I enjoyed playing mastermind with LLMs where they pick the code and I have to guess it.

It's not aware that it doesn't know what the code is (it isn't in the context because it's supposed to be secret), but it just keeps giving clues. Initially it works, because most clues are possible in the beginning, but very quickly it starts to give inconsistent clues and eventually has to give up.

At no point does it "realise" that it doesn't even know what the secret code is itself. It makes it very clear that the AI isn't playing mastermind with you, it's trying to predict what a mastermind player in it's training set would say, and that doesn't include "wait a second, I'm an AI, I don't know the secret code because I didn't really pick one!" so it just merilly goes on predicting tokens, without any sort of awareness what it's saying or what it is.

It works if you allow it to output the code so it's in context, but probably just because there is enough data in the training set to match two 4 letter strings and know how many of them matches (there's not that many possibilities).