What would you do and why?

Discovered a gem here: http://www.chess.com/article/view/how-to-evaluate-a-position?page=5

Glanced at the position and my instinct was that gxf was correct. Obviously only exf and gxf come into consideration, and exf is pretty harmless, the knight can come blockade the pawn on g6 and in many cases white will play f4, which makes the case even worse. I'm pretty sure gxf with pressure on the g pawn is definitely best.

But gxf results in knight taking the g pawn immediately. Then what?

Thing is, the knight isn't as great on f6 as it seems, since white's f3-pawn stops it getting anywhere meaningful. It would probably love to be on e5... which it could have gone to from d7. So black actually loses a little time there.

White's plan would be gxf e.p., stack rooks on the g-file, probably throw h4 in somewhere along the way and pressure the backward g-pawn.

I looked at exf first, and it looked decent but at the same time the passed g-pawn will be easily blockaded (making for a very slow win, or even draw.) gxf e.p. seems more dynamic and on looking closer, actually isn't half bad.

My intuition was for exf Bd4 f4 to cripple the knight, then play the king to attack the h-pawn

Yes. The Bishop has to operate on the other side of the pawns and not as a giant pawn in a chain.

If exf is correct then how do you protect and promote the passed pawn?

If gxf is correct then out goes the passed pawn theory.

After exf, try to go for pawn ending by forcing the exchange of rooks and minor pieces. That is one idea because in the current position, pawn ending is winning for white. So trying to simplify is one strategy.

I think not playing Bd4 was the critical mistake because that allowed knight to jump around with impunity. My intentions were noble but execution very poor (h4). I have myself started prefering knight over bishop in end games for last gew months, so I should have been even more alert to the pitfalls ahead.

That's a very good type of question to ask yourself "is this advantage real?  Can I do anything with it?"  But in many positions you can't calculate it all.  You have to trust that securing 2 (or more) advantages will give you the leverage to push for a win at some point in some way.  A protected passer in an endgame is by its nature advantageous.  Isolated attackable pawns (like black's h and f pawns) are, in their nature, disadvantageous.

I'm really surprised you say your engine scores this in favor of black.  Mine gives white about +0.40... but honestly I don't know why white isn't just winning.  Looking down the line my engine calculates it's planning to exchange rooks and give white thae open e file... which seems completely disastrous to me.

Maybe given lots of time it would revise its move.  You really can't trust an engine much in an endgame situation anyway.

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As for how players think about this position really what I did (and do in most pawn situations) is compare the following three structures in my mind.  White's general aim for his kingside is to create a passed pawn.  Barring any other big positional or tactical factors the first option will clearly favor white more than the other two.

Then in judging which move to actually play I check black's desires in this position... he would like to create a passed pawn on the queenside and or attack the weak queenside pawns.  He also wants to improve the position of his knight and king.  As long as my plan of exf doesn't help black in one of those ways (and as long as black doesn't have a killing blow I must defend right away) then it's the best choice of the three.

Wow, really?  In that position aren't white's f and e pawn just as much a target as black's g pawn?  Lets say your plan works and you trade your e, f, or h pawn for black's g pawn all of those only favor black I think.  The additional open files will let him pressure... well every remaining pawn that exists (whichever they are, depending on the trade).

So for this plan to be good you MUST win the g pawn... but I don't think you can / have the time.  Black can maneuver on the queenside.  This plan looks very risky to me.  After gxf as black I'd be playing for a win honestly

Wow, you too?

I'm going to have to read this topic from the beginning instead of jumping in at the end lol :)

Yeah wafflemaster, I'm pretty sure white's "edge" after exf5 is purely optical.

I like these exercises, so I'll bite.  However, my process assumes this isn't time trouble so be careful:

Imbalances: Knight vs. bishop, and the pawns are fixed on the opposite color of the bishop, so it's a good piece defending the weak squares. 

-The knight on the other hand isn't particularly restricted apart from the g5 pawn taking f6 away from it, Rh8 is passive, but it's connected and one move should get it into the game. We can immediately eliminate gxf6 ep as a candidate.

