Treblecross

Treblecross is a two-player abstract strategy game classified as a degenerate variant of tic-tac-toe and, in combinatorial game theory terms, as an octal game. It is played on a one-dimensional board, a single row of squares, starting empty. Unlike ordinary tic-tac-toe, both players place the same kind of piece, typically an X or a black chip, rather than each having their own mark, and they alternate turns filling any unoccupied square. The first player to complete a run of three pieces in a row, anywhere along the line, wins the game. Because it reduces tic-tac-toe to one dimension, Treblecross has been studied as a simple test case in combinatorial game theory; it is discussed alongside other octal games in Berlekamp, Conway and Guy's Winning Ways for Your Mathematical Plays, and it appears in game theory teaching material as an accessible example of an impartial combinatorial game with a fully worked out theory of winning and losing positions.