1.(4,4)
Chess on an Infinite Plane (vickalan - captaintugwash)

Btw: notice the new castling rule. Let me know if it's OK or not, or if you want to make a different rule for it. Once it's settled - good luck!

Finally I get to play vickalan!
I'm very happy with this "castling" rule (though "guarding" seems a better term!), it's precisely what I suggested a couple of years ago!
Good luck.
1... Q(4,26)

I remember you asking about castling. Evert also once said the guard is a good king defender, so it seems natural that the king jumps next to the guard for help. They're both slow movers so if there is a castle they may win or die side-by-side.😅

I'm calling vacation. Tug: feel free to play at your pace, I should return around February 11, where I'll play normally again.

If there's an opponent, I can mod the game. I placed a request (here) to see if there's someone to play against you.
Tug is the World Champion of "Infinite Chess" (tournament details here) so in this non-rated game, I'm playing White.
Game rules:
The Pieces:
Black and White each have the following pieces (quantity and name):
1 king
1 queen
2 chancellors
2 rooks
2 bishops
2 knights
2 guards
2 hawks
24 pawns
All pieces move as in classical chess, with the "extra" three pieces moving as follows:
Chancellor (C) - Moves and captures as rook + knight.
Hawk (H) - Leaps exactly 2 or 3 squares in any orthogonal or diagonal direction. The leaping move means it can jump over other pieces.
Guard (G) - Moves and captures the same as a king but is not affected by check.
Pawns play the same and promote at the same rank as in classical chess. White pawns promote at rank 8, and black pawns promote at rank 1. Pawns can promote to chancellor, hawk, or guard in addition to queen, rook, bishop, or knight. Pawns may capture and be captured en passant with the same rules as in classical chess.
Board Setup:

Castling: King castles with the guard (rather than the rook). All other rules of castling are the same as in classical chess. (New rule introduced in this game)
There is no fifty-move rule. Draws can only occur from stalemate, threefold repetition, agreement, or a proven case of insufficient material to force checkmate.
All other rules are the same as in classical chess.
Move Notation:
Numeric coordinates are used to identify piece locations as (file#, rank#). Parenthesis are used around each coordinate. Three examples of a move notation:
1) A rook moving from (8,4) to (1,4):
R(8,4)-(1,4) or R(1,4)
2) A rook moving from (1,4) and capturing a piece on (0,4):
R(1,4)x(0,4) or Rx(0,4)
3) A pawn advancing from (-1,7) to (-1,6):
(-1,7)-(-1,6) or (-1,6)
vickalan plays White. Good luck to Tug.