There are the finite number of obtainable positions in a board game. Players can make the single legal move on their turn. Legal moves change the board's position. If there is the legal move which changes the position from P to P', then it is the only move that does this and there is also a legal move that changes the board's position from P' to P. There exists a sequence of at least three moves from the beginning of the game beginning with move M that does not repeat a position until returning to the original position. Prove that preventing the first player from making move M on his or her first turn does not change the set of obtainable positions that might be achieved during the game.