Rook Endgames

Today I'm the proud owner of a loss from a "dead drawn" Rook+3 vs Rook+2 with all pawns on one side endgame. As I don't want to be such an owner again, I have decided to investigate the details of drawing this endgame all the way down to the possible Rook+1 vs Rook positions. Actually I think I played the position correctly for quite a while but that's clearly not good enough. So here's the theory:
Quite amazingly I lost as White in this position.
This just goes to show that chess is not easy. It's hard to get a sense of how to continue this type of position for 20 moves or more from grandmaster games because ( except for Carlsen! ) GMs generally take a draw here.
I'm going to play this out vs a computer until I can convincingly hold the draw here as practice. I will post the result when I have it.

Now here's how I should have played that:

While I'm on the topic I'm going to investigate some of the key drawing ( and winning ) ideas in the Rook+1 vs Rook ending as well. As GM Melik Khatchiyan points out in his excellent rook endgame video set on chess.com, it's not enough to know the theory in these positions. It is important to actually play out the positions to get practice vs a computer or a training partner.

This position happened during the game. I don't have all the moves to the ending but I found myself in this marginal situation after trying to play too actively. This is clearly the wrong strategy in an inferior rook ending of this type. As it turns out, this position is still a draw with correct play. I almost worked out the key idea but not quite and I lost.

Here are some interesting theoretical rook and pawn positions with some typical lines