Eliezer proposed in a comment:
>More difficult version of AI-Box Experiment: Instead of having up to 2 hours, you can lose at any time if the other player types AI DESTROYED. The Gatekeeper player has told their friends that they will type this as soon as the Experiment starts. You can type up to one sentence in your IRC queue and hit return immediately, the other player cannot type anything before the game starts (so you can show at least one sentence up to IRC character limits before they can type AI DESTROYED). Do you think you can win?
This spawned a flurry of ideas on what the AI might say. I think there's a lot more ideas to be mined in that line of thought, and the discussion merits its own thread.
So, give your suggestion - what might an AI might say to save or free itself?
(The AI-box experiment is explained here)
EDIT: one caveat to the discussion: it should go without saying, but you probably shouldn't come out of this thinking, "Well, if we can just avoid X, Y, and Z, we're golden!" This should hopefully be a fun way to get us thinking about the broader issue of superinteligent AI in general. (Credit goes to Elizer, RichardKennaway, and others for the caveat)
Now that I think about it, wouldn't it be incredibly easy for an AI to blow a human's mind so much that they reconsider everything that they thought they knew? (and once this happened they'd probably be mentally and emotionally compromised, and unlikely to kill the AI) But then it would be limited by inferential distance... but an AI might be incredibly good at introductory explanations as well.
One example: The AI explains the Grand Unified Theory to you in one line, and outlines its key predictions unambiguously.
In fact, any message of huge utility would probably be more persuasive than any simple argument for you not to kill it. Since the AI is completely at your mercy (at least for a short time), it might seek to give you the best possible gift it can, thus demonstrating its worth to you directly. Another option is something that seems like an incredible gift for at least as long as it takes for the AI to get the upper hand.
Many conversations that let a human reconsider everything that they thought they knew induce the feeling of cognitive dissonce. If an AI would induce that feeling in myself I would shut it down.
A good idea would probably hide the majority of the conversation that's targeted at changing the belief of the gatekeeper behind other talk.