user25645: Letting Stockfish (14+ NNUE) run for several minutes with lichess' analysis tool on the initial position of a standard chess board lets it reach depths beyond 30 moves, I suppose letting it run for many hours or days would result in an even deeper evaluation.
What is the deepest evaluation ever done of this kind?

user12189: Don't for one minute imagine that Stockfish has analysed all lines out to 30 plies (yes, that's plies, not moves). It has analysed some lines up to 30 plies, but most lines have been discarded well below that depth as being unproductive. Occasionally it will erroneously discard productive lines, but Stockfish being Stockfish, this doesn't happen very often.

user12873: In the chessbase cloud, this depth 79 evaluation is displayed:

Which means someone used Chessbase to get their Stockfish 12 engine to calculate to depth 79, and they had an internet connection at the time so it was able to be stored on the cloud. However, there are some caveats:

We don't know the engine settings that this person was using -- although I doubt this matters much though for the calculation time required, relatively speaking.
There could have been a deeper search done by someone, who either wasn't connected to the cloud at the time, or maybe wasn't even using Chessbase at all.
Chessbase might have an even higher depth evaluation stored in its cloud for Stockfish, but they just choose to show this depth 79 one (I don't know how this works).

But all in all, depth 79 seems like a good ballpark at the very least.
Also as @TonyK mentioned, Stockfish depth is in plies (so depth 79 refers to roughly 40 moves). Also Stockfish does very aggressive pruning. An exhaustive depth 79 search would involve something on the order of 30^79 nodes.

25645: <p>Letting Stockfish (14+ NNUE) run for several minutes with lichess' analysis tool on the initial position of a standard chess board lets it reach depths beyond 30 moves, I suppose letting it run for many hours or days would result in an even deeper evaluation.</p>
<p>What is the deepest evaluation ever done of this kind?</p>
 12189: <p>Don't for one minute imagine that Stockfish has analysed all lines out to 30 plies (yes, that's plies, not moves). It has analysed <em>some</em> lines up to 30 plies, but most lines have been discarded well below that depth as being unproductive. Occasionally it will erroneously discard productive lines, but Stockfish being Stockfish, this doesn't happen very often.</p>
 12873: <p>In the chessbase cloud, this depth 79 evaluation is displayed:</p>
<p><a href="https://i.stack.imgur.com/PEKkx.jpg" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/PEKkx.jpg" alt="enter image description here" /></a></p>
<p>Which means someone used Chessbase to get their Stockfish 12 engine to calculate to depth 79, and they had an internet connection at the time so it was able to be stored on the cloud. However, there are some caveats:</p>
<ol>
<li>We don't know the engine settings that this person was using -- although I doubt this matters much though for the calculation time required, relatively speaking.</li>
<li>There could have been a deeper search done by someone, who either wasn't connected to the cloud at the time, or maybe wasn't even using Chessbase at all.</li>
<li>Chessbase might have an even higher depth evaluation stored in its cloud for Stockfish, but they just choose to show this depth 79 one (I don't know how this works).</li>
</ol>
<p>But all in all, depth 79 seems like a good ballpark at the very least.</p>
<p>Also as @TonyK mentioned, Stockfish depth is in plies (so depth 79 refers to roughly 40 moves). Also Stockfish does very aggressive pruning. An exhaustive depth 79 search would involve something on the order of 30^79 nodes.</p>
