Originally posted by Pawnokeyhole
Imagine a variant of standard chess where each player can move the same piece twice on every go.
You might imagine that White, in virtue of starting off, would have an advantage in this situation. And indeed he does!
...[text shortened]... e White piece by way of compensation. What piece should he remove?
But if you can't do that, then we have the following choices: pawn, knight, bishop, rook, queen.
I don't think there's much value in removing a pawn. Removing either a bishop or a rook wouldn't be as effective as removing the queen, because the queen is basically a bishop and a rook combined. Removing the opponent's queen is always a good thing, so queen would be a good choice.
Knights are notoriously tricky to maneuver into place, but when they are in place they exert enormous pressure. They don't require line-of-sight to capture, and it's possible to fork several pieces at once. They can also use their 2-move advantage on the first move by jumping over the row of pawns.
So I think either the queen or a knight would be the best choice, and strangely enough I think removing a knight would be most effective.