Draw

One of the beautiful properties of Hex is that the game can never end in a draw, i.e., there is always a winner.

There are various ways of proving this, for example:

• A proof by David Gale that used the fact that exactly three hexes meet at every vertex.
• An elegant proof using the game of Y.
• Another proof using the game of Y.

In fact, David Gale showed that the no-draw property is equivalent to the 2-dimensional case of Brouwer's fixed point theorem (a non-trivial theorem from topology saying that any continuous map from the unit square into itself must have a fixed point).

In 2006, Yasuhito Tanaka proved another equivalence involving Hex. The no-draw property is equivalent to the Arrow impossibility theorem. dissertation help