I might have missed it but I don't think anyone has mentioned yet that the effect can greatly change depending on time of day, season, elevation, etc.
I use a polarizer all the time. Here in the south, in the summer, with a polarizer AND a red filter, I might get some okay middle-gray to light gray skies with open shadows (as opposed to blown-out skies or blocked-up shadow values). The polarizer doesn't do much in that season generally. In the winter the polarizer is much more effective. And when I travel north and go up to the Smokies, the polarizer is way, way more effective.
There's only been one time that I overdid it - I blocked up the shadows by using a polarizer in the winter and a 2-stop GND filter on the sky on a Velvia chrome, which made the sky totally black.
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