Even 1300s sometimes make the best move. Sometimes the best move is really easy to see or even mandatory, like if you are in check and MUST take that checking piece. Sometimes the best move is only obvious if you can look 20 moves ahead. Sometimes the best move is only obvious if you can look 5 moves ahead, but the line is so forcing that even 1300s can look that far ahead.

Despite decades of research, nobody has found a good way to make computers play like humans.

Then I can't refrain from asking: and what's the style of LLMs? For example the ChatGPT which is apparently rated around 1800? That should be completely different from that of a classic chess engine.

LLMs can be trained on chess games, but the tree of possible board states branches so fast that for any given position there is simply very little training data available. Even the billions of games played on chess.com and lichess are only a drop in the bucket compared to how many possible board states there are. This would have to be split further by rating range, so the amount of games for any given rating range would be even lower.

This means that the LLM does not actually have a lot of training data available to learn how a 1300 would play, and subsequently does a poor job at imitating it. There is a bunch of papers available online if you want more info.

LLMs already do play at elo ~1400-1800. The question was how does their style feels like to someone who can appreciate the difference between a human player and a chess engine (and the different styles of different human players).

I can’t speak for ChatGPT, but your intuition is correct that LLMs tend to play more like “humans” than Stockfish or other semi-brute force approaches.

ChatGPT will hallucinate and make impossible/invalid moves frequently, so I don't see how it could have a chess rating

That's not the case. Depending on the version, (Chat)GPT seems to be able to play between ~1400 and ~1800 elo, very rarely making invalid moves.

You've identified a potential strategy by which a computer can play like a 1300-rated player, but not one where it will "play like a 1300-rated human". Patzers can still find and make moves in your set of N (if only by blind chance).

Yeah, you would have to weigh the moves based on how "obvious" it is, such as how active the piece has been, how many turns until it leads to winning material, or other such 'bad habits' humans fall for.

This won't work. With that strategy, you can make a computer make play like a 1300 player, but not a 1300 human player.

That's kind of what they do for "training" bots and it produces something which plays NOTHING like a 1300-rated human.

I assume you could just give the computer a large set of 1300 rated games and train it to predict moves from that set :)

I think there's a real difference between "a computer"— in this context meaning an algorithm written by a human, possibly calibrated with a small number of parameters but not trained in any meaningful sense, and a "chess model" which works as you describe.

I think the chess model would be successful at producing the desired outcome but it's not as interesting. There's something to be said for being able to write down in precise terms how to play imperfectly in a manner that feels like a single cohesive intelligence strategizing against you.