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George Duke wrote on Sat, Jan 14, 2017 09:02 PM UTC:

Since this is Piece topic, it is new idea to have one or few pieces that can be moved by both sides (not that it has to be "popular"). Or that could be way to introduce the greatest, most popular all-time piece Centaur(BN): start it on e4 and let both sides own it and optionally move Centaur in lieu of regular move five times a game -- a difference from Seirawan Gating. Necessarily such "Blue" BN is uncapturable but figures fully in capturing opponent and mate. Starting the immortal Blue Queen(BR) or Blue Centaur on e4 will create more a-, b-, and h-file flank-play to avoid her/him, but Pawns may still vie for the center.

I submitted a CV as Blue Queen last fall and will resubmit it in final draft. Blue Queen is the problemists' piece owned by both sides. Actually any of the 2000+ pieces could be introduced this way at central square and available to both on regular 64. This is a whole new class of pieces uncapturable, befitting prefix "Blue." For example, BLUE DABBABAH, or stronger BLUE ALIBABA, not two per team or even one per side, but one for both shared at e4, or d4 or e5 or d5.

Or Gilmanesque BLUE MIRROR WAZIR CAMEL ALTERNATOR, starting at e4, and thus moving Camel-Wazir-Camel...stopping on either type of leg -- and movable by either player (because Blue). By extension, we could carefully sprinkle very large boards with several these very best available immortal Blue pieces, not too powerful to disrupt judicious play.

(On small 8 by 8 the Blue Queen or Blue Centaur phase starts Move 11, precluding 1 e4xe7 #. Blue Centaur quick mate is 1 e4-f6 #, dis-allowed by having ten normal opening moves then up to five optional Blue moves to end.)