The state of the game, not the behavior of playing it intentionally. There is a world of difference between the two.
It was able to model the chronological series of game states that it read from an example game. It was able to include the arbitrary "new game state" of a prompt into that model, then extrapolate that "new game state" into "a new series of game states".
All of the logic and intentions involved in playing the example game were saved into that series of game states. By implicitly modeling a correctly played game, you can implicitly generate a valid continuation for any arbitrary game state; at least with a relatively high success rate.
As I see it, we do not really know much about how GPT does it. The approximations can be very universal so we do not really know what is computed. I take very much issue with people dismissing it as "pattern matching", "being close to the training data", because in order to generalise we try to learn the most general rules and through increasing complexity we learn the most general, simple computations (for some kind of simple and general).
But we have fundamental, mathematical bounds on the LLM. We know that the complexity is at most O(n^2) in token length n, probably closer to O(n). It can not "think" about a problem and recurse into simulating games. It can not simulate. It's an interesting frontier, especially because we have also cool results about the theoretical, universal approximation capabilities of RNNs.
There is only one thing about GPT that is mysterious: what parts of the model don't match a pattern we expect to be meaningful? What patterns did GPT find that we were not already hoping it would find?
And that's the least exciting possible mystery: any surprise behavior is categorized by us as a failure. If GPT's model has boundaries that don't make sense to us, we consider them noise. They are not useful behavior, and our goal is to minimize them.
It was able to model the chronological series of game states that it read from an example game. It was able to include the arbitrary "new game state" of a prompt into that model, then extrapolate that "new game state" into "a new series of game states".
All of the logic and intentions involved in playing the example game were saved into that series of game states. By implicitly modeling a correctly played game, you can implicitly generate a valid continuation for any arbitrary game state; at least with a relatively high success rate.