The last thing I'd like to consider is that I'd like to try an unseen to my knowledge type of symmetry. The jokers will fill a place in the brouhaha squares but mirroring the center of the board like in mirror symmetry while the rest of the pieces have regular symmetry. This has the advantage of populating the board in a balanced way (as many pieces on both sides of the board), although one player will have a king side minor advantage while the other will have a non-king side minor advantage. I'd like to call this twist symmetry. Twist symmetry would mean that we split the pieces of one side in two so that one part has mirror symmetry to the opponent while the other has regular symmetry. This concept resembles the mathematical concept of Chiral symmetry but I'm not sure about a proof that it is the same thing.
The last thing I'd like to consider is that I'd like to try an unseen to my knowledge type of symmetry. The jokers will fill a place in the brouhaha squares but mirroring the center of the board like in mirror symmetry while the rest of the pieces have regular symmetry. This has the advantage of populating the board in a balanced way (as many pieces on both sides of the board), although one player will have a king side minor advantage while the other will have a non-king side minor advantage. I'd like to call this twist symmetry. Twist symmetry would mean that we split the pieces of one side in two so that one part has mirror symmetry to the opponent while the other has regular symmetry. This concept resembles the mathematical concept of Chiral symmetry but I'm not sure about a proof that it is the same thing.
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