I don't know that it would be fair? In 960, the back row has to mirror each other. If it doesn't then someone could have an advantageous position to start.
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I know of 960 and other variants, but has anyone ever played chess by just having completely random placement? I could see this being an extremely challenging game. No mirroring, nothing. You get what you get, so your queen could be in the corner or in the middle, etc.