A bishop and a rook, of opposing colors, start on opposite corners on the same side of a chessboard, oriented as in the following picture:
They then proceed to play a game of cat-and-mouse.
- The pieces make a move based on the rules of chess, meaning that the bishop travels along the diagonal while the rook travels along the parallels.
- When a square is moved across, it becomes uninhabitable and can no longer be moved across.
- The bishop always goes first.
- If a piece is either a) captured, or b) does not move on its turn, whether by choice or because there are no valid moves left, that piece loses.
Based on these rules and assuming optimal play, which piece is crowned the victor?
Bonus Question 1: The same rules apply, except now a tile only becomes uninhabitable when a piece finishes its move on that tile. Still assuming optimal play, which piece wins this variation?
Bonus Question 2: If the bishop starts in the top lefthand corner instead of the bottom lefthand corner, and the rook is now allowed to go first, which piece is crowned the victor? (Answer this question for both variations of uninhabitable squares.)
Note: The open-ended tag is included because there is ambiguity associated with the restriction of "optimal play". A perfect answer will not only detail the victory condition of the winning piece, but also detail why the plays made can be considered "optimal" for each piece.