Not sure how useful this is but I simply asked ChatGPT what it thinks its skill level is. This is using GPT-4.
After some previous questions...
Me: "Would you be able to estimate your ELO?"
ChatGPT: "As a language model, I don't have a specific ELO rating. However, my knowledge of chess strategies and tactics is based on the information I have been trained on, which includes games played by humans with various ELO ratings. My level of play might be roughly equivalent to an ELO of around 1200-1500, but please keep in mind that this is only an estimate, and my actual performance could be higher or lower depending on the specific position or game."
Me: "As a generative AI, are you actually able to reason which move to make next in chess? Or are you somehow just predicting the next likely move based on training data."
ChatGPT: "As a generative AI language model, my primary function is to predict the most likely text given a certain context. When it comes to playing chess, I am not "reasoning" in the same way that a dedicated chess engine would, which involves evaluating positions and searching through a large number of potential moves using specialized algorithms.
Instead, I generate my chess moves based on patterns and sequences I've seen during my training, which include a large number of chess games and discussions about chess strategy. My knowledge is derived from the text data I've been trained on, and I apply that knowledge to suggest moves that I think are appropriate for a given position.
While this approach allows me to play at an intermediate level, it is not as precise or accurate as the methods used by dedicated chess engines. My suggestions might not always be the best moves, and my understanding of the game is limited by the quality and quantity of my training data."