Duke of Edgehill

In the short story The Golden Ball, the Duke of Edgehill is engaged to the wealthy socialite Mary Montresor. Mary, who calls the duke "Bingo", however does not consider the engagement final. She says she got engaged to him "just to see if she could". Everyone had told her it would be difficult but it wasn't. Mary been continuing to set up tests for prospective husbands and "nine and a half" people had already failed the test. The Duke was considered a "half" but she does not explain why--whether he only took half the test, only failed half of it, or even if she considered him only half a man.