What does "never give a sucker an even break" mean?

Don't allow a person who's easily duped a fair chance, as in He's always trying to give out expired coupons for his store, firmly believing in never giving a sucker an even break. Probably a direct quotation, it has been attributed to showman P. T. Barnum (responsible for the oft-quoted “There's a sucker born every minute”); and comedian W. C. Fields (who popularized it in one of his films); and theater manager Edward Francis Albee, the most probable of the three. [Slang; early 1900s]