6k1/1R5p/6p1/p7/8/7P/r5P1/6K1 w - a6 0 33
Is it possible for White to hold a draw in this position? If so, what is the strategy?
Typically I lose these ones and draw when it's me with the extra pawn...
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This should be a draw as far as I know and the first step is to get behind the pawn with your rook. Now if black pushes the pawn to the second rank it is an easy draw, because he can never move the rook without you taking the a-pawn and if he tries to protect the a-pawn with the king you will just give checks from behind.
8/R6p/6p1/8/8/1k5P/p5PK/r52 w - a6 0 33
In this position you just check with Rb8+ and go on checking until his king leaves the a-pawn. Then you go straight back to attacking the a-pawn otherwise Rh1+ wins for black.
So what he might try is pushing the pawn only to a3. Then he has a place on a2, to hide his kings from the checks. But now the problem for black is that he doesn't threaten to move his rook away and queen the pawn, therefore your rook isn't shackled to the a-pawn. That means as soon as his king leaves the kingside pawns, you just snatch them off with your rook.
8/8/R5p1/5k1p/7P/p5K1/6P1/r52 w - a6 0 33
Something like …Ke4 Rxg6 Kd4 Rg5 Kc3 Rxh5 Kb2 Ra5 ...
Given that his king has to run all the way to the a-line, then move the rook and make two pawn moves to queen the pawn, this should give you enough time to push your own kingside pawns. When you finally have to give your rook for the a-pawn, ideally your kingside pawns (supported by your king) are so far advanced that his rook cannot deal with them.
I would recommend reading Nunn's "Secrets of Rook and Pawn Endgames."
There is no simple answer to your question, because some positions are draws, others are wins. Also, skill makes a huge difference. A player who knows the right techniques will always outplay someone else in this kind of position.
For example, BlindKungFuMaster is pretty typical in making a lot of incorrect assumptions. Even though I am the same strength as him, I bet I would easily beat him as Black in this position even though we have the same rating. First of all, Black will not move his pawn and box in his rook as shown in that answer, but will fight with his rook in front of the pawn.
There are a lot of subtleties in these positions.
Your best move: study Nunn's book cover to cover.