Playing The Rating

PLAYING on in an equal position against lower-rated opposition leads to the occasional debacle.
But on the whole it is a worthwhile exercise - after all, there is a reason why an opponent's rating is lower.
In round three of the Olomouc seniors this afternoon, I had Black against a player with a Fide elo of 1568. I knew from Chess-db.com that he also had a national elo of 1716, but my Fide rating of 1881 meant I was determined to play on until the position was completely exhausted.

White has just played 30.Bd2-c1 and offered a draw in Pavel Kirs - Spanton

Black has the better bishop, but White's king is well-placed and the d6 pawn is backward. My main analysis engines Stockfish10 and Komodo9 reckon the position is dead-equal.
30...Rc8
Played on the off-chance White might agree to exchange rooks, which I felt would make the position marginally less drawish; or, at least, would make it easier for either side to slip up.
31.Rc2
White obliges - a perfectly reasonable decision, but one which gave me hope as the nature of the position is somewhat changed.
31...Rxc2 32.Kxc2 Kc6 33.Bb2 b5 34.axb5+ Kxb5 35.Bc3 Bb4
The engines' evaluation has not flickered - the position remains dead-equal. But here White has a tricky decision.

Should White exchange bishops, avoid an exchange by withdrawing his bishop to b2, or leave the bishops in opposition and attack on the kingside with, say, g4? 

*****
*****
*****
*****
*****
36.g4?
I expected 36.Bb2, when I planned 36...Be1 to induce 37.f3, when I hoped to fix White's three kingside pawns with my g and h pawns. However, the engines reckon this is nothing for White to worry about - their evaluation remains 0.00.
36.Bxb4?! looks very iffy, eg 36...Kxb4 37.Kb2 a5 38.Kc2 a4 39.bxa4 Kxa4 40.Kc3 Ka3, when White's king will have to give way. One line runs 41.h4 Ka4 42.f3 Ka3 43.g3 Ka4 44.g4 g6 45.Kd3 Kb3 46.Kd2 Kc4 47.Ke3 Kc3 etc.
36...g6?
Letting White off the hook. Winning is 36...Bxc3 (or 36...hxg4, followed by exchanging bishops)37.Kxc3 hxg4 38.hxg4 a5, with play similar to the 36.Bxb4?! variation given in the previous note.
37.f3?
But now the win is back on. Correct was 37.Bb2.
37...hxg4 38.fxg4
38.Bxb4 Kxb4 39.fxg4 g5 transposes to the position in the game after 41.Kc2.
38.hxg4 Bxc3 39.Kxc3 a5 is a worse version of the game.
38...Bxc3 39.Kxc3 g5 40.Kb2 Kb4 41.Kc2 a5 42.Kb2 a4 43.bxa4 Kxa4 44.Kc3 Kb5
But not 44...Ka3? 45.Kd3 Kb4 46.Ke3 Kc4 47.h4! gxh4 48.g5 e5! with a draw.
45.Kb3
White offered a draw (after pressing his clock).
The text loses tamely. It was worth trying 45.h4!? gxh4 46.g5 h3 47.g6 h2 48.g7 h1=Q 49.g8=Q. Both sides queen, but after 49...Qe1+ 50.Kd3 Qe4+ Black will be two pawns up and should win comfortably.
45...Kc6 46.Kc3 Kd6 47.Kd3 e5 48.dxe5+
If 48.Ke3, then 48...exd4+ will transpose to the game.
48...Kxe5 49.Ke3 d4+ 50.Kd3 Kd5 51.Ke2 Ke4 52.Kd2 d3 53.Kd1 Ke3 1-0
If 54.Ke1, then the quickest win is 54...d2+ 55.Kd1 Kd3 56.h4 gxh4 etc.