L game

The L Game was invented by Edward DeBono to illustrate lateral thinking. It violates a number of classic assumptions concerning board games, to make a board game with very few pieces that remains interesting to play.

L game starting position

The game is played on a 4x4 board. Each player has an L-shaped piece, three spaces long and two wide. There are two 1x1 neutral pieces. The pieces are initially placed with the angle of each L on a central square, and each neutral piece in the crook of an L. On each move, a player must move first his L piece, and then may move a single neutral piece. The loser is the first player unable to move his L piece to a new position.

In a game with two perfect players, neither will ever win or lose, unless one thinks of something better to do, and loses on purpose.

One basic strategy is to use a neutral piece and one's own piece to block a 3x3 square in one corner, and use a neutral piece to prevent the opponent's L piece from swapping to a mirror-image position. Another basic strategy is to move an L piece to block a half of the board, and use the neutral pieces to prevent the opponent's possible alternate positions.

These position can often be achieved once a neutral piece is left in one of the eight killer spaces on the perimeter of the board. The killer spaces are the spaces on the perimeter, but not in a corner. On the next move, one either makes the previously placed killer a part of one's square, or uses it to block a perimeter position, and makes a square or half-board block with one's own L and a moved neutral piece.

One of the problems with the game is that defensive play can continue indefinitely if the players are too cautious to move a neutral piece to the killer positions. If both players are at this level, a sudden-death variant of the rules permits one to move both neutral pieces after moving. A player who can look three moves ahead can defeat defensive play using the standard rules.

All possible final positions

All positions, red to move, where red will lose to a perfect blue, and maximum number of moves remaining for red.

By looking ahead one move and ensuring one never ends up in any of the above positions, one can avoid losing.

There are 2296 different possible valid ways the pieces can be arranged, not counting a rotation or mirror of an arrangement as a new arrangement, and considering the two neutral pieces to be identical. Any arrangement can be reached during the game, with it being any player's turn. Each player has lost in 15 of these arrangements, if it is that player's turn. The losing arrangements involve the losing player's l-piece touching a corner. Each player will also soon lose to a perfect player in an additional 14 arrangements. A player will be able to at least force a draw (by playing forever without losing) from the remaining 2267 positions.

The author has seen no commercial versions. One of the best ways to make a board is to use a corner of a chessboard. Pawns are used as neutral pieces. Stiff wire (e.g. from a coat-hanger) is used to construct the L pieces and an angle to mark two sides of the board.