Because indeed, what would a "deck half" be ? It sounds like we have
something which someone built, which is comprised of two halves, with
only one of them being a deck. Or perhaps we have a half which is "of
the deck kind". Strange indeed.
Are you familiar with the genre of the "combining mecha"?
Without knowing what you're familiar with, it's hard to come up with a specific example, but there are any number of shows/comic books where two things combine and become something else. Say, two animal mecha combine to become a robot.
The Duocon subgroup from the Transformers has this characteristic. For example, a car and a helicopter combine to form the robot Battletrap:
Each vehicle is therefore a {qoq bID}, a "robot's half", the type of which is not a robot.
In contrast, a {bID qoq} is "half a robot", maybe like if you took a sword and cut Battletrap down the middle from head to toe.
Anyways, if it's not much trouble, please read the following example,
and tell me whether you agree with my understanding of how {bID} works
in conjunction with singular nouns.
There's a pizza on the table; half of it has mushrooms and half has meat.
If I say {bID pItSa' vISop}, then it means that I'll eat half of the
pizza without specifying which half I'll eat. Perhaps I'll eat the
mushroom half, perhaps the meat half, or perhaps I'll eat from both.
What matters though, is that when I finish, half the amount of the
pizza will be gone.
This is how I would understand it.
If I say {pItSa' yav 'atlhqam bID vISop} then it means "I'll eat the
mushroom half of the pizza".
Do you agree with the above ?