3-Spot
The Board
3-Spot is played on a three-row, three-column grid. The bottom three squares, each marked with a spot, are point squares.
The Pieces
There are three rectangular pieces that each can cover a 1-by-2 area of the board. The first player controls the blue piece. The second player controls the red piece. Both players control the white (neutral) piece. The pieces are initially arranged on the board as follows:
Rules
To move: Move your colored piece (i.e., the blue piece or red piece, whichever you control) so that it covers a 1-by-2 area of the board such that at least one of the squares covered by your colored piece was not covered by it immediately before you moved it. Count the number of point squares covered by your colored piece, and add that number to your score. Then, move the white piece such that it coveres a 1-by-2 area of the board such that at least one of the squares covered by the white piece was not covered by it immediately before you moved it.
To win: Have fewer than 6 points while your opponent has at least 12 points, or have at least 12 points while your opponent has at least 6 points.
Both players' scores begin at 0. Point squares covered by the white piece do not count toward a player's score.
Suppose it is the first (blue) player's turn at the following example position:
The blue player first moves the blue piece. The blue player may decide, for example, to move the blue piece to reach the following state:
We count the number of point squares that the blue piece covers after the blue piece has moved. The blue piece covers one point square, so the blue player gains one point. The blue player must then move the white piece. The blue player may decide, for example, to move the white piece to reach the following position:
It is now the red player's turn.
Strategies
- General: Interesting strategies arise in this game because of the nature of the win condition. At certain points you may want to score as many points as you can, but at others you may want to force the opponent to score points while you seek to avoid scoring.
Variants
- Misere: Win by either (1) staying below 6 points and forcing your opponent to score at least 12 points or (2) scoring 12 points while keeping your opponent under 6 points.
- Optional Neutral Piece Move: A player may choose to not move the neutral piece after they move their colored piece.
- Point Squares: Any board square can be a point square.
- Point Winning Condition: The winning condition can be defined by an arbitrary function that assigns to each possible pair of the players' scores one of the following outcomes: (1) a win for the first player, (2) a win for the second player, or (3) not yet a win for either player.
Pictures
References
Edward De Bono. "The 3 Spot Game." Edward De Bono's Web. http://www.edwdebono.com/debono/3spot.htm.
GamesCrafters
Attila Gyulassy (Backend, Solving)
Cameron Cheung (GamesmanUni GUI)