At a quick glance this whole ending seems very drawish.
Rook and pawns ending

The advanced pawns don't really effect an advantage here. The order of importance in rook and pawn endgames is 1) rook activity 2) king activity 3) pawns. Black's rook is a bit more aggressively/actively posted on your 2nd rank, I'd say kings are equal, and white has a passed pawn -- so like others say it's really pretty equal and looks like a draw.
After move 40 it's a dead dead draw, nothing to worry about after that. To answer if there's any play In the final position, to show how little winning chances there are you could actually take away white's b and d pawns and still have a theoretical draw. You do have a passer but it usually takes both the king and rook working together in such an endgame to promote it (or a distraction to the enemy king/rook). The d pawn is too far away from your king to make it, but most importantly your rook is in it's ideal position behind the action where it can effectively rain down infinite checks.
A good way to lose a drawn endgame is to play for a win, and considering your opponent's rating, you went about this in the right way trading off the kingside pawns. Moves 41 and 42 to get behind your passer was not bad at all, but too ambitious if you thought to queen it -- because rook activity is #1 41. Rg8 is more appealing in a position like this, and notice in the final postion your rook is at it's best on the 8th rank.
Good game :)

o agree with most of what you say, except this order of importance thing...in fact how active the rook is, for example, depends fundamentally on the kings and pawns. If someone has apassed pawn on the 6th rank, your rook becomes pretty passive, because it must contantly guard.
In that case I'd argue that the pawn's value comes directly from tying the rook to passivity, only because the rook is so important does the pawn's limiting effect has value... although that may just be a relative point of view -- I was just giving the general rule of thumb for these endgames to point out that evaluations (such as in this example) of "his pawns are further advanced" or possible ones such as, he's a pawn up, pales in comparison to how active your rook+king are. Sure, there are exceptions, and advanced/protected passed pawns are a good one :)

The Schliemann variation, like any other gambit, can either go into a long endgame, your allow for a quick trap. You exchanged a lot in your game to go into an endgame. I try to keep more pieces on the board and make it complicated or allow chances for tactical combinations. Here is a game I played in a tournament with this opening.

Hmm, I guess I decided that on my own without reading it anywhere. I assume there would be too many exceptions to my "order of importance" thing for any author to explicitly say it... so maybe I should keep it to myself.
But this is how I think, especially in endgames, I sort of assign each piece a weight so to speak (depending on the specific position too, I like to "weight" and re-weight pieces in my mind as a game goes on) In a B vs N endgame if your bishop can tie the enemy king down to defense on the king side the way I imagine the situation is now it's your king vs their knight on the queen side. Because the king > the knight you will have the advantage (generally speaking of course, I know there can be fortresses, tactics, etc).
So in rook endgames I imagine it most effective to tie the rook, 2nd most effective to tie the king, and least important to solely win a pawn. And so I evaluate a position based on the relative value of pieces. If white's king is slightly better but black's rook is slightly better then I might imagine it as roughly equal but black is more comfortable. If black's rook is much better and white's king is just a little better, then black has an edge and so on. Obviously an advanced supported pawn can "out weigh" an active rook depending on the poition, but a standard pawn I don't give much weight... this unspoken part may be the worst of it.
This is also how I justify the drawishness of R+P endgames to myself. If each side has an equally healthy rook and king, the difference of a pawn may not matter. If your king and rook are healthier you can draw even when down multiple pawns. While if you have extra pawns but a rook that's out of play, your winning chances are microscopic.
I was pleased drawing this agains a stronger player, but I can't help but feel that both sides could have done better at times. I thought Black's advanced pawns might give him the edge.
I'm White