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"Once the king has moved as that piece to get out of check, can that same piece be used to get out of check again, or would they have to have another knight (or whatever piece it was)?"
The answer is yes, that captured piece could be used to Imposterize your King again.
As expected, this would make it very difficult for your opponent to Checkmate you! Of course there still could be some things to work out. I'm always open to suggestions for this new game idea, so feel free to speak your mind :·)
"Also, i'm assuming the king could only move like this when in check?"
(ascunde) Dacă vrei să te joci cu un jucător de aceeaşi nivel poţi seta BKR ul necesar la o nouă invitaţie .nimeni care u are BKR ul cerut nu va putea accepta invitaţia la acest joc nou. (Katechka) (arată toate sfaturile)