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Encyclopedia > Black Path Game

The Black Path Game (also known by various other names, such as Brick) is a two-player board game described and analysed in Winning Ways for your Mathematical Plays. It was invented by Larry Black in 1960.


Rules

The Black Path Game is played on a board ruled into squares. Any square that is not empty is filled with one of the following configurations:

 +-------+ +-------+ +-------+ | / | |   | | | | | / | |   | | | | |-' ,-| |-. `-| |---+---| | / | |   | | | | | / | |   | | | | +-------+ +-------+ +-------+ 

These tiles are the three ways to join the sides of the square in pairs. The first two are the tiles of the Truchet tiling. One edge on the boundary of the board is designated to be the start of the path. The players alternate filling the square just after the end of the current path with one of the three configrations above, extending the path. The path may return to a previously filled square and follow the yet-unused segment on that square. The player who first causes the path to run back into the edge of the board loses the game.


to do: add some images of game positions


Strategy

The first player has a winning strategy on any rectangular board with at least one side-length even. Imagine the board covered with dominoes. The first player should always play so that the end of the path falls on the middle of one of the dominoes. If both sides of the board are odd, the second player can instead win by using a domino tiling including every square but the one containing the first player's first move.


  Results from FactBites:
 
file_nav_name Encyclopedia Index (8075 words)
Game development is the process by which a game is produced.
Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions...
An extensive form game is a specification of a game in game theory.
Black Hands-On - PlayStation 2 News at GameSpot (1026 words)
Black is as much fun to watch as it is to play, and that fact owes in part to the broad interactivity of the levels--or at least, the one we've seen so far.
Beyond the hardcore shooting, the mechanics in the Black demo were totally straightforward--kill all the enemies in your path, and progress through to the end of the level.
Black is scheduled for release on the PS2 and Xbox early in 2006, and we'll bring you more on the game, hopefully including some video, in the coming months.
  More results at FactBites »


 
 

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