Row Shifting as a Puzzle Mechanic in Generalized Connect Four

Connect Four is a well-studied two-player game for fixed board sizes, however, the complexity of the generalized game is still open. Here, we look at a variant of Connect Four that allows for row shifting. Shift-Tac-Toe is a two-player game similar to Connect Four with the goal of getting 3-in-a-row to win. What makes the game unique is that each row is connected and can be shifted left or right, which causes pieces to fall into a neighboring column or to be removed from the board. Here, we show that the standard $3 \times 3$ game is a first player win and provide a perfect game-tree AI, and then we look at a generalized version of the game. We show that as a one-player puzzle, knowing whether n- in-a-row can be achieved with only shift moves is NP-complete. We also provide an implementation of the game allowing for arbitrary board size, shift size, and number of players.