This is a sequel to Moving a Rook
The rules of the two rook game are as follows:
- Initially two rooks are placed on a chessboard with one rook in the bottom left corner and the other rook
on one of the two adjacent squares.
- A move consists of advancing either rook any positive number of squares either up or to the right, as
long as the move does not end on or pass through the other rook.
- The players take turns making moves until the two rooks occupy the upper right square and one of the two
- The player to make the last move wins.
Define a winning strategy for one of the two players in this game.
This seems like a win for the player who is not in the corner.
If he moves first, he can move to the corner in two moves. Since he has no more moves, and the 1st play still has some, Player 2 wins.
If he moves second and he starts above the 1st player, then the 1st player is forced to move right. The 2nd moves right, staying above the 1st player. When they reach the last column, the first player has no move and the 2nd can take the corner.
Similarly, if he moves second and he starts to the right of the 1st player, then the 1st player is forced to move up. The 2nd moves up, staying to the right of the 1st player. When they reach the last row, the first player has no move and the 2nd can take the corner.