ΔE 36.3, loose: different enough that you should pick on purpose. Forged Red is a little darker, more muted, warmer than Rich Gold.
Not as a straight swap; see the closer alternatives below. Loose match (ΔE 36). Forged Red is a little darker, more muted, warmer than Rich Gold.
The same difference applies the other way round: Rich Gold is a little lighter, more saturated, cooler.
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 Rich Gold on the colour wheel See Forged Red on the colour wheel
All matches: Rich Gold equivalents · Forged Red equivalents