Poly-Y is a two-player abstract strategy game. The two players, blue and red, take turns filling in hexes on a pentagonal board. A player captures a corner if there is a path of that player's color touching both sides adjacent to the corner as well as any third side. (A corner hex counts as touching both adjacent sides.) The goal is to capture a majority of the corners.
It is actually possible to prove that the first player can always win with optimal moves. To balance the two sides, it is customary to play with the swap rule: the first player plays an initial move, then the second player gets a one-time chance to swap sides.