I don't understand basic endgames?

So when I traded the rooks, I was supposed to see that black can win a tempo with a3, then I lose the opposition and can't stop the other pawn?
How am I supposed to see all this stuff when I trade into an endgame? I can't calculate to the end of the game.

This was my thought process during the game:
- My king captures the c pawn in time.
- My king reaches the f file just as his king reaches the h file.
Here I stopped calculating because:
- He can't promote the h pawn.
- If he runs over to the other side, I'll take the h pawn and make it in time to trap him on the a file in the exact same way.

How the heck does a random pawn move by him defeat my entire plan?

First off -- where was your Rook before you moved it to c3 ?    If it could have moved to c4, that would have been preferable -- forcing his King backwards.     You are a pawn ahead and may be able to squeeze a win out of this position.

as far as a random pawn move defeating your whole plan -- as it turns out, it was not so random -- as it brought that pawn 1 very important square closer to Queening.

Pawn and king endgames are very mathematical. They're straightforward and there's not much room for variants, but that doesn't necessarily makes them basic.

This particular endgame looks sort of an advanced one (at least to me) and not that easy to calculate. Endgames are not my forte, but from what I understand from looking at it your strategy was based on sort of putting black in a zugzwang to get opposition. In king endgames where you're trying to get opposition and such, 1 tempo can make all the difference in the world. 

After 46. Kf3 black has to choose between pushing one of his 2 pawns. If they push the h pawn, then you play a4 and it's black turn again and they have to lose opposition. But when they push a4, you have to play a3 and black now gets to play h4 and now you're the one forced to lose opposition. Since you have the ability to push your pawn 1 or 2 squares, by playing a4 first they sort of "waste" a move and gain 1 tempo. Similarly, had you played 47.a3 then black would have 47...a4 and once again you lose opposition and the game. 

Well that's what makes chess so hard and so fun. It's not easy, I don't think that most players <2000 can calculate that far either.... it has a lot to do with the ability to calculate but also while taking into consideration these concepts and themes of opposition and gaining tempi, etc... but I am not an expert at that. I don't think I would have figured this out otb, I only know because stockfish tells me lol, but like pretty much everything else in the world, it's just a matter of discipline and practicing and learning from your mistakes. Easier said than done, tho... Next time you have a similar endgame and time to (try to) calculate, you will consider whether pawns can go 1 or 2 squares. Whether which pawn your opponent moves first makes a difference etc. And even if you mess up the math, the fact that you considered those moves is already a progress.

Hi.

This was not a "basic" endgame.

The position after 42. Kd3 is difficult to evaluate for an amateur player (like us).

It is even difficult for stronger players, if they are short of time.

So, do not be too hard on yourself for missing all that stuff.

But now, you now have the motivation to study this kind of pawn ending. Grab a book, search for the relevant sections, study them... and then go over this ending again, perhaps then you can understand the subtle differences between the good moves and the bad moves. It will be more useful for you than other types of training, because it occurred in one of your games.

I do not know the time control for this game. But if it was a blitz game, it is possible that you will need to devote a lot more time to study this ending, than the time you spent actually playing the whole game. ¡It is worth it! Better than playing more games, or some mechanical puzzles unrelated to your games.

Greetings.

50...h2+ is the wrong idea, it loses a precious tempo.  After 50...Kf3 instead (racing over to the queen side), it will take white an extra move to capture the h pawn.  In this case, white can still draw because the a pawns are too far up the file, and the white king can drop under black king.  However, with the a pawns lower down on the a file, this strategy wins (but not after ...h2+, which allows white to capture the pawn and remain close to the black king).

If you are playing a slow game, then yes, you should try to calculate this. Yes, it is hard. Chess is hard.

If it's a blitz game, then calculating is probably impossible.

That's just not true. 46.h4 is the drawing move. After that, black can't win.

As I see it, it is sort of true but only half the answer. h2+ would be the drawing move in a position where a-side pawns would be one square closer to the white side (i.e. a3 and a4):

So the black side made not one but two mistakes:

1. h2+ which gives up a tempo

2. The a-pawns need to be one square closer to blacks promotion after zugzwang. This makes sure that the white king cannot "squeeze in" to the first rank promotion square once the race for the a-file begins.

Both of these need to be taken into account by black to win.

I reread Knights_of_Dooms post again and it is actually exactly the same point I was making.