Is it only possible for your engine evaluation to go DOWN during your turn?

When looking at the analysis of my games, I notice that the computer's evaluation of the position seems to only ever go down for a player after they have made a move.

This intuitively makes sense. I'm guessing it's not possible to "surprise" the computer with a very good move. Instead, your best possible move is already baked into their calculation.

Is this a general truth about the positional analysis engines, even at the higher/highest levels? Does Carlsen ever play a move which makes his calculated evaluation go UP?

No, they go up too. Every single game you have won must have seen the evaluation going up (at least from your side), unless you won on time .

Your question is ill-formed. But whether you mean against a human opponent or against an engine playing at its best (i.e. not a hobbled version), an evaluation can go up or down after your move.

No, following *my* move, the evaluation for my color only ever stays the same or goes *down*. Likewise, following my opponent's move, the evaluation for them either stays the same or goes down.

That is, if the analysis engine currently says I am at +1.0 (one pawn ahead), and I make the best possible move, the engine will still say I am at +1.0.

I haven't ever seen a game where this isn't true but that's why I asked here.

You have the right idea. At best, the perfect move simply maintains the current evaluation.

However since engines aren't perfect sometimes you can play the move they want you to play and the eval will go up because now it's calculating deeper. Or you can play a move they don't want and the eval will go up because engines aren't perfect. This is especially true when using limited hardware and/or thinking time.

Its possible for the eval. to go down after you opponent's turn. Happens every game almost, esp. during live games of top players.

You see evaluation of -0.80 and then white makes a move and it goes up to -0.45.

Those little fluctuations not counting, you are right that there wont be wild swings after the opponenet's move. So an eval of -0.8 won't switch to +1.8 after white made a move.

There have been (very rare) positions in the past where the computer failed to spot the right move, most notably during the Vlady vs Pete World Championship Match game 8 where Peter played Qd3!! deep on move 25. in a position that was still Kramnik's prep.

Kramnik and his team had looked at the position with a computer an evaluated it as equal but pleasant and winnable endgame for white (Kramnik). The Peter played Qd3 and Kramnik realised he was lost. Some engines even today find it hard to spot Qd3. I know because I put the position in Lichess analysis and it failed to suggest Qd3. The chess.com engine suggested Qd3 right away though, when I put it here.

Having said that its possible that the position has been 'fed' to chess.com computer to suggest Qd3 in the position, and it would on its own fail to spot it. I can't be sure of that, but I have seen Lichess analysis completely miss Qd3 and show the position totally winning for white and then you play Qd3 and the evaluation flips completely.

I remember I even made a thread on it.

Then there is Shirov's Bxh3! which is said to be the greatest move ever played. It is said that some computers still fail to find Bxh3, the winning move.

That said, it is true that today's computers must find it hard to be shocked.

Thank you, JayeshSinhaChess, great example!

So it sounds like it can happen, but it's pretty rare.

Although certainly when one computer beats another, it's probably because of differences in calculation, and so in that sense the evaluation engine can be "surprised" by a move. Having listened to some of the AlphaZero coverage, it sounds like that's indeed what happened in that case.

I dont understand why some people use computer analysis at depth 20? Stockfish strength at depth 20 is rated around 2000-2400, it will massively miss a lot of evaluations. Why dont plus icon for further analysis.

Check my analysis , the depth 43. I never trust stockfish analysis if the analysis depth is below depth 40. Depth 40 give stockfish is approx 3000-3100 rating.

P.S, Computers are also extermely weak at low depth /low node or low time control.

At what depth computer failed? How much duration of analysis they did? May I ask?

Why I ask?

Because computer analysis in 15 years ago using Fritz 5 in pentium 2 computer for 1-2 minute of analysis would be surely weaker than my blitz rating/analysis.