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Also, if we were requiring that friendly Bishops occupy squares of opposite colors, it could be possible to deduce that the last Bario on light-colored squares (or dark) has to be a Bishop. If there were four Barios left, two on light and two on dark squares, being a Knight, a light-square Bishop, and two Rooks, and I move one of my light-square Barios as a Knight, that would set of a chain reaction that would define all four pieces -- and, in the version that seems most natural to me, would therefore reset all my pieces, though not my opponent's. One reason I like the idea of requiring opposite-color Bishops and independent, one-player resets is that it would make this kind of combination more likely, and more desirable.
I just had another thought: what if captures with Barios were obligatory? No, that wouldn't work, unless you change the geometry and opening setup. But oh, what combinations ...