A Rook Endgame

Yeah, actually, pushing the passed pawn is a mistake.  If White doesn't improve the position of his king before advancing the pawn, he throws away the win.

White wins w/o difficulty, with 1.Rc7+, 2.Rc5, and 3.Kc6, followed by pushing the pawn.

This is not correct. (This time I looked it up in a tablebase to be sure.)

1. Rc7+ Kc8 2. Rc5 allows black to draw 2. ... Rh2 3. Kc6 (as suggested) Rh6

I think this is called Philidor's defense when you have the king cut off from the 6th rank.

tony, I get into a longwinded discussion, because I won't have the tablebase OTB and it's good practice for me to figure out how to calculate a win in this position. If I can get someone to explain their thinking to me in a particular line, I can learn something.

Sometimes I look something up in a tablebase and the moves look like magic.

Incidentaly, if we shift all the pieces two lines to the right then the position with a central pawn becomes drawn.

One of the great difficulties of these endings for me is that this kind of "little" differences often chance the result and over the board it's alwayss difficult to remember which positions are won and which not. You cannot really use any general principles here as often the central pawns are easier to promote in rook endings.

Rook endings are trick sometimes... try searching up the Lucena position or the Philidor position. I find them useful sometimes.