16 bits gray 0 to 32768 - why?

Question

This question might have been answered before but I could not find a clear one searching the forums.
First I understand 32768 and not 32767 (from 0 that would be 15 bits) because it simplifies the math and accelerate processing.
Can someone confirm this?
Second this is only 15 bits so where is gone the 16th one, Why is it hidden and what is it used for?
I need to understand exactly how and why it works like that and how a Tiff gray 16 bits would convert in Photoshop because I use this format to process 3D scans of surfaces... convert the depth values of my 3D in levels of grays, processing in Photoshop and then reexporting to 3D for routing.

Answer 1

ok you have a point here.
So out of the last bit that in theory could give 32768 extra values, only one is actually used
But if the 16th bit was fully used then the maximum value would be 65535, and loosing the midpoint, or a 17th bit would have been necessary to get the value 65536... to get the midpoint back. Am I right?
About calculations:
HSB using B
100% gives 32768 reading with eyedropper
1% gives 164 (seems not correct, should be 328) in grayscale reading with eyedropper but  R G and B all at 326 (seems not correct, should be 328, note that file is grayscale 16 bits but values readable in RGB)
2% gives 328 (seems not correct, should be 656) in grayscale reading with eyedropper but  R G and B all at 652 (seems not correct, should be 656)
10% gives 1773 (seems not correct, should be 3277, but in any case 164x10 is 1640 so 10% is not 1%x10, so we don't have anything linear here as you suggested) in grayscale reading with eyedropper but  R G and B all at 3274 (seems not correct, should be 3277)
etc
99% gives 32355 (seems not correct, should be 32440) in grayscale reading with eyedropper but  R G and B all at 32442 (seems not correct, should be 32440)
This gets me quite confused