The (i,j)-4 × 4-outflanking-stab game (OS game)

Let i, j, m, and n be positive integers such that m, n ≥ 2. An (i, j)- m×n-Outflanking-Stab game is played on an m×n board by two players: White and Black. Each player has n tokens, which can be moved like the rook in chess. White’s tokens are arranged in the 1st row, and Black’s tokens are arranged in the mth row. In each turn, White moves i times, and Black moves j times. There are two ways to capture oppenent’s tokens, which are outflanking and stab. A player loses if he cannot move any token, or his tokens are all captured. The game ends in a draw if there is no capture in the last max{i,12+3j} moves. In this thesis, we provide some strategies for the (i,j)-4×4-OS game.