Hex is a popular game with some interesting mathematical properties. John Nash gave an easy proof that the first player can force a win, his famous "stealing strategies" argument. His proof gives no indication as to how what the optimal strategy actually looks like.
There is also a nice AMM paper by David Gale in which he shows that the fact that Hex can not end in a draw is equivalent to the Brouwer fixed point theorem (for higher dimensions, one needs a higher dimensional version of Hex).
One variant is called Y. Both players attempt to create a group connecting all sides of a triangular board. As with Hex, there are no ties possible. A commercial version adds 3 points of positive curvature, with 5 neighbors instead of 6.
