Its these sorts of half assed explanations that lead to the confusion these posters are having. You've had to come back and add a lot of extra detail to correct it, and its still not complete. There is no "rule of thumb" that is easily distilled down to a short statement like you made and I called it out. The actual explanation needs to be much longer, and fully understood, before the quick version makes sense. Leaving out the context is exactly why the posters are confused. And you're still only scratching the surface of their questions, impedance matching is beyond the idealised discrete models and leads into transmission line/waveguide effects.
I've not really added detail, just restated the context of this discussion which was connecting an AWG with a 50R source impedance to an oscilloscope using a 50R coax. Within that context, my three observations about 'halving' and so on are correct and readily proven so by simple experiment. These aren't generalized 'rules of thumb', they are specific assertions that I'll defend empirically, but only precisely as stated. I haven't attempted to produce a treatise on transmission lines and I'm mainly addressing comments which seem to indicate a desire to needlessly add unnecessary terminations that won't solve the OPs problem or any other.
But thats it, there is no halving. The OP starts off by asking why the measurement doesn't come closer than several % of the exact number, a few posters reply with possible causes for that. The OP comes back and asked about termination (without ever mentioning the specific frequency), clearly not understanding when/why termination is important.
The thread stated with several % error, how accurate are 50 ohm sources/terminations? how accurate are 50 ohm cables? Tolerancing of those could easily explain a few % error from reflections, a cheap/poor BNC connector could be enough, even in your suggested open termination. Halving is about as relevant to engineering as Zero, only ever an approximation and vague reference. Thinking about voltages like assigning numbers to a variable in software gets people stuck like this all the time. Its an electronic circuit, resistances are inherent and non zero, currents are unavoidable and non zero, tolerances of the parts/equipment used are non-zero, there will be noise/interference that is non-zero. They should not be abstracted away with "rules of thumb" and ignored, when the original post is questioning a few %.