Chess will never be solved, here's why

The categories of moves you need to consider when evaluating play (and you can name these what you will)

1. Error (changes the evaluation by half a point)

2. Blunder (changes the evaluation by a full point)

3. Suboptimal move (A move that retains the theoretical outcome or current evaluation, but does not force as few options for opponent as possible. This includes engine or human play that aims for a draw.)

4. Optimal move (retains current evaluation and leaves as few moves as possible for opponent that retain current evaluation.

What you can take away from this is, even if engine play is free from errors and blunders against their current opponents, unless they're facing explicitly optimal moves, you cannot conclude they're unbeatable.

Edit. And evaluation meaning objective outcome in this post

optimal v suboptimal is subjective because there could be more moves available from one move to another but they are harder to find for engines, and dont forget the difference betwee "evaluation" and win/lose/draw position.

That's true of course, sometimes there is only one move available but it's obvious. However, choosing a move that leaves fewest options for opponent I think is the most objective measurement for optimal and my assumption is that against human or engine play, on average, this way of playing challenges them the most.

@12264

"1. Error (changes the evaluation by half a point)" ++ Yes.

"2. Blunder (changes the evaluation by a full point)" ++ Yes.

"3. Suboptimal move (A move that retains the theoretical outcome or current evaluation,
but does not force as few options for opponent as possible."
++ No. If it retains the game-theoretic value, then it is a good move.
The number of options i.e. good moves as replies does not matter.
The likelihood of the opponent to err is not correlated to the number of options.
It depends on the weaknesses of the opponent.
If an opponent is weak at defending, then he is more likely to err if you attack him,
regardless of how many good replies he has.
If an opponent is weak at attacking, then he is more likely to err if you coax him to attack, regardless of how many good replies he has.
If an opponent is bad at rook endings, then he is more likely to err if you go into a rook ending, regardless of how many good moves he has.
It is subjective: depends on the opponent, or your perception of him.

"4. Optimal move (retains current evaluation and leaves as few moves as possible for opponent that retain current evaluation)"
++ No. All moves that are neither error (?) nor blunder (??) are optimal moves in the game-theoretic sense. In the practical sense some may be subjectively more or less optimal depending on the weaknesses of the opponent.
That is one reason why the ICCF WC Finalists start by analysing all games of their opponents:
to search for weaknesses, elements he undervalues or overvalues.

@12266

"choosing a move that leaves fewest options for opponent
I think is the most objective measurement for optimal"
++ The only objective measurement for optimal is retaining the game-theoretic value.
There are subjective reasons why one good move is better than another against a particular opponent in a particular situation, but that is subjective, depends on the perceived weaknesses of the opponent. In practice leaving many good options may even be better,
to force the opponent to consider them all, use up thinking time and get tired.
1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 a6 leaves white many good options,
but is considered the best move, and was played in 10 ICCF WC Finals games.

Apart from that there are also moves that logically cannot be better than other moves.
1 a4 cannot logically be better than 1 e4 or 1 d4, though all draw.
1 Nh3 cannot logically be better than 1 Nf3, though all draw.
It is game knowledge that the center, d4-e4-d5-e5 is important as high ground,
so moves that control the center make it more likely for the opponent to err.
It is game knowledge that time is important, and that 3 tempi are enough to win,
so moves that lose a tempo for no good reason are more likely to lead to later errors.
1 Nf3 d5 2 Ng1 still draws, but is logically inferior.

Would you count Qa7+ as optimal and Qxc7 or Qxb5+ as suboptimal here? (All moves maintain the game theoretic value.)

@tygxc #12267

Not much point in agreeing or disagreeing with the use of these terms when you don't use them in the way people working in the area of chess solutions conventionally use them. All you're saying is you want to give them a different set of meanings from those chosen by the person you're addressing. You don't have any special authority to insist on your own meanings.

@12271

The definitions are not mine, but those of GM Hübner.
'I have attached question marks to the moves which change a winning position into a drawn game, or a drawn position into a losing one, according to my judgment; a move which changes a winning game into a losing one deserves two question marks.'

