Photoshop :: How Layers Are Going To Interact Based On Their Opacity

If I have 2 layers at 50% opacity and a white layer underneath, those combined layers should equal 100% opacity and so I should not be able to see anything below the lower layer. Instead what I find is that you have to stack over 15 layers at 50% before they even start to appear opaque (and at 15 they still aren't).
 
What's the math going on behind here? I would have assumed that, with an 8-bit image, you have 256 levels of transparency so at 50% you've got both layers at 128; 128-128 = 0 or no transparency so why does photoshop still allow something to be visible underneath that? While we're at it, why does 100% look fully opaque but 99% looks dramatically different without a layer underneath? Maybe the math is adding up but 50% opacity is actually more like 5% opaque?
 
Is there a blending mode I can use that will similate the build up of opacity more accurately? I'm really annoyed with the fact I can't really predict how layers are going to interact based on their opacity; I wish I at least understood the science behind it so I could alter my process to produce the results I want.