How to outsmart chess engines

In 2006, Vladimir Kramnik once again dared to challenge a leading chess engine, Deep Fritz, as the last World Chess Champion. He gained advantages in the first two games but was unable to win. He lost the match largely due to the second game:

White has only one move that doesn't lose.

Since that competition in 2006, no chess player has competed against an engine in a serious match. Due to the enormous power of these programs, this is no longer possible in a match of equal strength 19 years later. However, there are still positions that a human can play more successfully than an engine. And by this, I don't primarily mean fortresses that an engine doesn't evaluate correctly due to its computational horizon, but rather positions that an engine essentially evaluates correctly: balanced endgames.

Here's an even position from my last team match in which, based on the score, I was supposed to play for a win.

Philidor Endgame: The Third Rank Defence

The Philidor Endgame is one of the three most important rook endgames in which one side has a rook and a pawn on the fifth rank (from the attacker's perspective). The defending king is in front of the opposing passed pawn, against which it can, in conjunction with the rook, hold a draw: The king occupies the pawn's promotion square, and the rook establishes a barrier on the third rank (from the defender's perspective), which the attacking king cannot cross without first moving its pawn to this rank as protection. The defending rook can then attack the king from behind and secure the draw by checking and attacking the passed pawn.

This defense on the third rank is discussed in more detail here:
Chess Endgame Fundamentals: Philidor Position

Philidor Endgame: The Passive Defense

If the defense can no longer be established on the third rank, sometimes "the passive defense" is sufficient: The king occupies the promotion square, the rook makes waiting moves on the back file.

For practical play, it is important to choose the pawn for which the passive defense is insufficient.

White can commute with his rook on the back rank without Black being able to make any progress.

Philidor vs. h-pawn (edge ​​pawn)

Against the g-pawn (knight pawn), this passive setup is also sufficient. If the side with the extra pawns overdoes its winning attempts with the king h3, rook h2, pawn g3, and the move g3-g2, White can still win.

Against the f-pawn (bishop pawn), the passive defense is insufficient.