Green’s Dictionary of Slang

rich adj.

1. [early 19C+] surprising, highly unlikely; usu. that’s rich.

2. [mid-19C–1910s] (US) pornographic.

3. [mid-19C+] very funny, absurd; esp. used ironically.

SE in slang uses

In compounds

rich face (n.) (also rich nose) [seen as the product of a diet of rich food]

[late 17C–early 19C] a red and/or heavily acned face or nose.

rich friend (n.) [euph.]

[early 19C] a prostitute’s keeper; i.e. a wealthy man rather than a pimp.

rich one (n.) [the term was used by upmarket prostitutes with ref. to the wives that their clients dared not leave altogether]

[late 19C] a wealthy, but unloved wife.

In phrases