MazeWorks - Hex: Basic Strategy II



Hex: Basic Strategy II

Put up in a place
where it's easy to see
the cryptic admonishment
T.T.T.

When you feel how depressingly
slowly you climb,
it's well to remember that
Things Take Time.

About Hex

The Inventors

Basic Strategy I

3 Problems

Applying the basic strategy to a larger board, it is clear that if White opens on the center hex b2 of a 3x3 board, she can force a win.

the center opening
This move creates two bridges at once, one to the upper right edge (a1/b1) and one to the lower left edge (b3/c3). Black cannot stop either connection from being made, and White will win on her third move.

In fact, the situation on the 3x3 board is identical that of the 2x2 board: if White opens anywhere on the main diagonal (hexes a1, b2, or c3) she can force a win. It is also true once again that if White opens on an acute corner (a3 or c1), Black can force a win:

an acute opening
Black wins by responding with a move to the center hex, creating bridges a1/a2 and c2/c3. Black is now guaranteed to be able to create a chain from the lower right to upper left edges, winning on his third move.

Finally, a 4x4 example: White opens on the main diagonal, at b2. Black responds with a defensive move at c4. This response blocks White from playing c4 (forcing a win), and defends against the winning moves b3 and c3. The simplest 4x4 win

A 4x4 win for White
It's a good move for Black, but White can still win by playing a3. Now White has three bridges in the chain: a1/b1 from the upper right edge, a2/b3 between the two White pieces, and a4/b4 to the lower left edge. White can thus ensure a connection all the way across the board, and will win on her fifth move.