[FEN "rnbqkbnr/p7/Pp1p1p1p/1PpPpPpP/2P1P1P1/8/8/RNBQKBNR w KQkq - 0 1"]
If black were to just shuffle the rook between h8 and h7 until white makes a capture or puts a piece on a square defended by a pawn, can white win (assuming black plays the all best moves after white tries something)? The only way white can win is by sacrificing material, but on the other hand white does have a large spatial advantage and can make any setup they want.
The first case I'm wondering about is if white knows black's plan to just shuffle until white tries something. I feel like this case is probably winnable. The other case is if white just plays 'optimal' moves and assumes black will totoo, which is harder to proveprobably a draw.