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Sure, but so does the number of paragraphs in the english language, and yet LLMs seem to do pretty well at that. I don't think the number of configurations is particularly relevant.

(And it's honestly quite impressive that LLMs can play it at all, but not at all surprising that it loses pretty handily to something which is explicitly designed to search, as opposed to simply feed-forward a decision)

Not true if we’re talking sensible chess moves.

What about the number of possible positions where an idiotic move hasn't been played? Perhaps the search space who could be reduced quite a bit.

Unless there is an apparent idiotic move than can lead to an 'island of intelligence'