Not worth a rap. The rap was a base halfpenny, intrinsically worth about half a farthing, issued for the nonce in Ireland in 1721, because small coin was so very scarce. There was also a coin in Switzerland called a rappe, worth the seventh of a penny.
“Many counterfeits passed about under the name of raps.” —
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894