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The problem, if any, would be that it is always the Anti-King which gets checkmated, and that the King is here only to prevent the players from discarding all their pieces or to lose by double check. So, if you want to checkmate the King nearly as often as the Anti-King, it's no use weakening the Anti-King by allowing the enemy pieces to jump it. Stronger armies, say with a Cardinal and a Marshal on a 10x8 board - not 10x10 which also weakens the Anti-King, unless you post the Pawns on the third line as in Grand Chess -, make the King more vulnerable, but the setups of Capablanca Chess or Gothic Chess make it also more difficult for the Anti-King to avoid mate, because the Cardinal and Marshal have less difficulty in escaping the zone of the Anti-King than Rooks, Bishops or Knights, and it might be better to report them on the outer files.
Actually, when I play, the anti-King isn't always the one that gets checkmated. I think initiative plays a large role - if you can force the anti-King to move around, you can move your pieces in for a checkmate without obstruction, or at the very least, severely impede your opponent's development. I alternate fairly equally between which enemy king I checkmate at the end. An interesting case that can occur in Anti-King chess is a sort of checkmate of both the king and anti-king. In a game I played with the Java program, a pawn was checking the anti-king, but I moved it forward to check the king. The pawn wasn't protected, so the king could take the pawn, but that would leave the anti-king without check. Inversely, the anti-king could have moved into check, but the king would still remain checked as well. This, of course, demonstrates that a single pawn can force mate. Quite an interesting game.
Though V.R.Parton is mentioned in 2002-2004 comments and the write-up, Anti-King is extreme form of his CONTRAMATIC Chess 1961, not yet cited: (Summarized from p.70 Pritchard's ECV) (1)One's own move, that puts or leaves enemy King in check, loses. (2)If opponent's King is in check, a player must move to remove that check. Of course Aronson's version has King too and required continual checks for A-K etc., but it looks like special case with new array from among Parton's Contramatic games.
I've got a question considering mate. What happens when a player mates the other player in the same move its own anti-king gets unchecked (thus being mate too). Who wins then?
'The rules of Anti-King Chess I are identical to those of FIDE Chess, except for the addition of an Anti-King for each side, the movement of the Pawns, the King's special move, and the initial setup.'
'The Anti-King is a King that is in check whenever it is not attacked by opposing pieces. If a player ends their turn with their Anti-King not attacked, they are checkmated and lose.'
It would be simpler to state that it is illegal to make a move leaving or placing your Anti-King in 'check', that is, not attacked by opposing pieces.
I've got a question considering mate. What happens when a player mates the other player in the same move its own anti-king gets unchecked (thus being mate too). Who wins then?To repeat what David says in different words: you can't do that. It's the equivalent in regular Chess of moving your King into check in order to check the opponent's King.
It would be simpler to state that it is illegal to make a move leaving or placing your Anti-King in 'check', that is, not attacked by opposing pieces.Well, very likely. I tend to err on the verbose side in my writing.
No, Anti-Kings neither check nor checkmate Kings.
Here is a CV with two Kings like Muller's example for negative-value piece. In Anti-King win is by checkmate of regular King or removing check from other's Anti-King. Two other CVs with two Kings are Two Kings Chess and Double Chess.
Both Aronson's Berolina Pawn version and Anti-King Chess II have strategy to keep the side's Anti-King in check. In AKC-I with Berolina note that Anti-King is initially attacked by four pieces checking, and it will take a while to get them "safely" out of the way. Anti-King Chess II may benefit from changing Anti-King move to Knight move only as subvariant.
How do these relate to negative values? That pieces may want to be removed, if possible, in end game in order to have no forces nearby to attack opponent Anti-King, but their over-all average value would be positive just taking on negative value at end. Player may just settle for checkmating regular King.
Fergus Duniho's insightful strategy for actual game played 13 years ago: Strategy, where few pieces were captured.
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