Reflected light will wash out the blacks, to the extent of the average picture level of the scene. Dealing with Ambient light is much easier, because you can raise the black level in your calibrations (or more basic settings), to account for the consistently elevated black levels. Depending on the choice of screen, this can result in some really good pictures, although obviously nothing beats a truly dark environment.
Calibrating, or adjusting, for reflected light is basically impossible, because the elevated black level from the reflections is constantly changing, and with white walls, this will be changing A LOT, and will also be reflecting A LOT. You could potentially calibrate for this, by raising your black level to account for perhaps a 30% average picture level, but your contrast ratio with white walls will be very low (around 50:1 in my testing) if you do this, and that's really not an acceptable solution.
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