[tuxiano]

Sometimes if you play a move and the first plies (i.e. half moves) of the main variation the computer starts "understanding" and its score changes accordingly. Those are the cases where more hardware power could be useful and make the engine realize the change from the starting position. More often, the "non-engine" move relies on some blindness of the engine, so the computer starts understanding its strength only when it's too late. In these cases is unlikely that more power could bring benefits. Typical cases are

- fortresses [0]. One side has more material but the position can't be won by the superior side. As the chess rules declare the draw only after 50 moves without captures or pawn pushes, current engines can't look this far away and continue manouvering without realizing the blocked nature of the position. Some engines have been programmed to solve this problem but their overall strength decreases significantly.

- Threefold repetitions [1]. The engine believes the position is equal and move the pieces in - let me say - pseudorandom way. Only at some point it realizes the repetition can be avoided favourably by one side. Also this topic is frequently discussed in the programming forums but no clearcut solution has still emerged.

If you are looking for positions where human play is still better than engine's, the opening phase is the most fruitful. Most theoretical lines were born by human creativity and I doubt a chess engine will ever be able to navigate the intricacies of the Poisoned Pawn Variation of the Sicilian Najdorf [2] or the Marshall Attack of the Ruy Lopez [3]. Neural networks engines are strategically stronger than classical AB programs in the opening phase but they suffers from occasional tactical blindness. Engine-engine competitions often use opening books to force the engines to play a prearranged variation to increase the variabililty and reduce the draw percentage.

[0] https://en.wikipedia.org/wiki/Fortress_(chess) [1] https://en.wikipedia.org/wiki/Threefold_repetition [2] https://en.wikipedia.org/wiki/Poisoned_Pawn_Variation [3] https://en.wikipedia.org/wiki/Ruy_Lopez#Marshall_Attack