Kevin Pacey wrote on Fri, Jul 21, 2017 10:16 PM UTC:
To give a theoretical case where a king does happen to outperform a minor piece under such an allowed swapping of a king condition, let's pretend that in the following (linked) diagram it's okay for Black to be playing without a king. The winning objective is to be the first to promote a pawn (if deemed impossible, then it's a draw, though if a player has no legal moves then he loses if he has less pawns). In this position I may be wrong, but I think White wins by attacking the Black queenside pawns with his king, and no matter how Black tries to defend he will eventually end up in zugzwang thanks to the given pawn structure. Of course, there are countless other positions with an equal number of pawns where the bishop either draws or wins, besides losing:
To give a theoretical case where a king does happen to outperform a minor piece under such an allowed swapping of a king condition, let's pretend that in the following (linked) diagram it's okay for Black to be playing without a king. The winning objective is to be the first to promote a pawn (if deemed impossible, then it's a draw, though if a player has no legal moves then he loses if he has less pawns). In this position I may be wrong, but I think White wins by attacking the Black queenside pawns with his king, and no matter how Black tries to defend he will eventually end up in zugzwang thanks to the given pawn structure. Of course, there are countless other positions with an equal number of pawns where the bishop either draws or wins, besides losing:
http://play.chessvariants.com/pbm/drawdiagram.php?code=8%2Fp1p3p1%2F5b1p%2F8%2F8%2F4K2P%2FP1P3P1%2F8