Where did I go wrong in this rook endgame?

I played the following rook endgame as Black. Where did I go wrong? According to the chess.com computer analysis I am completely winning after move 32.Rxa7 but I cannot figure out the winning method.

That position is a pretty well known book draw. The engine eval means nothing in endgames like this. It needs to be showing at least +2 for you (sometimes a lot more) for it to be winnable.

Can you eloborate on why it is a draw after move 32?

It did not become obvious to me until the end of the game that it was a draw, but I had several options a long the way. For example, I could have refrained from playing ...b2-b3 to perhaps be able to setup a Lucena position by walking my king to b2. I could also have played gxf5.

Yeah, leaving the pawn on b3 would have been a better try, but from what I remember that's also a draw in a position like this.

After the pawn gets to b2 the white king can shuffle between g2 and h2 and black has no way to win. If the black king approaches the pawn there's infinite checks from behind.

You can win it when the kingside pawns are in an arrangement that allow you to force the weak side's king to the bishop's file. Then for example in your game you could play Rh1.

I think that 31. .... Rc1 + should be a very simple win because your rook is in the right place, behind your pawn and you can get your king right into it.

I'm far from an endgame expert, but I think Black had excellent winning chances after 32.Rxa7. But 32...Rc1+ looks like a step in the wrong direction. Once White gets his rook aggressively posted behind your passed pawn, while your rook is passively placed in front of your passed pawn, your winning chances get a lot worse.  Yo might want to look at 32....b5 33.Rb7 b4

Very nice move, that did not occur to me in the game. I automatically recaptured but chess is not checkers! Surely it must be winning given that Black's rook is no longer passive on b1.

I tend to agree with your comment after it became obvious to me in this game. I thought that tactics with a rook check would somehow work out for me. In certain positions like llamonade2, pointed out in his post above, this would be the case but not in this case.

Next time I put my rook in front of my pawn, I will hopefully be more aware of the specifics. 

Trapping your own rook IN FRONT OF the pawn seems like a weird decision. I'd defend it from the side to get more rook mobility.

Correct, but until you've had a bit of experience, putting your rook in front of the pawn and securely defending it seems natural. After about the 100th time I heard or read "Keep your rooks active!" I finally started to get it

This makes sense, but when the pawn is so far back it means your rook will be on your 3rd rank, and actually it would be pretty easy for white to draw in that case too.

Putting it in front gives the best winning chances, and a rook in front of a knight pawn on your 6th can be technically challenging to defend (although I've forgotten the details). The basic reason is that it's closer to your king than, say, a rook pawn on the 6th.

So far what I've said is from books and "pros"

But here's a rule I came up with (in other words it may be bogus).

If the pawn has crossed the center line I may try defending from the side (bonus if the rank is clear of pawns giving extra mobility)

But if the pawn hasn't crossed the mid line, then put the rook in front.

Some of this is from painful OTB experiences trying to win this sort of rook endgame (but drawing) even though my middlegame had good chances.

For example in the OP's game, looking from start to finish, there were far too many trades going into this endgame. Black had many chances to fight during earlier stages and didn't have to choose this endgame to be the main battle so to speak. In general you'll notice stronger players fight longer before transitioning to the next phase... and you can think of every trade as a minor new phase, in other words I don't just mean middlegame to endgame, I mean every step in between.

No, it belongs behind the pawn where it also defends the second rank. This way, it is white who is forced to have the passive rook and meanwhile, black's king marches up and can't be harassed. White's other pawns are wrecked and white can't defend it all, so the correct line is 31. .... Rc1+

Ok, well, 32...Rb8 is illegal and 32...Rb7 is illegal and loses a rook, so good luck with that.

I've no idea what you're talking about. Probably better to pay attention and not be quite so completely full of yourself.

I'm just sayin', if it were a game, you'd have a 50% chance of me letting you play it... because half of the time my next move would be Rxb7.

31. ...Rc1+, stupid.

Hey, lets play "count the squares"

I count 5 for you, and 11 for me.

I know 11 is pretty high. It's like... "more than two hands worth"

By the way I'm just screwing around. I've seen you post for years and I don't have a bad impression of you... which also likely means you're twice my age.