Chess 960 is a version of chess where the pieces are arranged behind the row of pawns. The same random arrangement (with the constraints of the king being between the rooks, and the bishops being on opposite colours) is given to both players.
Consider a version of chess where, instead of this position being randomly chosen, each player gets to choose their starting arrangement (simultaneously, without knowing the other players' choice. What would be the best position(s)? To what extent would some positions be 'good' inherently, vs to what extent would it depend on what your opponent does.
If you're up for a much more creative problem, consider a version in which you can set your 16 pieces (considering light and dark bishops as separate pieces) on any of the 32 squares on your half of the board. How would you go about it? Would doubled pawns be ok? Would you start many pawns on the 4th rank? Or create a pawn shell around the king? Would you begin with some batteries?