How to find 'Thermopylaes' with engines?

Question

Motivation

“You must take your opponent into a deep dark forest where 2+2=5, and the path leading out is only wide enough for one." – Michail Tal

I am looking for ways to systematically find lines where one player is forced to find series of precise moves.

Background

The battle of Thermopylae was fought in 480 BC between the Achaemenid Persian Empire under Xerxes I. and an alliance of Greek city-states led by Sparta under Leonidas I.

During two full days of battle, the small force led by Leonidas blocked the only road by which the massive Persian army could traverse the narrow pass.

The performance of the Greek defenders is well known as an example of the advantages of training, equipment, and use of terrain as force multipliers.

Glossar

In chess, I consider a 'thermopylae' to be an only-move that must be found by ones opponent in order to not blunder away their game. Similar to the historic example, it is a narrow pass, an only road, and when studied and prepared at home, it gives rise to a possible advantage through training, equipment, and use of terrain. (You get the point...)

Example 1

Consider the equal position given below where Qd1 is a thermopylae from blacks view since both Qd2 and Qd3 (and every other move of course) lead to a significant advantage for black.

[fen "rqr3k1/3n1ppp/bp2pb2/1N1p4/PP1Q1P2/2P1BR2/4B1PP/R5K1 w - - 0 1"]

Example 2

In the equal position below, white needs to find Be4 to not blunder away the game. If this is found, the game 'widens' after Ke6, but remains 'narrow' after Nb4, asking again for precise moves from white.

[fen "r4r2/5k2/3p4/2pn4/2R5/p7/2B2PPP/1R4K1 w - - 0 35"]

Question

Is there a way to (have engines) systematically go through tabiae (the ends of opening lines) and extract lines that lead to such thermopylaes, possibly a multitude of these down a certain line? (I understand this will include a number of trivial recaptures and forced moves, but I'll go with that.)

Answer 1

Your concept of "Thermopylae" is just what chess player call a "forced move". The problem is, smost forced moves are trivial (for example, recaptures or moving out of check), while others can be hard to find. The number of alternatives does not always determine the difficulty of a position.

Engines are not designed to estimate how hard to find a move is for a human. You could certainly try to tweak the evaluation function so that lines containing lots of forced moves get a bonus, but this doesn't mean the new engine will be harder to play against. Rather, it'd be an engine that likes playing some sort of "hope chess".

As Federico Poloni suggests on his comment, every puzzle collection is a collection of "Thermopylae", so sites like Lichess that generate puzzle based on games played by their users are certainly doing a scan of this sort.

Still, the vast majority of those puzzles are terribly easy, so it looks like this method wouldn't be particularly useful for opening preparation, specially if we take into account that current opening theory will hardly ever end right before a hard-to-find forced move. After all, who would have a line on his repertoire that requires him to find an outstanding move on the spot or else get a lost position?