-White's central rooks look strong, but aren't really doing much. First priority should be to allow them to activate, maybe with a pawn sac.

-Black has two pawn islands vs. white's three, and white has doubled isolated pawns, white certainly wants to keep minor pieces and at least one set of rooks. 

-black has kingside pawns fixed on the opposite color of the white bishop, so they can't be targeted. 

-black has the better placed king, but is temporarily blocking the pawn.

I'd say white is slightly better here, though it might be equal.  First thing try for an advantage.

1.a4 looks worth considering: 1.a4,bxa4 2.Ra1 though king and knight are perfectly placed to defend the newly passed pawn with Nb6 and Kb5

1.exf5 looks great, creates a passed pawn and blows open the position for my rooks, if I have nothing better I can play this with the idea of rook activity then place a bishop on d4 to both control some important kingside territory the pawn will go to and activating the rook. 

1.exf5 is there any refutation? There's no rule saying black is obligated to recapture so 1...Ne5 2.f6 or 2.fxg6 are horrible for black.

1.exf5 pushes clock.

I played exf and lost. I am trying to figure out if I commited a basic mistake right after exf which was guaranteed to lead me to graveyard or was it a slow death through subsequent weak moves. I am trying to find out flaw in my thought process which led to ultimate demise. I did try to protect the passed pawn through 23.h4 - so it seems I had some idea of what the need of the hour was - but I feel my choice of how to protect was wrong. It will be nice if someone tells me, "after exf, you should have done THIS because of THIS reason". That will teach me a concept for similar situations in future.

Well it's not just the passed pawn, it's the weak black kingside pawns and knight vs bishop going on too.  After exf Bd4 does everything Bd2 does and more.  After that f4 or h4 with Kg3-h4 (or f4) to follow to attack the pawns and activate the king is the general idea.  Playing a few moves myself it's not quite as easy as I originally thought... but IMO it's still a good plan.

I feel like if white can control the e file then that combined with the kingside a win should be possible.  This is just general thoughts no calculation.

Then calculation would go along these lines...

In the game yeah the bishop retreat was passive but you're not losing or anything.  However trading both pairs of rooks off was bad.  In that knight vs bishop endgame black's knight > white's bishop and black can start thinking about playing for a win.  The knight has a nice square on g6 where it can target your weak pawns while blockading the passer.  Meanwhile the bishop's mobility is hindered by the fact that so many pawns are on dark squares.  Furthermore the loose h and f pawns of black can no longer be pressured because the bishop can't hit light squares.

Well... maybe black can curl into a defense.  I at least think black is on the defensive there.  Alternatively gxf targeting the g pawn seems like a very slow way to go for an advantage on the kingside and gives black a chance for active play IMO.

^ Ooookay so getting the knight to g6 isn't as easy as I thought it would be. Rather it seems almost not possible. Shows that calculation > gut feel. But black can still defend somewhat. For instance in your lines after 26. Re7 Nf8 27. Re8 Kd7 28. Ra8 c5 29. Bg7 (29. Bf2 Rh8 then ...Ng6; the a-pawn shouldn't be needed to draw...) Rxg7 30. Rxf8 Ke6 31. Rh8 Kd5 and I've no clue if black has enough counterplay, but I'd bet on white winning/drawing.

There's the inferior (?) 23...Rhg8 24. Rxe8 Rxe8 25. Kg3 Ne5 26. Bxe5 (26. Kh4? Nxf3+) dxe5 and perhaps black can combine the eventual central passer and king invasion via c4 to try for a draw, although again I wouldn't bet on black winning (27. Kh4 etc looks fatal.)

My main concern with exf is that white is playing it very safe, denying black any winning chances, but it might devolve into a draw as the pawn structure is temporarily quite static. gxf gives more dynamic play, but for both sides; exf is safer (which is good.) And those lines you gave allayed my fears of white not being able to convert to a win before black gets organised.

Black doesn't have to initiate the exchange of rooks. He can just play Rhg8 after Bd4--accepting the possible tempo drop in order to contest the e-file.