Copyright (c) 1950s Martin Gardner
This game is played on an empty 8x8 square board:
Two initial moves. Notice that the game can be played with just one color.
Martin Gardner presented this game at the Scientific American magazine (#230, Feb. 1974, 106-108), showing a symmetric (of both axis) winning strategy for the 2nd player on boards with even dimensions. One can change the board size (both sizes should be odd) and/or add a PIE rule (stating that one player makes 3 drops and the other choose sides) in order to play the game with no known winning strategy.
There is a variant called Crosscram (or Domineering) where one player only drops vertically and the opponent horizontally. There is a ZRF to play Crosscram with Zillions.