An Analysis of a New Partizan Game Using Combinatorial Techniques

John Horton Conway\u27s combinatorial game theory was applied to a new partizan game with a complete analysis as the result. Mathematical values were assigned to the countably infinite number of positions in the game. Direct computation of the first eight values and extension via the Principle of Mathematical Induction made the assignments possible. Examination of these values (which repeat with period 2) shows that the game, played on a strip of squares, can be won by the first player if the strip is of odd length and can be won by the second player if the strip is of even length. Further examination of the values leads to a completely general symmetry strategy for the first and second player wins in the appropriate cases