What is your favorite endgame position

maybe f6

It's too popular to leave you with the board until midnight, but still pretty cool. :-)

(#32)  No, 1. Kb2 loses to Kd6.

(#32)  No, 1. f6 loses to gxf6.

1. Kc1 loses to Ke7.

1. Kc2 Kd6. What's next?

I guess?

That's correct. I mentioned this is a good position for beginners to learn. It teaches that with a lone white king against a black K+P, some important principles apply. If the black king and pawn are on the same rank, taking the distant vertical opposition allows White to draw. If the black king is one rank ahead of the pawn, taking the direct vertical opposition is needed to draw. If the black king is two ranks ahead of the pawn, White will lose unless Black makes a mistake.

maravilloso

Kc2!? is surprisingly the only drawing move here. The idea is actually fairly simple though; White is simply out finessing Black via distant opposition; When White will block the Black King, it won't be able to get two squares in front of the pawn (and therefore a textbook draw with perfect play).

Of course, to be fair, I have seen this endgame before (a long time ago), but the ideas stick with you

Here is another good teaching position, which will help the beginner learn some of the basics of the Q vs P ending.

White to play and win

Two positions I found

It looks like both are drawn... Maybe neither a4 or c4 is the correct move.

Those two drawn positions are the ones the beginners usually find first. At that point they have already learned something important about the Q vs P ending.

There is a rather obvious dual on the last move.