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Breakthrough is an abstract strategy board game invented by 2001 8x8 Game Design Competition, even though the game is trivially extendable to larger board sizes. It has some similarity to checkers, but the strategy is completely different.
The board is initially set up as follows, with number signs representing black pieces, zeroes representing white pieces, and periods representing empty squares:
To play the game on a different-sized board, just fill the front two and back two rows with pieces; the board need not be square.
Choose a player to go first; play then alternates, with each player moving one piece per turn.
The rules are as follows:
The black piece can move into the squares marked a, b, and c.
If White had pieces in the squares marked A, b, and C, the black piece could capture either A or C; it would replace them if it chose to capture. Note that capturing is not compulsory, nor is it "chained" as in Checkers.
The first player to reach the opponent's home row — the one farthest from the player — is the winner.
Handscomb, Kerry. "8x8 Game Design Competition: The Winning Game: Breakthrough ...and two other favorites." Abstract Games Magazine, Issue 7, Autumn 2001. "Breakthrough." http://www.gamerz.net/~pbmserv/breakthrough.html
Breakthrough can be played by email, using Richard Rognlie's Play-By-eMail Server.