Why Doesn't Photoshop's Opacity Add Up?

I've always wondered this but now it's beginning to bug me as I'm experimenting with layer stacking to reduce/modify noise.
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.

sixthcrusifix wrote:
For some reason I was thinking that the layer at 100% was having too much influence on the look of the picture.
You were correct. If one layer is 100% opaque and the others are less opaque, then the 100% layer will have more influence than other layers. You're not going to calculate a mean image that way.
I've scored through that because I misunderstood what was meant. I guess it will give a mean of the layers if each layer has an opacity percentage of 100/n, where n is its position in the stack, with 1 being at the bottom.
Ps CS6 and CS5.1 (and maybe earlier) Extended feature image stacks that can calculate a mean image.
http://help.adobe.com/en_US/photoshop/cs/using/WS1E389632-4B37-425e-8EAB-1384C0B432D3a.htm l
With a standard version of Ps, floating point 32-bit mode can be used to calculate a mean image by summing your images and dividing by the number of images. Gamma adjustments in the process are required if your source images do not have a linear colour profile because Ps will convert them to linear on opening into a 32-bit document. Let me know if you want help with that.
Edit: see scored through paragraph.

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