Green’s Dictionary of Slang

insignificant, worthless, pointless.

1938		D. Runyon ‘A Very Honorable Guy’ in Runyon on Broadway (1954) 413: He is a guy I consider no dice. In fact, he does not mean a thing.
1944		J.T. Farrell To Whom It May Concern 25: I wrote two pages of the second chapter of my novel. I re-read it. I fear it is just no dice.
1950		R. Service ‘McClusky’s Nell’ in Rhymes of a Roughneck 15: Ye know this camp’s a den o’ sin, ye know that Dud’s no dice.