OK, but the LLM is still playing without a board to look at, except what's "in its head". How often would 1800 ELO chess players make illegal moves when playing only using chess notation over chat, with no board to look at?

What might be interesting is to see if there was some sort of prompt the LLM could use to help itself; e.g., "After repeating the entire game up until this point, describe relevant strategic and tactical aspects of the current board state, and then choose a move."

Another thing that's interesting is the 1800 ELO cut-off of the training data. If the cut-off were 2000, or 2200, would that improve the results?

Or, if you included training data but labeled with the player's ELO, could you request play at a specific ELO? Being able to play against a 1400 ELO computer that made the kind of mistakes a 1400 ELO human would make would be amazing.