ΔE 19.3, loose: different enough that you should pick on purpose. Let Them Eat Cake is a little darker, more muted, cooler than Royal Purple.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 19). Let Them Eat Cake is a little darker, more muted, cooler than Royal Purple.
The same difference applies the other way round: Royal Purple is a little lighter, more saturated, warmer.
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 Royal Purple on the colour wheel See Let Them Eat Cake on the colour wheel
All matches: Royal Purple equivalents · Let Them Eat Cake equivalents