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Is there a plain Halfchess, on a 4x8 board? If not I can suggest one, with four Pawnsm=, no Bishops (to avoid asymmetry in square-colour control), and one of everything else. I can also suggest a variant of that with Cardinal-Queen-King-Marshal at each end so that the power of two Rooks, two Knights, and two Bishops is concentrated in just three pieces.
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