Perfect chess IS a draw… or is it

Here’s my logic:

If you think about how the evaluation bar works, you cannot do anything to improve your own evaluation in the game. This is because the computer sees all of your best moves, and gives you the evaluation that you would have assuming that you play all of the best moves.

Therefore, if it is not you that improves your evaluation, then it must be your opponent that makes your evaluation higher if they make an inaccurate move.

But if both players play “perfect” chess, then by that logic the eval bar would never change because neither lets the other get a disadvantage, and thus, perfect chess must be a draw.

But then that led me to some other questions that I don’t know the answer to:

If the computer calculates all the best moves to keep the game equal, then does that mean that there is one “preferred” move order that is considered the perfect game?

If perfect chess is played, is the +0.61 eval that white starts with enough of an advantage to give them a win?

I’m curious as to what you guys think of my logic and both of the questions.

Right, objectively speaking, there's no such thing as a move that improves the position. Moves either maintain the evaluation or make it worse for the player moving.

Before I talk about the other questions, it's worth noting that engines don't find the best move. Engines improve from year to year which would not be possible if they were perfect.

Ok, moving on. In most positions there is not a single best move. It's useful to point out that there are only 3 real evaluations for a move:  1) White wins 2) draw and 3) Black wins. If you need any convincing that most positions have many (sometimes more than 1 dozen) moves that are good enough to maintain this "true" evaluation then you can look at endgame tablebases. If you've never used one, it gives evaluations like "white wins in 47 moves" and it instantly gives this sort of eval for every legal move.

The 0.61 evaluation is not real for various reasons, and is not a win for white for at least one reason. First of all the number depends on the depth, the hardware, the software, etc. Secondly even if the depth, hardware, and software are identical (you can trick an engine into calculating the same line twice simultaneously) even then it will not come up with the same number... and even if somehow the 0.61 number were real, it is not a win for white because the drawing margin of endgames is too large. I.e. being ahead half a pawn (or often even a whole pawn) is not enough to win most endgame positions.

#1

"If the computer calculates all the best moves to keep the game equal, then does that mean that there is one “preferred” move order that is considered the perfect game?"
++ No, chess is a draw and there are many different move orders to achieve a draw.
We already have over 1000 perfect games of chess: drawn games in the ICCF correspondence world championship. They play at 5 days per move with engines allowed.

"If perfect chess is played, is the +0.61 eval that white starts with enough of an advantage to give them a win?"
++ White starts with +0.33. That reflects that white is 1 tempo up. We know from gambits that 3 tempi = 1 pawn. You need an advantage of 1 pawn to win a game of chess: the plan is to queen the pawn. You cannot queen less than 1 pawn. So the advantage of +0.33 is not enough to give white a win.

On the other hand white has a broader choice of moves that keep the draw and black has a narrower choice of moves that keep the draw. That explains why white wins more often.
White can afford to lose a tempo, then white just becomes black, e.g. 1 e3 e5 2 e4.
Black can afford to lose a tempo: 1 e4 d5 2 exd5 Qxd5 3 Nc3 Qd8.
By the same reasoning white can afford to lose 2 tempi: 1 d3 e5 2 d4 exd4 3 Qxd4 Nc6 4 Qd1.
Black cannot afford to lose 2 tempi, then he is 3 tempi behind and 3 * +0.33 = +1.