How Can I evaluate this position correctly?


I've been finding that it helps to divide endgames into possible plans.
At first I thought this was a draw, and in exactly the manner you described, but the more I look at it the more it looks like Black will win. We'll have to see what better players say.
I'm not sure what you mean by "calculate this out."
8/pkpb3r/1p2p1R1/3pP1B1/3P3p/2P5/PP6/1K6 w - - 0 39
It looks to me like the problem is that White must keep his queenside pawns intact to prevent Black's king from invading queenside while White must simultaneously keep his bishop posted on the kingside to prevent Black's h-pawn from queening. One way or another it looks to me like Black will be able to invade, either with his king escorting the h-pawn in, or by forcing White to compromise his queenside pawn structure, whereupon Black's king (or maybe bishop, if the a-pawn is left on the wrong color) will invade there. Clever play by Black--he must have analyzed all this before entering into this type of endgame!

Hey Sqod, Thanks very much for your response. What I meant my "calculate this out" was "reason about the position to conclude whether it is a draw or not". The reason I didn't go for this line in the game was because I felt that I couldn't hold the many queen side pawns with just a King and without the help of my bishop. I felt that any practical chances would involve keeping the rooks on the board.
Given the two variations that you posted, I think I know why we can conclude (without calculating every line) that it is lost for White. If White is to hold his queen side pawns, his king should be able to defend all the pawns by itself. If Black can successfully split up White's pawns then the White King will struggle to defend all his pawns because of the disconnect. As the variations you posted showed, the key move c5 by Black serves to break up White's pawns, rendering Black incapable of defending.
Though I too, would love to hear what others have to say. Thanks again for your post!

Though I too, would love to hear what others have to say. Thanks again for your post!
You're welcome. I enjoy learning more about such endgames.

Yeah, forcing white to move the a pawn, then (after moving the king up) eventually playing c5 to put a white pawn weakness on the 4th looks like the winning idea.
Just a note about your bishop... this is a "bad" bishop. It's called this because all your pawns are on the same color. This 1) limits your bishop's mobility 2) abandons the other color (in this case you have difficulty stopping the enemy king going to any light square he wants) and 3) since enemy pawns tend to end up on the opposite color of your pawns, your bishop will be passive because it can't attack any enemy pawns.
So earlier in the game your moves 24 and 37 are very bad. I wouldn't have considered playing either of those moves for more than a moment. That's what stands out to me the most about what happened before the endgame. If you focus on trying to improve your poor pieces, I think it will help you a lot.
So in the game, on move 22 or 23, the "obvious" move is Bh4. Bringing the "bad" bishop to the outside of the pawn chain is a standard way to improve it. As they say, beginners play by moving their best pieces, masters play by moving their worst pieces.

Hey poode_noodle, thanks for the insight. What do you think I should have played instead of Ng5 on move 37?

Hey poode_noodle, thanks for the insight. What do you think I should have played instead of Ng5 on move 37?
Well, now that I look at it, black's bishop pair is annoying, so getting one of them off the board isn't so bad... but the general idea I was talking about is still good i.e. try to leave yourself with your best pieces.
Just looking a bit I'd calculate 37.Bg5 to see if it's something I want. If black captures it, since the rook is behind the passed h pawn that might be a dangerous position to go into for white. So if not Bg5, I'd move the king (the king has to be activated in an endgame just like any other piece) or maybe even move a pawn if black has nothing dangerous to do (even later in the game pawn moves might waste time when you can activate pieces instead).
One of the basic ways to help your drawing chances is to trade pawns, which is why I might consider trying to push some up on the queenside.

By the way I also notice you played Rf1 then later Rg1.
The only reason rooks like open files (well, one of the main reasons) is in the future they want to infiltrate into the enemy position, usually to attack weak pawns on the 7th.
After black played h5, your rooks are drooling over the h file. That's where they really want to be, because they can immediately pressure the pawn. They hate the f file because no piece likes to stare at a friendly pawn (it restricts them), and they don't like the g file because e.g. infiltrating on g7 is probably not going to happen with a dark square bishop in the area.
What you played for, the f5 pawn break, is a good idea... but too ambitious because it's going to take a lot of moves and in the game your pieces went passive trying to support it. If it were a slow position, lets say everything is locked, no queens even, both kings safe, then you can go for these slower moving plans. In that case your rooks don't mind helping support a pawn break. But when there are threats and things are moving fast you should focus on piece activity. h5 is a passed pawn, and also black was clearing the h6 square for his bishop which has dreams of skewering your king and queen. So Rf1 f4 f5 is a good idea, but save it for later, first try to get all your pieces active.
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I see this as the main reason for your move 28. I assume losing a pawn was on purpose. It was probably appealing to finally activate both rooks and bishop all at once, but ideally you do this earlier without giving up a pawn
That endgame position with opposite color bishops is most likely a draw because if white tries to get the king to support the passed pawn, your king can oppose and stop that in time, and if white goes queenside I don't see how white can breakthrough either.

When I looked at it quickly, it seemed like a definite draw. Obviously black has some "edge", but the white king can just block out the black king when necessary.
However, as black, definitely play out the position, since only black has chances - even if the pawn is lost, black can't really lose.

But just one note about the opening - the way you played against the Hippo is a bit weird, with Nc4+Qd2. It's not what I'd do, since the knight need not move twice to c4 (it has nowhere to go really), and the Qd2+0-0-0 idea doesn't seem quite right (...d5 after Qd2 for black seems pleasant). I would have just played Qe2+0-0, looks a bit better.
Obviously, you can play a lot of things against the Hippo and be OK.

I tried working out a draw, I couldn't find one. It's a pretty simple idea, after forcing a3 (I tried lines where white keeps the king on c1 as long as possible to prevent this) black brings the king to e.g. b5, eventually plays c5, and that's it. You should be able to work out the details just knowing that much.
Of course the engine will show a steady eval for the top few moves, so it seems like a draw... but also, of course, the engine is stupid. After you play the reasonable plan it suddenly realizes black can win and gives huge evals.