> remember even a few positions? Sure they could
A rough estimate of number of positions across all X move games is X^10. For 15 moves it is hopeless to remember even a relatively small part of them. Typical game has 40 turns, 1 move per player, so 80 moves.
2) An LLM is not going to memorize vs generalize when there is no training pressure to do so. You might expect it to memorize book openings that occur over and over in the training data, but not some random non-celebrity game that occurs once in the Lichess dataset and is never again referred to.
> They can't possibly remember even a few positions. Don't you know the legend about rice grains on a chess board?
If the wise man was a bit wiser, he'd have asked for his rice on a snakes & ladders board (100 squares, not 64) and would have had 2^36 more rice, which is equally irrelevant.