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Sorry, but this makes my head hurt.

>>> best chess engines are still worse at analyzing openings than humans.

>> Is that actually the case, or perhaps humans try a lot of sub-optimal opening lines?

> Sub optimal from the perspective of the AI

There's no perspective involved: optimal play is perfect play, assuming the opponent also plays perfectly. If a move is sub-optimal for White that means White has a better move, no matter what the opponent plays.

Sure, in practice a non-perfect-player might do better playing a sub-optimal move A rather than a better move B, because they don't know how to continue after B or because their non-perfect opponent ends up replying even more sub-optimally to A.

But just because I can manage to pull a fool's mate on someone that doesn't make it an optimal opening. One could say I might be "optimizing" for fun or for time, but if you redefine optimality arbitrarily then the original claim might as well be "chess engines are worse than humans at analyzing openings because they play better than humans".

PS: I'm not claiming that chess engines are better or worse than humans. And, incidentally, playing an inferior move while hoping the opponent makes a mistake is bad even if it works, as it really hinders your progress.

Of course there's perspective involved.

Restricting yourself to perfect opponents is very silly firstly, because there are no perfect opponents because chess is unsolved. So right out of the gate our definition assumes the counterfactual for all chess games every played and is both inaccurate (does not describe actual chess) and impractical (cannot be implemented)

Secondly, if there were such an opponent (which is not at all clear there ever will be), there is no way within the rules of chess to detect whether or not we face it in a given game. Imperfect opponents are allowed to play chess, and assuming they are all perfect while a defensible strategy is merely one of several.

Thirdly, it leads to very counterintuitive results. Consider the case in which chess is solved and well-balanced (e.g. a perfect opponent P can force a draw). We modify P to create opponent NP. NP behaves as follows: if NP's opponent is consistent with P, NP will implement P (e.g. force a draw), if NP's opponent deviates from P, NP will lose (forefeit or make bad moves). Therefore everyone can beat NP except "optimal" algorithm P, which can only force a draw. So now we have an "optimal" algorithm with a 0 tournament rating.

In reality the whole "perfect opponent" thing is mostly a notational convenience for Zermelo's Theorem. Which is very interesting and useful if you are writing a proof, less interesting if you are trying to win a chess tournament. A more practical definition of "optimal" is something like "wins a lot of games".

You're going off a tangent here. There's nothing in my argument that relies on having an optimal opponent only; forget about the "assuming the opponent also plays perfectly" part for a moment, the key part is getting the best move no matter what the opponent plays.

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