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I guess the extra move would often make it even more difficult to checkmate though, as such a king could reach more different fields in one round? On the other hand it might sometimes be easier, because such a king wouldn't be able to jump over other figures that are in the way.
I'm not sure how much of a 'revenge' the Mounted King is. The King as Knight is more difficult to maneuver for players used to the regular move. On the other hand, the King is more difficult to checkmate when it is now a Knight, though Chess variantists generally consider the Knight to be slightly weaker than the Commoner which moves like a King. Also, players may not want their King to become a Mounted King if the regular move is more strategically viable for them. Despite the fact that new variants often do not fulfill their intentions, I think this King transformation is something to be considered for other games and as a fun rule variant on boring old Chess.
Thank you all for your comments! :-)
Charles Gilman is right, I didn't intend the undeniable similarity with the Lord of the Rings title. I'm actually from Germany and chose the German title 'Vergeltung des Königs' which differs from LOTR '(Die) Rückkehr des Königs' much more than the English translation does now. I've also written a little introductory story which isn't related to LOTR. I'll probably add an English translation here soon, but I feel a little uncomfortable with it as my English is unfortunately far too bad to be able to preserve the tune of the text. :-\
Thanks for the hint, John Smith. I must admit that I didn't do any calculations or simulation to confirm that the mounted king is capable of a suitable revenge. However, I suppose an equation like (king / mounted king = commoner / knight) might not work here? Both king and mounted king have a restricted offensive quality compared to their non-royal counterparts, as one can never risk losing the royal one. But I'd guess that the king loses more of the commoner's offensive strength than a mounted king loses of a knight's offensive strength.
I'd definitely agree that a mounted king can be weaker than a king sometimes. For example, when being in one of the board's corners, the mounted king can be checkmated by a queen alone. A normal king can't be checkmated by a lone queen, can he? But that's a really defensive non-revenge position. If I'm right, a central mounted king should be stronger than a central normal king and also harder to force to the edge. I might be wrong though.
There's another aspect. While a king can never checkmate another king, a mounted king can checkmate a king* with a little help. Maybe more important for the variant's name, a king cannot take a queen (unless she's suicidal and asks for it), but a mounted king can. I think this might justify the name 'Revenge of the King' even if a mounted king would turn out not to be stronger than a king in general.
Charles, I actually thought of a combination of king and knight moves (so a 'royal centaur') at first myself. But then I thought that such a piece would be much too difficult to checkmate, so I turned to the idea of a mounted king. Does anyone have experiences with checkmating royal centaurs? A centaur could potentially escape to 16 different fields while king as well as mounted king can only reach 8 different fields in one round. If checkmating the second form of the royal piece gets too difficult, players could be inclined not to take the opponent's queen even if they can. This would make the queen an even stronger piece on a balanced field on the one hand and make a queen's loss desirable for a losing player on the other hand in order to force a draw, which might occur too often then.
Uhm, when checking if someone already had invented this variant, I stumbled across Knightmate. It's not the same but it does feature a royal knight which is essentially the same as the mounted king state. So, looking deeper into people's experiences with Knightmate might also give further clues about the strength of this royal figure.
*Of course, a regular king can also checkmate a mounted king. So seeking revenge may not always be the best choice, just as in reality. Rage may lead to one's own downfall.
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