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 (the first player) and Black (the second player). Each player has 𝑛 tokens, which can be moved like the rook in chess. White gets 𝑖 moves per turn, and Black gets 𝑗 moves per turn. There are two ways to capture oppenent’s tokens, which are outflanking and stab. A player wins when he makes the opponent cannot move any token or all opponent’s tokens are captured. In this paper, we prove that for the (𝑖,𝑗)−4 × 4−OS game, White has a winning strategy if 𝑖 ≥ 4, or 𝑖 ≠ 1 and 𝑗 = 1 while Black has a winning strategy if 𝑖 = 1 and 𝑗 ≥ 2. Keywords - Makneeb, OS Game, Checkers, Chess, Board Game, Multimove.