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Even-Uneven variations
The 1d6 system uses a single d6 where even values are added while uneven values are subtracted. Also 6 and 5 both explode, but following rolls are only added if the value is the same again (6 or 5) — can explode multiple times.
As syntax I’d suggest +-d6 (or ±d6 for those who can type that), with +-d6! for the exploding variant.
It can be generalized to +-dN.