Neither Winning, Nor Losing

My young students this week are seeing this position from an online game played a couple of days ago.

White to move

White has many ways to win this game with overwhelming material superiority, but Black's last move, 40...Rf8, presents White with a problem. A student's immediate suggestion of 41.Nf7+ is good enough to move towards checkmate. 41.Ng4 or 41.Rf7 leads to a shorter forced checkmate sequence.

In the game, White played 41.d6?? oblivious to the purpose behind Black's last move. The game was soon drawn by repetition: 41...Rf1+ 42.Kg2 Rf2+ 43.Kg3 Rf3+ 44.Kg2 Rf2+ 45.Kh3 Rf3+ 46.Kg4 Rf4+ 47.Kg3 Rf3+ 48.Kg2 Rf2+

Taking the rook at any point leaves Black in stalemate.

The second position arose in the Spokane Chess Club's Fall Championship 20 years ago. 

White to move

Again, White has an overwhelming advantage. The simple 54.Rc6 would end things quickly.

My opponent played 54.h7??

After 54...Rxb7 55.Rd6 Rg7+ 56.Kh6 Rxh7+ 57.Kg6 Rg7+ we agreed to a draw.