Category Archives: Three Player NIM

Three Player Nim

In the game of Nim, several piles of sticks are placed on a table.  Two players take turns removing sticks from the piles. On each turn, a player must remove at least one stick, and may remove any number of sticks provided they all come from the same piles.  The first player without a stick to remove loses.  We will consider 3-player Nim.  Three players, A, B, and C, rotate turns in playing Nim.  The first player without a move loses. The goal for each player is, naturally, to avoid losing and each would prefer to make the last move, if possible.  Develop a theory of 3-person Nim and generalize your results.