No matter whether I test it online on lichess or locally: Stockfish shows different variations and evaluations depending on the number of variations displayed.
Where does this behaviour come from, and how to find out SF's true objective evaluation for a position?
These images are from a locally run Stockfish 15, where it analyzed the position after 1. e4. It was interesting to watch how the different openings rise and fall in Stockfish's evaluation. For example, Stockfish considered the Ruy Lopez as the best for White against 1. ..e5, but didn't find anything against it after looking deeply enough, so it switched to the Italian, which it had thought not to be promising for an edge all the time up to depth 44. This is similar to what we see in top-level chess nowadays, the Italian game is back after a long break!
However when rerunning the experiment with only 3 variations, Stockfish still tries to combat the Berlin defense. It even thinks that the Caro-Kann is the best reply against e4 and only changed mind at depth 46, where it considered 1. ..e5 the best and 1. ..c5 slightly better than the Caro-Kann.
I have noticed the same on lichess frequently. (Side note: this isn't a question about openings; it happens in other positions as well.)
