How to draw a rook pawn endgame when you're 1 pawn down?

I played this game recently at my local chess club. My opponent was a very strong player (more than 700 points higher rated than me) and I tried desperately for a draw, but sadly failed

How could I have played this endgame better?

How does white win if you dont play 7. ... kg7, a blunder and instead burn a move with rb2?  White has to try something like say r(a)2, in which case you have to offer a rook trade since you cant afford to let him double.  So 7. ... rb2 8. ra2 ra7 and again, how does white make progress?  White is going to have to take a pair of rooks off, or if re2, than you take a pair off.  If given a lot of time to think, Stockfish actually likes 7. ... rd8 best, rating it +.5 at a ridiculous depth of 46, but other stuff may draw as well.  The important thing was avoiding the blunder.  

I'm not sure why it's a blunder... is it always bad to trade down when you're trying to draw an endgame like this?

I thought that my objective was to trade down until we reach a king+pawn vs king endgame, then make sure I have the opposition and it will be a draw. Or is that the wrong strategy?

Its a blunder because white transitioned into a won king and pawn endgame.  Usually its easier to draw with rooks on the board, and even easier with 2 rooks on the board (although 2 rooks hugely depends on the position).  But the biggest thing about rook and pawn endgames?  You must know how to evaluate the king and pawn endgames so you know if trading is ok or not.  After white's 12th, black has no pawn moves at all.  This is almost always a terrible thing, as it allows white to pentetrate with the king and/or time pawn breaks perfect.  Here, play could go 12. ...kf6 13. kf4 kf7 14. kg5 kg7 15. f4 kf7 16. f5 pxp and here you can see white will win black's remaining pawn and the game.  

I would have played this differently and keep one rook on the 7th rank to protect the king. So 1...Rc7 or 4..Rc7. White will put a rook in front of the e-pawn anyway to protect against the doubled rooks. The computer thinks very tactical, but for us it is important to come up with a good setup.

Also often you want to keep at least one rook on the board when you are down a pawn and that is definitely the case here. 

I've never heard this rule before, but I guess it makes sense intuitively. I will remember this in the future. Thank you!

This is a very important rule of thumb to know - I've gained a draw or was forced to accept a draw many times when I or my opponent followed this rule.

You can't draw this. You're a pawn down and he's miles better than you.

Hahaha nice username you troll

This is the most secure way to a loss. Most king and pawn endings a pawn down are lost.

Your initial pawn structure (f7-g6-h5) is one of the best to defend a rook ending (white did not have the option putting a pawn at g4 unchallenged), and so keeping one pair of rooks was OK to draw (with some difficulty, of course). Or you could keep all rooks on board, but your "trading everything" idea was a losing one.

As suggested at #2, after a move like 7...Rb2 or 7...Ra2, white cannot make real progress without trading one pair of rooks, and reach a 4 vs 3 single rook ending, about which a ton of stuff is written. Some lite theory on it:

https://thechessworld.com/articles/endgame/rook-endgames-4-vs-3-flank/

ArtNJ, pfren, and DierdreSkye have all made this point, but it can't be emphasized too strongly: The first rule of holding a pawn down rook ending  is keep it a rook ending! I'm miles below pfren in strength, but I have been in many pawn-up rook endings and at a complete loss how to proceed when my opponent decides to force/allow the exchange of rooks, after which I won easily. 

@Deranged: "How to draw a rook pawn endgame when you're 1 pawn down?"

By tying down the opponent's heavy pieces to the defense of pawns or his own King and, at the same time, preventing him from doing the same to you. Most endings (not only Rooks') require active play (to keep threatening). Point being that the "attacker" can disengage at his own leisure to reorganize his pieces, increasing the probabilities of the "defender" not having enough tempos to establish a new and effective defensive setup.

The pawn inbalance is meaningful when it's possible to create a passed pawn, either because it can promote or because its blockade will distract the defender's pieces from "attending" other defensive duties (such as protecting other pawns or his own King).

