I doubt that there's anything more complicated to the AI getting free than a very good Hannibal Lecture: find weaknesses in the Gatekeeper's mental and social framework, and callously and subtly work them until you break the Gatekeeper (and thus the gate). People claiming they have no weaknesses (wanna-be Gatekeepers, with a bias to ignoring their weakness) are easy prey: they don't even see where they should be defending.

It involves the AI spending far more time researching (and truly mistreating) their target than one would expect for a $10 bet. That's the essence of magic, according to Penn and Teller: doing far more setup work than could be expected given the payoff.