If I understand correctly, the claim is that the ultimate AI's algorithm for "reading your mind" is to run an entire simulation of the entire universe, so if you are ever faced with such a situation, there's a good chance you are the simulation. If the universe is sufficiently deterministic, the AI would then be able to predict that you would use a die to decide, and simulate the exact amount of force you would have used to toss it.

Right, I was considering that. However, that opens up a whole can of worms regarding whether knowledge can be known in a deterministic universe, not to mention a simulated one. Fascinating possibility for discussion, a welcome change from the mostly programming-based threads.

If you're willing to assume that it's possible to simulate the universe deterministically, then by definition you know everything about the universe (both simulation and real). But I don't think that is a justifiable assumption at this point.