2 vs 1 pawn endgames can be tough. Can you figure out how to draw with Black?

If you have any questions, ask me- there are a lot of lines and I only posted the most important ones.

Wow, those aren't "natural" feeling moves at all.  I'm really terrible at endgames.  :)

Here's a thought process that might help you understand this position. The third rank is taboo for Black most of the time; if he ever steps on the third rank c4 and White is making progress (although White needs to make sure he can stop Black's pawn in time). However, Black must hold the opposition; be it regular opposition or "distant" opposition with three squares in between instead of one.

Also, Black has to be very careful of the fourth rank - and this is the key thing to realize. Even if Black gets on the fourth rank with opposition (such as with 2...Kg4) White can sidestep until Black goes to e4. On e4, Black's King can't continue to step in that direction, but he's also lost time going around the pawns; the d-pawn forces him to step way out of his way to f5. White's King can go straight to the Queenside, but if Black's king is on the fourth rank he has to go to the Kingside one square and then back. If Black anticipates this and tries to leave the fourth rank (for example, if Black decided to play 3...Kf5 in the 2...Kg4 line) then he loses the opposition (in our example, 4.Kf3) and White can break through and win (like 4...Ke6 5.Kg4 with the diagonal opposition).

These moves didn't feel natural to me either. I made this a long time ago, but if I remember correctly, it took me quite a while messing around with the Nalimov tables before I understood these ideas instead of just seeing the lines. By the way, although I "created" this position, it wasn't anything to do with endgame skill - I just chanced upon it playing around with the tablebase. Besides, probably somebody has already discovered this position...

The continuation 1....Kg3 does not work: 2.Kf1 Kf6 3.c4 dxc4 4.d4 c3 5.Ke1 stops the c-pawn from queening and wins.  In this very interesting puzzle, I think that Black draws by following just 3 simple rules.

1) Always move the K into the same file as White's K.

2) Maintain a gap of 3 or 5 squares between the K and the White K. Except when White's K is on e1 when a gap of 3 squares can not be maintained. In that case either a gap of 4 or 5 squares would be just fine.  But if the White K gets out of the e-file, then a gap of 3 or 5 squares will be just fine.

3) When the White K goes to the 4th rank then Black reduces the gap to just one square - meaning stay on the 6th rank such as if 1.Kc4 then 1....Kc6.

Here's an illustration on how to maintain a gap of 3, 5 or 1 square:

 

Yes, you have the idea. By the way, to decrease confusion, I think you mean 1...Kg3.