There is no law of probability theory that forbids you from assigning probability 1/3^^^3 to the next bit in your input stream being a zero

True, but it seems crazy to be that certain about what you'll see. It doesn't seem that unlikely to hallucinate that happening. It doesn't seem that unlikely for all the photons and phonons to just happen to converge in some pattern that makes it look and sound exactly like a Matrix Lord.

You're basically assuming that your sensory equipment is vastly more reliable than you have evidence to believe, just because you want to make sure that if you get a positive, you won't just assume it's a false positive.