You can't explain yourself? I followed your link. It looks like part of why half-silvered mirrors "work" for the purpose of seeing someone without them seeing you is that one side is kept brightly lit while the spying side is kept dark. I think "beam-splitter" is possibly a more accurate term for my question, which I looked up and found

Another design is the use of a half-silvered mirror. This is a plate of glass with a thin coating of aluminum (usually deposited from aluminum vapor) with the thickness of the aluminum coating such that part, typically half, of light incident at a 45 degree angle is transmitted, and the remainder reflected.

(Wikipedia) Of course, this doesn't actually explain anything - why should there be a thickness of aluminum such that part of the light is reflected while the remainder is transmitted?

Would a beam-splitter still work if the silvered and non-silvered parts were much larger (i.e. a chunky block pattern)? If you fired a single photon at that would it still make sense to calculate amplitude as you do in this post (considering the two outward paths and multiplying one by i, the other by 1)? Perhaps the distance between a silvered part and a non-silvered part needs to be close to the wavelength of the photon?