Grayscale levels for 2bp devices

Hi, I was wondering if anyone can give me some input on this. I wrote a 2bp converter a while ago, and later I realized that in screenshots of Windows CE, the gray levels aren't uniform.

My naive expectation would be that there are 4 colors:

0% (black)
33% (dark gray)
66% (light gray)
100% (white)

When I check out screenshots of Windows CE 1.0, however, those contain the following levels

0% (black)
52% (dark gray)
78% (light gray)
100% (white)

Now, my question is, are these the "official" values? Is this specified anywhere? When converting images to 2bp, of course the right values need to be used for dithering, otherwise things will look off.
I'd appreciate any information on this topic!

Be careful because JPG corruption will change the values.

I have a 2bp conversion filter in the support section for converting in photoshop, I would take that as credible. Ultimately though there is no colour info in a 2bp.

Values are

00
01
10
11

What the screen outputs is down to the hardware.

yeah, but if you take those naive values, everything looks off/too dark.
I know little about the topic, but I assume it's some kind of gamma correction.

I'm fairly sure that those 4 grayscale values aren't supposed to be linear, and that it's probably defined somewhere what that "curve" should look like

My photoshop colour table uses
#ffffff
#c6c6c6
#848484
#000000

https://www.hpcfactor.com/support/cesd/200039/creating_optimised_handheld_pc_wallpapers_in_adobe_photoshop

As I say, I'm pretty sure that it is tuned to the display heuristics and not to an RGB map.