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Hi Aurelian
I was going by H.G.'s comment suggesting the lieutentant to me on the 13th November in the Diagram Testing Thread. You subsequently asked if he was correct on the Betza notation he gave for that piece (you mentioned the captain piece type in Spartan Chess in your question , but I assumed you meant the lieutenant). I cannot seem to find other discussion about the lieutenant piece type, except for when I subsequently named that piece myself at other times.
No matter, it is not importan, I do remember thinking it is a good idea but not much besides that :)!
I've added (to the Notes Section of this game's page) a paragraph about the mutator variant possibility of substituting champions (also known as WADs) for the waffle pieces used in this variant, in case anyone ever wishes to experiment. I've also made a note that a WAD+K can force mate against a lone K on a 12x8 board, as Dr. Muller once related.
[edit: Note that another mutator variant idea of mine (Wide Frog Chess) would be Wide Chess to be played with Frogs in place of the Lieutenants in the setup. Frogs move like threeleapers (leap 3 cells by rank or by file) or move like ferz' (stepping one cell diagonally). On 12x8 I'd put a frog at 3.33(or 3.5 approx.).]
Here's a (10x8) variant I stumbled onto that has castling rules somewhat similar to that of Wide Chess, in that a king may pass over squares under attack (though not finishing on such a square, nor is castling legal if the K is initially in check). So, a sort of precedent for (part of) the special fast castling rules used in Wide Chess (and subsequently in a number of other CVs I've invented since):
https://www.chessvariants.com/large.dir/21st-century-chess.html
Here's another sort of precedent, perhaps, in that in the following (12x12) CV, a king, if not in check, may (with its initial move only) leap to an unoccupied (& unattacked) square on its back two ranks (including possibly 'over' any attacked square)- though this does not include a change of position by a rook or any other piece, as part of the special leap process:
I quite like the simple approach you have to this variant.
However, both the working elephant and the lead elephant are fairly similar pieces. They are both very good pieces, but I would think in a game with standard chess pieces +2, that the 2 additional pieces would be better off more divergent.
Just a thought....
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Are you sure it is not I who has suggested the Spartan lieutenant? I remember at least reinforcing the idea. But please don't change the article for such small minutia :)!