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Endgame shots

My opponent played b4 - both of us calculated that White cannot win the g pawn without giving up the h one. Is this correct?

first_shot

I suppose being better versed in K+R vs K+N would have alerted us to the possibility of the knight getting dominated: 1. Rxg7! Rxg7 2. Rxg7 Nf4+ 3. Ke3 Nxh5 4. Rg5 +-

There is another theme in the position, whereby white can break through on the kingside. I ended up playing it at the wrong moment and losing the game but this was the time for it:

second_shot

1. Rd2 Rxd2+ 2. Kxd2 Nf5 3. Rxg7! Taking the rook leaves the h pawn unstoppable)