Yes, you absolutely can. I just did it and despite an initial warning that it couldn't play the game (always fun to see these) it absolutely did. The way it wo

Yes, you absolutely can. I just did it and despite an initial warning that it couldn't play the game (always fun to see these) it absolutely did. The way it works is that each time it's tasked to produce a new response, it can view the entire history of the game. It knows that if it's said "higher" to 65 then it would be inconsistent to say "lower" to 64. Eventually this process terminates and the AI admits I "got" the number. The chat transcript up to that point is consistent with a "win". What's wild though is that I can ask it to "regenerate" it's response. Over and over. Using this, I can convert a situation where a transcript which leads to a "too high" response into one that reads "too low". I'm, in essence, simulating fresh games each time and sampling over the choices of random numbers that GPT offers. But it should also break the illusion of GPT specifically "having a mind". As I was chatting with it interactively, it was not really selecting a number but instead evaluating the probability of my particular guess sequence having the set of responses it actually saw. It then samples possible continuations. The more questions I've asked (and the more informative they were) the less variation remains in that selection of possible consistent continuations. Or perhaps more consistent is the idea that within any single "call" to GPT to generate one further token (not even one further response) it may "have a mind", a particular choice of number, or it may not. It's actual behavior is indistinguishable either way. A whole chat dialogue, indeed even the rolling out of tokens from a single response it gives, are certainly (autoregressive) probabilistic samples over this process in either case. (Edit, also worth noting that some evidence suggests GPT, including 4, is pretty bad at randomly drawing numbers.)