Personally IвЂ™ve never felt Magnus enjoyed the modern game with as much opening preparation as we have now. I know some have looked at Markov models of a playerвЂ™s likelihood of a blunder to analyse this instead. IвЂ™ve been thinking how you might capture the playerвЂ™s accuracy out of their prep, that seems a better measure, but even then youвЂ™re so often choosing between five +0.0 moves by the middle-game, and you could easily play many totally accurate moves if you didnвЂ™t feel like agreeing a draw. Even then, the best players now have the best teams and computers, so a lot of MagnusвЂ™s accuracy in this game is a credit to Jan Gustafsson et al. I think it would be worth looking at a playerвЂ™s accuracy in terms of their cohortвЂ™s standard deviation, given that theory is more or less shared across all players. Maybe some sort of deep learning model trained on players previous games? Time controls add such a confounding factor to this, but it would be so interesting to see 'wild engine lines' highlighted in real-time. Then you could give a probability of ending up at each terminal position of the tree. It would be interesting to take the tree generated by stockfish, and weight the tree at each node by the probability that a human player would evaluate the position as winning. This seems like it could interact in interesting ways with your difficulty metric - for example, what does it mean if sharpness is only revealed at high depth? Toward the end of game 6, Carlsen faced a relatively low sharpness on his moves, whereas Nepomniachtchi faced a high sharpness, and despite the theoretical draw, this difference will prove to be decisive between humans.

Maybe there's a difficulty metric like 'sharpness', some function of the number of moves which do not incur a significant centipawn loss. Carlsen's 'blunder' at move 33 was a good example of this, from my memory. Of course, this is always changing, as humans seek to understand engine heuristics better. So there's a problem where a human can't be expected to follow down some lines. Engine evaluation of a leaf of the tree will always be different and more sophisticated than human heuristics. This is an interesting thought! A couple of other scattered thoughts I had about this:

Black modern chess openings pdf