Is also important to have (at least) some basic and solid knowledge of which "technical endings" to seek for or to avoid. For instance, the position you had is likely a draw, as even trading a pair of Rooks may require an exchange of a pair of pawns, when 1R+3P vs. 1R+2P endings (healthy and on the same flank) are mostly a draw, while K+Ps endings are mostly a win for the side with the extra pawn (yet you have to know which and why aren't, as a resource to draw a difficult game).

As to why the pawn structures f2–g3–h4, f7–g6–g5 and the likes are desirable, has to do with the situation of the Kings, when there's only one pawn chain base for the King to protect, the other two pawns are protected "economically" (no pieces involved), and the whole structure shelter the King from lateral and frontal checks (which may force him to abandon his post, or at least give a free tempo to the rival). Then, the fewer pieces you use to defend the more with the freedom to create threats, which may lead to his attacking pieces having to go defensive instead. And as long as he can't progress into a better position (getting a passer mostly) because being tied down to the defense, his extra pawn won't matter. That's how you draw an Rs+Ps ending when in material deficit.

This is a very easy rook ending that can guarantee 100% draw! I am pretty confident to draw against 3500 rated Stockfish!

How I will do?

I will just move my rook in there circle up and down and burn my tempo.

1. one thread by white. g4!! (which can be enforced by putting pressure on your h5 pawn with rook on 5th rank. In that break, dont take hxg4?? Still likely draw but more difficult to defend with side pass on "h" file. Instead counter his rook with your rook on 5th rank , and if he take "gxh5" then gxh5!

2.  "f" file break, leave it alone, "fxg6 will be countered by fxg6.

3. "e" file march, leave it alone, block with rooks "e5"

4. King march, leave it alone, cos your weakness is on "f7" king march is nothing to harm you.

If you analyse the position by all possible breaks, and you know how to defend, you can grab a cigar or wine or sing a song.

(Of course, you need to build up those theories from basic KRP vs KR and think about possible breaks one by one. But if you dont know the basic lucena position or philidor position, my post is quite useless/ difficult to understand though)

In general you want to play actively in rook endgames, not passively. Therefore your responses don't make much sense. First of all there is no way for white to play e5 as long as there are two pairs of rooks on the board. So white got to trade one pair of rooks first. And then your recommendation is blocking with rook? If you trade white's e-pawn for black's f-pawn it is still a draw. So I don't see the point, but it is hard to argue without some actual positions. 

One idea behind this pawn setup is that white has to trade pawns if he goes for g4. hxg4 is indeed best in most cases. You forgot to mention that your idea loses a pawn. Even if it is a draw, why would giving up a pawn make it easier? Some explanation is missing.

How does I lose a pawn?  I explained it already.

And why does black allow enemy rook in 7th rank?

My First move would be Rd7!!

Ah the diagram was wrong,

first move should be Rd7! (not kg7 which is non=sense), After that all plans are the same.

Yea, I would have done something similar as I said in #5, Rc7. I prefer to move the other rook and keep the e-pawn pinned. The first 6 moves in the game were objectively not wrong. So I let white play 8.g4 and then you lose a pawn by force.

This is great counsel.  I can understand it!

why do you make losing lines on black! Keep rooks in 5th rank and 7 th ranks are fine.

Come on, this is a symmetrical rook endgame with extra pawn , objective easy draw.

Dont make losing moves yourself.

So, I played my plan against my 4 cores, average 5 million nodes per seconds. SF at 2+2 min blitz time control,same time control as me. (Average depth of SF is approx 35 which is decent, and would be approx 3300 to 3400 CCRL rating in that hardware and time control)

SF cant penetrate me. And I stopped after 20 moves, as I know it is draw.

And again dont show me losing moves from black, I wont play your losing moves. And if you really think white can win , give Stockfish black pieces (let SF think the same time control as you) and  show me how you can forced win.

I'll repeat after the first 6 moves of the game, the position is a DRAW. Those moves were not losing. It is nice if you can put your rook on the 7th to protect your king, but sometimes that is not possible. 

I'll show 2 more lines were hxg4 is clearly best.