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Notes -
I paid a decent amount of attention when they did the LLM-vs-LLM chess tournament. You could read a bunch of the 'thinking' tokens (I use single quotes not to make fun of the term, but to only note that it is genuinely difficult to unpack what the word does/does not mean besides being conventionally used for a particular set of tokens). Some of them were genuinely impressive. Some were outright gibberish. Obviously, they were typically better in the opening phase of the game, where there is likely gobs of information on the internet/in books spelling out the reasoning behind particular moves. But that is not to say that it was never impressive later in the game. Of course, that competition used a pretty significant harness that objectively retained the true state. To what extent that matters and/or can be overcome is an ongoing question.
One possibility for trying to make progress in testing this distinction is to consider chess variants, particularly novel ones that are very unlikely to have anything in the training data. 960 is almost this, but something about it is at least in the training data, even if very minimal in comparison; to start, I don't even know that I'd go that far. "Let's play a game of chess where the knights and the bishops switch starting places," might be a good start. Harder versions would be, "Let's play a game of chess where the knights move like bishops and the bishops move like knights." It's logically the same, but you have to keep track of a difference in notation as well as reasoning. I imagine this would actually make the game harder for most people, since they're so used to thinking in one way. Good players will likely make more reasoning mistakes in calculating longer lines, but will probably be able to double-check well enough immediately before making a move that they're not likely to attempt all that many illegal moves (unless they are pretty severely time-constrained). Classic engines would have essentially no degradation in performance (because you'd have to bake in the difference). I'm not quite sure how to think about what kind of degradation to expect from LLMs or, having observed some level (or no) degradation from them, how one would interpret it; but I'd be interested to see. One could get a bit more whacky, like, "Knights can no longer simply jump over pieces; at least one of the two possible L directions needs to be open," possibly also throw in for the fun of it, "Bishops may now jump over one piece along their route," or something. I played Knightmare Chess long ago when I was young. There are a ton of tweaks you can do to mess with stuff. For humans, it is fun to keep track of various rule modifications and try to reason through it.
At the very least, if LLMs absolutely tank in these sorts of variants, just spamming illegal moves all the time, while humans are able to at least moderately cope, it would be some amount of useful information. Of course, one must always have the disclaimer that it is certainly possible that with enough progress and compute, LLMs may even outperform humans. We sort of just don't know.
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