Bocajaka wrote on 08/14/08 at 20:28:13:
This is seriously discouraging

I feel like I get 75% wrong.
Perhaps my problem is even more fundamental than I thought. Maybe I do not fully understand basics such as opposition.
Take this one for example:
White to move and draw
In endgame terms this is in the category "very very easy" but I have no clue of what candidates or whatever to consider. I feel lost!!
Let me just ensure you that I am not retarded or anything (I know that for a fact), but endgames are very difficult for me. How easily do you see the drawing line here?
This one is certainly NOT "very very easy". In one line White has to make a series of only moves to draw.
It is very hard for a human to solve such positions by calculation alone. You have to know what you are aiming for and what you are trying to avoid, which means you simply must know and understand the relevant basic positions.
Considerations:
a) If the position reduces to K+ h-pawn v K it's an easy draw.
b) if it reduces to K+g-pawn, the position Pg5, BKg4, WKg2 is drawn unless Black has the opposition.
c) If the Black king is allowed to push the white king back, then the white position will rapidly become critical.
d) Based on b) above, if it were Black's move and he played the obvious 1...Kf5 then White could immediately force a draw by 2 g4+! hxg4 3 Kg3.
e) White's king is therefore in its best position for the moment, both for holding up the black pawns and preventing the advance of Black's king.
So, White should play 1 g3! (only move to draw) and now I think the main lines are:
1...Kf5 2.g4+! hxg4+ 3.Kg3 Kf6 4.Kxg4=; this resource is vital in many K+P endings.
1...h4 2.gxh4 gxh4 3.Kg4 or even Kg2=
1...g4+ 2.Kg2 [All other moves draw, except 2.Ke4?? Kg5 3. Ke3 h4 4. gxh4+ Kxh4 5. Kf2 Kh3 6. Kg1 Kg3 and Black reaches a basic winning position (king on the 6th rank ahead of the pawn).] 2…Kf5 3.Kf1 Ke4 4.Ke2 Kd4 5.Kd2=;
1…Kf6 (probably the best winning try, hoping to induce an error from White in the coming manoeuvring phase.) 2.Kf2 (only move)
and now:
a) 2… Ke5 3.Ke3 o.m. Kd5 4.Kd3 o.m. g4 (4...h4 5.gxh4 gxh4 6.Ke3=) 5.Ke3 o.m. Ke5 6.Kd3 o.m. = Black can gain the opposition but it does not help him, since the f4 square is unavailable to him and the white king cannot be pulled outside the square of Black’s g-pawn, so the sac …h4 achieves nothing.
b) 2...g4 3.Ke3 Ke5 (3...Kg5 4.Kf2 o.m. =) 4.Kd3 Kd5 (4...h4 5.gxh4 g3 6.Ke3 Kf5 7.Kf3=) 5.Ke3 Ke5=;
c) 2...Kf5 3.Kf3 o.m.=
Please let me know if anyone finds any errors in the above, or if I’ve missed out any important lines or ideas.
I'm thinking Ke2, taking the indirect opposition also holds, as black has no way to penetrate into the position