Activity vs Material in the Rook Endgame

Apr 12, 2016, 3:52 AM |
I've heard the maxim many times; in rook endgames, activity counts more than material. It makes sense; activity leads to tactics, and tactics can gobble up material, help in queening, and in this game, lead to checkmate.
My opponent here had a choice between activating his king, who is currently stuck in the corner, and gobbling up my isolated pawns. He saw the chance to create passed pawns, and played Rc3, eyeing c6 and a6 greedily. I ignored him and played Kg5. Rxc6 was followed by Kf4 and at this point, he should really have seen the threat.
He didn't see the threat, and played Rxa6?? which leaves him a pawn up, but about to be checkmated. With the obvious Kg3, my active king and rook are ganging up on his cornered king, and no matter what he plays, Re1# is coming. 
So that was eye-opening for me; it was an abrupt end to what I had first thought would be a protracted endgame. Good illustration of the dominance of active pieces over material advantages in such endgames.