ΔE 11.0, fair: the same colour family, but not a straight swap. Gory Red is a little darker, more muted than Carmine.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 11). Gory Red is a little darker, more muted than Carmine.
The same difference applies the other way round: Carmine is a little lighter, more saturated.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Carmine on the colour wheel See Gory Red on the colour wheel
All matches: Carmine equivalents · Gory Red equivalents