Chess on an Infinite Plane (hitthepin - captaintugwash)

Well there's the "Four Hawks opening" where both white and black quickly develop the hawks to the squares behind king and queen, before moving anything else. That would be an interesting battle in the centre.


Then there's the "Pi opening" where white moves the queen backward to square (4, -3141592654), perhaps further back if we wishes to waste this tempo more accurately.

Not sure about this, the chancellor would be subject to a developed attack from the bishop after 2. (4,4), white gets a strong centre while black is forced to move the chancellor twice. Unless he values the bishop over the chancellor, of course. It might be an interesting tactical gambit, but I wouldn't go for it with my current understanding of this format.
Probably best to wait for the board...