The (i,j)-4 Γ 4-Outflanking-Stab Game (OS game)

Let π,π,π, and π be positive integers such that π,π β₯ 2. An (π,π)βπ Γ πβOutflanking-Stab game is played on an π Γ π board by two players: White (the first player) and Black (the second player). Each player has π tokens, which can be moved like the rook in chess. White gets π moves per turn, and Black gets π moves per turn. There are two ways to capture oppenentβs tokens, which are outflanking and stab. A player wins when he makes the opponent cannot move any token or all opponentβs tokens are captured. In this paper, we prove that for the (π,π)β4 Γ 4βOS game, White has a winning strategy if π β₯ 4, or π β 1 and π = 1 while Black has a winning strategy if π = 1 and π β₯ 2. Keywords - Makneeb, OS Game, Checkers, Chess, Board Game, Multimove.