After playing horribly in the opening, my opponent played a couple of suboptimal moves which suddenly allowed me to exchange some pieces and get the following unclear position.
I thought about giving the h pawn away, giving White two potentially useless h pawns if he captures gxh4. However, I thought that making use of it would require trading my g pawn for the White f pawn, which seems to be impossible.
[White "Villain (2200)"] [Black "Hero (2000)"] [fen "2B3k1/5pp1/4pn2/8/3P3p/4P1PP/5P1K/8 b - - 0 1"] 1... Ne4 2.Kg2 hxg3 3.fxg3 *
The position after fxg3 was when I needed to formulate a plan. I thought of several options, all of which are more or less passive defenses, as I think moving my pawns would only weaken them and gain nothing in any position.
First idea: Leave my king on g8, and sacrifice the knight to get a fortress. More precisely, force White to move his pawn to g6 and trade the knight and f7 and e6 pawns for White's other pawns (king, pawn g6, light-squared bishop vs. king g8, pawn g7).
[Event "Draw"] [fen "6k1/6p1/3K2P1/8/4B3/8/8/8 b - - 0 1"]
However, I didn't see any way to force this: if White can keep any pawn not in g6, he wins if I sacrifice the knight.
Second idea: Leave my king to protect the g pawn. This forces White to exchange the e pawns. Then I can use my king to stop the passed d pawn and my knight to stop the kingside pawns. However, from what I calculated (and analyzed afterwards), it seems it is not sufficient. This is just an example of what I think could happen; I haven't checked every move thoroughly, but the general idea is still the same: Black can block White's d pawn, but White can always force a win due to Black knight's limited mobility and zugzwang.
[White "Villain (2200)"] [Black "Hero (2000)"] [fen "2B3k1/5pp1/4p3/8/3Pn3/4P1PP/6K1/8 b - - 0 3"] 3... Nd6 4.Ba6 Kf8 5.Bd3 Kg8 6.Kf3 Kf8 7.e4 Kg8 8.d5 exd5 ( 8...Kf8 9.e5 ) 9.exd5 Kf8 10.Ke3 Kg8 11.Kd4 Kf8 12.Kc5 Ke7 13.Kc6 g6 ( 13...f6 14.Kc7 Ne8+ 15.Kc6 ) 14.Kc7 Ne8+ 15.Kc6 f5 16.g4 fxg4 17.hxg4 g5 18.Bg6 Nf6 19.d6+ Kd8 20.Bf5 Ng8 21.Kd5 Nf6+ 22.Ke6 Nd7 23.Kf7 Ne5+ 24.Kf6 Nc4 25.d7 1-0
During the game I remembered that KBPvKN with the advanced pawn can be a win in some positions. However, I didn't remember when that happens, and I also couldn't see any way to force the exchange of all kingside pawns before allowing White to advance his pawn this far. In post mortem, I was able to blitz a win against the opponent in a position similar to this (without the g pawns), even though he claimed it is an easy draw.
Third idea: Use my king to stop the d pawn, exchange my e pawn to White's d or e pawn and force him to defend the isolated pawn so he can't make progress. This is what I decided to do in the game, making by endgame skills look ridiculous.
[White "Villain (2200)"] [Black "Hero (2000)"] [fen "2B3k1/5pp1/4p3/8/3Pn3/4P1PP/6K1/8 b - - 0 3"] 3... Kf8 4.Ba6 Ke7 5.Bd3 Nf6 6.Kf3 Kd6 ( 6...e5 7.dxe5 Nd7 8.Kf4 Ke6 9.Bc4+ ) 7.Bc4 Nh7 8.h4 Nf6 9.g4 Nd7 10.g5 f6 11.Kg4 Nb6 12.Bb3 e5 13.gxf6 gxf6 14.h5 Ke7 15.h6 Kf8 16.Kf5 1-0
Something like 6...e5 was my idea but I couldn't make it work in any position. For example, after 6...Kd6 7.Bc4, I realized the f7 pawn would hang. I saw no other way to make my position any better: any pawn move would weaken them and any king move would give White more space. Only after 13.gxf6 I realized that my plan of moving king to stop the d pawn allowed White's king to break through easily.
Question: Did I miss something? Was one of these plans drawing after all, or is there a resource I didn't see, or is the game simply lost?