Training is supervised, so you don't need bare sets of moves to encode the rules; you just need a way of subsetting the space into contrast classes of valid/invalid.

It's a lie to say the "data" is the moves, the data is the full outcome space: ({legal moves}, {illegal moves}) where the moves are indexed by the board structure (necessarily, since moves are defined by the board structure -- its an abstract game). So there's two deceptions here: (1) supervision structures the training space; and (2) the individual training rows have sequential structure which maps to board structure.

Complete information about the game is provided to the NN.

But let's be clear, the othellogpt still generates illegal moves -- showing that it does not learn the binary conditional structure of the actual game.

The deceptiveness of training a NN on a game whose rules are conditional probability structures and then claiming the very-good-quality conditional probability structures it finds are "World Models" is... maddening.

This is all just fraud to me; frauds dressing up other frauds in transparent clothing. LLMs trained on the internet are being sold as approximating the actual world, not 8x8 boardgames. I have nothing polite to say about any of this