Copyright (c) 1950s Martin Gardner

This game is played on an empty 8x8 square board:

TURNS - At each turn, each player must drop two orthogonal adjacent stones on two empty cells.
GOAL - Wins the player that makes the last move.
An opening example

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.