusion at E6


abcdefghij12345621

Red threatens to connect via D4. Blue must respond in one of the marked hexes.


abcdefghij1234562341

The H4 piece is connected to the bottom with template III-1-a, and is connected to the top in two non-overlapping ways:


abcdefghij1234562341

and


abcdefghij1234562341

Intrusion at F4


abcdefghij12345621

The Red piece at D4 is connected to the bottom. Blue has two direct attempts to block:

Block at F2


abcdefghij1234561324

Red is now connected to the bottom via template III-1-a. Note that neither of Red's threats overlapped.

Block at E3


abcdefghij1234561243

The Red piece at H3 is connected to the top and threatening to connect to the bottom. Blue has one defense:


abcdefghij123456218649753

And now Red has connected. Attempts by Blue to block the use of the D4 piece as a ladder escape can be shown to not work.

Intrusion at G2


abcdefghij12345621

Blue has four options that don't immediately reduce to another edge template:

Block at E4


abcdefghij12345621

Red's G3 piece is connected to the top via F3 or H2.


abcdefghij1234562143

Here Red has created a Ladder escape fork. If Blue blocks the ladder Red plays at D3.

Block at D5


abcdefghij123456625413

And Red has connected. If blue choose to play at E6 instead of E5:


abcdefghij12345687625431

Block at C6


abcdefghij123456625431

Block at E6


abcdefghij123456234651

Play continues...


abcdefghij1234564321

Intrusion at D6 or F6

The D6 case is shown here, but Red's responses work symmetrically for the F6 case.


abcdefghij12345621

Red's F5 piece is connected to the bottom. To prevent its connection to the top, Blue must move in one of the marked tiles.

Block at F4


abcdefghij12345634561287

Or, if for move three Blue played G3:


abcdefghij123456213456897

And Red is connected. Note that this method does not require the three right-most tiles. This means that this method can be used by Red in the symmetrical case of Blue intruding at F6.

Block at G2


abcdefghij12345612465387

Note that Red's F3 piece is connected via the two marked tiles. If Blue had played G3 for move three:


abcdefghij123456123456

And Red connects via template III-1-a.

Block at H2, G3, or G4

Red's responses are similar in all three cases:


abcdefghij123456124365

abcdefghij123456214365

abcdefghij123456243165

Intrusion at C6 or G6

The G6 case is shown here, but Red's responses work symmetrically for the C6 case.


abcdefghij12345621

Red's F4 piece is connected to the bottom via template III-1-a. The only move preventing the F4 piece from connecting to the top is G2. Intrusions into the template are met by Red with parallel moves which maintain the connection to the bottom while guaranteeing a connection to the top. F5, F6 and E5 are met by E4 while E4, E6, D5, D6 and C6 are met by G4, connecting Red to both the top and the bottom.

Block at G2


abcdefghij123456123456

And Red cannot be stopped, the F4 piece being a valid ladder escape. If Blue had played E6 for move five:


abcdefghij12345612346857

And if Blue had played F5 for move five:


abcdefghij123456123465

Red threatens to connect in two non-overlapping ways, while the E4 piece is connected with template III-1-a.