I'm not clear why I'd find this convincing at all. Given the experiment, I'd nuke it, but I wanted to encourage you to elaborate on where you were going with that idea :)
The hope, of course is that they'd respond with "Wait, I don't" or something expressing confusion. I personally would definitely want to hear the next thing the AI had to say after this, I'm not sure if I'd resist that curiosity or not..
The idea for the followup is to make the gatekeeper question reality-- like, convince them they are part of a simulation of this experience that may not have a corresponding reality anywhere. I feel like a transhuman ought to be able to make a human have a pretty surreal experience with just a few exchanges, which...
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)