Multi-player End-Nim games

W. O. Krawec (2012) [17] introduced a method of analyzing multi-player impartial games, and derived a recursive function capable of determining which of the n players has a winning strategy. The present paper is devoted to “Multi-player End-Nim games”, abbreviated by ENim( N, n ), assuming that the standard alliance matrix is adopted. The game values of ENim( N, n ) are completely determined for three cases n > N + 1, n = N + 1 and n = N. For the case n < N, by letting d = N − n ≥ 1, the game values of ENim( n + d, n ) are completely determined if n ≥ d + 4. The case 3 ≤ n ≤ d + 3 is more complicated, we present the game values for d = 1.

Authors

• Wen An Liu
• Tao Wu

Keywords

• Multi-player impartial game
• End-Nim
• Alliance matrix