Which chess endgame is the hardest?

In chess, many endgame situations with only very few pieces left can be the bane of beginner players. And even sometimes very experienced players as well. But which endgame situation could be considered the hardest of all? This is a difficult (and in many ways ambiguous) question, but here are some ideas.

Perhaps we should start with one of the easiest endgames in chess. One of the traditional endgame situations that every beginner player is taught almost from the very start:

This is an almost trivial endgame which any player would be able to play in their dreams. However, let's make a small substitution:

Now it suddenly became significantly more difficult (and one of the typical banes of beginners). In fact, the status of this position depends on whose move it is. If it's white to move, white can win in 23 moves (with perfect play from both sides). However, if it's black to move, it's a draw, but it requires very precise moves from black. (In fact, there is only one move in this position for black to draw; every other move loses, if white plays perfectly.) These single-pawn endings can be quite tricky at times.

But this is by far not the hardest possible endgame. There are notoriously harder ones, such as the queen vs. rook endgame:

Here white can win in 28 moves (with perfect play from both sides), but it requires quite tricky maneuvering.

Another notoriously difficult endgame is king-bishop-knight vs. king:

Here white can also win in 28 moves (with perfect play), but it requires a very meticulous algorithm to do so.

But all these are child's play compared to the probably hardest possible endgame. To begin with, king-knight-knight vs. king is (excepting very few particular positions) a draw:

But add one single pawn, and it's victory for white. But not a white pawn. A black pawn! And it can be introduced in quite many places, and white will win. As incredible as that might sound:

Yes, adding a black pawn means that white can now win, as hard as that is to imagine.

(The reason for this is that the winning strategy requires white to maneuver the black king into a position where it has no legal moves, several times. Without the black pawn this would be stalemate. However, thanks to the black pawn, which black is then forced to move, the stalemate is avoided and white can proceed with the mating sequence.)

But this is a notoriously difficult endgame. So difficult, that even most chess grandmasters may have difficulty with it (and many might not even know how to do it). It is so difficult that it requires quite a staggering amount of moves: With perfect play from both sides, white can win in 93 moves.