No details in the dream indicated what to do when you rolled more than a 16 on either die, or how to resolve transporting a king into check. Obviously you could roll a d16 to eliminate the former problem, but maybe a roll of 17 or better indicates that you should skip swapping boards. Maybe if the king finds itself in check the player could be allowed to rotate the sub-board 90 or 180 degrees to move him out of check, otherwise skip the swap as if you rolled a 17+. Castling, the pawn's double move and en passant capture would probably all need to be scrapped in this variant. Would a pawn that magically appeared in the last rank suddenly get a promotion? That would certainly make things wild and wooly.
Being able to respond to white without the boards mutating seems like a tremendous advantage to black.
I don't recall every reading of a game exactly like this on the Chess Variants Pages, but it wouldn't surprise me to discover that it already exists.
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