I don't think either of you understand how multicoating and matte displays work.
So a matte display will have the exact same intensity of glare as a gloss display with no difference whatsoever at all. The ONLY difference between a matte and a gloss display are that the matte display BLURS the reflections, making them less DISTRACTING. This is accomplished with literally a sticker that the manufacturer puts on top of the screen, costs a few cents to do.
A multicoated display is a peice of glass that has been treated with exotic and very expensive chemicals, Magnesium Floride tetragonal birefringent crystals and Silcon Monoxide, that's deposited on the glass using high temperature plasma they slightly alter the wavelengths of light hitting the screen, to actually absorb the incoming light but have no effect on the outgoing light.
So actually you can see yourself in a matte display, it's just a very blurry version of yourself. Try going outdoors in the sun with a matte display and a multicoated display and you won't even be able to see what's underneath the matte display, it will be completely obscured by just a big white blob that overpowers the screen with reflections. Go outside in the sun with a multicoated display and it will actually absorb the reflected light and stand a much better chance of being readable.
Matte just gives the illusion of improving reflections when in reality they just blur them. Multicoating actually eliminates reflections as if they never existed in the first place. The reamaining reflections are an order of magnitude weaker.
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