I ran a casino and wrote a bot framework that, with a user's permission, attempted to clone their betting strategy based on their hand history (mainly how they bet as a ratio to the pot in a similar blind odds situation relative to the aggressiveness of players before and after), and I let the players play against their own bots. It was fun to watch. Oftentimes the players would lose against their bot versions for awhile, but ultimately the bot tended to go on tilt, because it couldn't moderate for aggressive behavior around it.
None of that was deterministic and the hardest part was writing efficient monte carlos that could weight each situation and average out a betting strategy close to that from the player's hand history, but throw in randomness in a band consistent with the player's own randomness in a given situation.
And none of it needed to touch on game theory. If it did, it would've been much better. LLMs would have no hope at conceptualizing any of that.