Indeed such studies do exist, similar to the fortresses you speak of. In my experience timely underpromotions seem to be the Achilles' heel of most current engines, and I remember at least one example that I'll show in the annotated diagram below.
It's a beautiful endgame study, with white to win (I strongly recommend trying it on your own before you see the solution here) and the difficulty lies in the fact that most lines that avoid stalemate end up in endgames that are in fact drawn (endless checks or impossible to make progress, at least as far as I remember) despite
a large material imbalance (I'll show such lines as subvariations below). And since there's no immediate forced draw (by repetition or stalemate), the engine keeps evaluating the position wrongly and misses the winning solution.
I remember this study from a couple of years ago (I'll add the reference to the problem if I can find it), and I recall at the time the engines couldn't solve it (or maybe they needed days to see it, but I never let them run for that long):
Here's the FEN: 5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1, to test whether an engine can solve it, simply give it the FEN and see whether it can find the critical line specially without you showing it our analysis and principal variation below (because once you do, the engine caches the line and remembers the solution thereafter within that analysis session).
[title "White to play and win (don't remember the source at the moment)"]
[fen "5K2/p2p4/p7/4P3/P7/8/1R4pp/6nk w - - 0 1"]
1.Rb1 {stop knight moves and force black to exhaust remaining pawn moves} a5 2.Rd1 {Important waiting move with the rook, as there are no waiting moves with the king, as any king move to e-file blocks our own pawn, Kf7 blocks a key diagonal soon to be made clear, and Kg7 allows black to promote with check, for that see the added subvar} (2.Kg7 a6 3.Ra1 d5 4.e6 d4 5.e7 d3 6.e8=B d2 7.Bh5 d1=Q 8.Bxd1 Ne2 {and promotion's unavoidable, black's winning.}) a6 3.Ra1 {one of the critical moves missed by engine, at least not coupled with the right promotion, as to why a1 and not b1 for example, you'll see shortly} (3.Kf7 {a reasonable attempt would be to keep the rook on d1 and make a waiting move with king to force black's d pawn to move, and as such is what the engines also typically suggest but they end up in drawn endgames such as this very line} d5 {d6 leads to trivial mate as white promotes and black's still left with pawn moves to spare!} 4.e6 d4 5.e7 d3 6.e8=Q d2 7.Rxd2 Nf3 8.Rf2 g1=Q 9.Rxf3 {This position is not winning for white but the engine fails to see it due to calculation truncations and the overwhelming material imbalance is simply misleading it. Surprisingly, there are no ways to make progress, if my memory serves me well this is an actual fortress despite the engines giving it high centipawns.}) (3.Kg7 {alternative similar line to Kf7 that ends in a fortress as well} d5 4.e6 d4 5.e7 d3 6.e8=Q d2 7.Rxd2 Nf3 8.Rxg2 {else g pawn promotes with check and black wins.} Kxg2 {and black holds as white has no way to make progress, as the king cannot get close enough to overwhelm the knight. Again, surprisingly, there are no way to make progress, the fortress holds.}) d5 (3...d6 {leads to an even quicker loss for black as the d pawn's too slow and allows white a beautiful quick mate with a knight} 4.e6 d5 5.e7 d4 6.e8=N d3 7.Ng7 d2 8.Nh5 d1=Q 9.Ng3# {Therefore, d5 is black's only real attempt at salvaging the position.}) 4.e6 d4 5.e7 d3 6.e8=B {bishop underpromotion is the only way to win here! It's very simple once you see it, but otherwise everyone, including engines would opt for queen promotion without a second thought!} d2 7.Bh5 d1=Q 8.Bxd1 {right on time to blind the rook and prevent the stalemate} Nh3 {Ne2 no longer works for black as our king's on f8 not exposed to a queen promotion with check.} 9.Bc2+ Ng1 10.Bb1 {Bingo! that's why we needed Ra1 and not Rb1, the c2 square is needed to reroute the bishop to e4 with check while blocking the rook and giving black one more knight move to spare.} Nf3 11.Be4+ Ng1 12.Ra2 Nh3 13.Rxg2 Nf4 14.Rg3+ Ng2 15.Kg7 {waiting move} Kg1 16.Rxg2+ {and the win is trivial from here.}
I hope this is close to what you expected. Some remarks:
- The lines with queen promotion lead to non-trivial draws that engines tend to fail to realise as the calculation truncation inherent to their working disables them from seeing a forced line that draws by force (say either by repetition or stalemate), moreover, the large material imbalance that is created with a queen promotion wrongly biases/fools the engine's evaluation such that it probably doesn't even consider a bishop promotion (as within the analysed depth it evaluates the position with the queen as favourable.) This is not to say that for humans it is easy to realise these fortresses, by no means, but after some time spent calculating few lines one starts to realise that objectively white has no means to make progress and convert. Eventually, one realises the bishop underpromotion is the only way to win.
- My guess is that if you give the initial position to an engine, it will opt for lines with rook on
d1 and followed by a queen promotion as its principal variation, and constantly evaluating the position wrongly with a large centipawn value (20+). Meaning they fail to see the fortress. However, once you show it the line with 3.Ra1 followed by the bishop promotion and Bh5 it will see the forced checkmate and no longer reconsiders its previous attempt of e8=Q.
- For humans it is much easier to spot the solution as without much calculation one conceptually realises that stalemate has to be avoided when capturing black's promoted piece on d1, therefore a queen is out of the question. Moreover, the tedious part is rather connected to the lines with Rd1 plus the queen promotion which are more easily dismissed after a few tries as one eventually realises that despite being a piece up there's no way to make progress whether by winning black's queen or forcing checkmate. And once we've spotted the solution with
e8=B the win becomes so trivial that we don't even need to consider alternative lines (even if they may still be winning).
- The fundamental difference between how humans tackle such problems (specially in endgames) compared to engines lies in our ability to foresee the end of a line conceptually without actually doing the concrete calculation, exactly similar to how we find fortresses in endgames but engines fail to see them. This allows us to contemplate alternative lines much more quickly than engines would do.