Game-theoretically there are only good moves, errors (?), or blunders (??).

this is conflating definitions here. the original poster was referring to moves that made it the hardest for the engines to deal with, not for maintaining the current game state. of course, im not surprised you wouldnt follow basic context.

id address your other fallacies tygxc but they are all too off topic and unnecessary. The chief one being that conventional game knowledge is not mathematically rigorous logic.

its quite sad that you tried to shut down an otherwise interesting conversation to self insert your own usage as the only way to achieve objectivity.

there were plenty of other possible ways to measure, for example based on measure engine performance to certain algorithms, or longest think time to game state proof, but no, only what tygxc thinks matters.

It is inappropriate to redefine the terms error and blunder in an entirely non-standard way. Both half point and full point errors are blunders. And the terms "half point error" and "full point error" are adequate, clear and not in disagreement with normal usage.

yet again, a reminder to all that the ICCF championship games have LITERALLY NOTHING to do with solving chess, as none of their games are backed up with proof.

No doubt Hübner included that text because he was aware that he was using the terms in non conventional senses in his tract. He doesn't appear to be advocating a general adoption of the terms.

There can be little confusion about the terms "half point blunder" and "full point blunder" and, if those terms are adopted, then little confusion about the term "blunder". An error could be anything.

The use of the term "perfect" to mean a move which is not a blunder is not intuitive but that applies to a lot of jargon. You have to just use it in discussion with the meaning agreed. It's less likely to be confusing than "good" which could mean very many things,

@12227

"meaning agreed"
++ Per Prof. van den Herik: 'the game-theoretic value of a game is the outcome
when all participants play optimally'
Thus all moves that are neither ? nor ?? by definition are optimal play.
Meanwhile here are 115 games with optimal play by both sides.
Certainty: 1 - 1/116² = 99.993%

wow i didnt know that 99%=100%

you learn something new every day.

and by the way, put that equation away for probability. it literally uses the assumption that the games are perfect to begin with. it also assumes errors are independent, which is blatantly false.

so tygxc, since when did 99% =100%?

That took 4 years with a team of grandmasters and computers. One of which was faulty.

@MARattigan, a suitable refinement (to rectify the problem you identify) for the general case of combinatorial games with results that are Win/Draw/Loss is to define an order on positions as follows

1. P > Q if the game result with best play from P is better than the game result with best play from Q
2. In the case where the game result is the same (so 1. does not differentiate) P > Q if either the result with best play is a win and the game from P is shorter or the result with best play is a loss and the game from P is longer. When the optimal result is a draw, there is no necessity to differentiate further (note for some purposes it might be useful to deal with achieving the fastest forced draw, but this is not part of the problem you identified).

Here "best play" is play where both players play according to the order.

As this is self-referential, a little routine work is needed to show that this is well-defined.

i.e. a position is better if the result is better, and if the result is the same a shorter win is better than a longer win and a longer loss is better than a shorter loss.

This does not differentiate between all positions, but those that it fails to differentiate can be considered "equally good".

Of course, this is applied to a set of moves in a position by comparing the positions reached after those moves.

"unless they're facing explicitly optimal moves,"
which pertains back to the fact that chess is Not Solved -
which means 'optimal moves' so much of the time is just a concept.
If somebody can be check-mated on move and there's only one move to do it - then that's an optimal move.
But most of the time such a move isn't available - nor a 'mate in x moves' sequence.
In tactics puzzles - there's usually a move or moves available that are clearly 'optimal'.
But such positions are a small fraction of all positions.
In other words - Chess is Not Solved. The Reaper.
That is the Rome and current capital city that 'all roads' lead back to.
'all roads' is figurative but not 'literal' even figuratively.
---------------------
regarding classifying blunders versus errors versus 'suboptimal play' (with the default being that that's somewhat vague because 'optimal play' usually isn't established (the Reaper again) ....
if a classification system is devised that's designed to be comprehensive - that doesn't mean that system is practical.
For example - a computer makes plays that are 'punishable' ...
but deeply so. Not easy to detect and not easy to refute ...
then failure to punish that play is itself a kind of 'error'.
One can try to semanticize and say 'No! Errors are errors and they're all 'errors'!'
Only to serve the words and semantics - not the practicalities.
I think you'd find that programmers have to serve practicalities not semantics.