The second player can always win, but to ensure his doing so he must
always place his rook, at the start and on every subsequent move, on the
same diagonal as his opponent's rook. He can then force his opponent
into a corner and win. Supposing the diagram to represent the positions
of the rooks at the start, then, if Black played first, White might have
placed his rook at A and won next move. Any square on that diagonal from
A to H will win, but the best play is always to restrict the moves of
the opposing rook as much as possible. If White played first, then Black
should have placed his rook at B (F would not be so good, as it gives
White more scope); then if White goes to C, Black moves to D; White to
E, Black to F; White to G, Black to C; White to H, Black to I; and Black
must win next move. If at any time Black had failed to move on to the
same diagonal as White, then White could take Black's diagonal and win.
r: black rook
R: white rook
+-+-+-+-+-+-+-+-+
|r| | | | | | | |
+-+-+-+-+-+-+-+-+
| |A| | | | | | |
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
| | | | | | | | |
+-+-+-+-+-+-+-+-+
| | | | |B|D|F| |
+-+-+-+-+-+-+-+-+
| | | | | |R|C|E|
+-+-+-+-+-+-+-+-+
| | | | | | |I|G|
+-+-+-+-+-+-+-+-+
| | | | | | | |H|
+-+-+-+-+-+-+-+-+