To lose out; to get less than one is entitled to. Exactly what kind of stick is being referred to is no longer known, but possibly it is one used in fighting or in a tug-of-war, in which the person holding the longer end has the advantage. “He having gotten (as we say) the better end of the staffs, did wrest our wills at his pleasure,” wrote Thomas Jackson in 1626
(Commentaries upon the Apostles Creed). Around the turn of the twentieth century in America, “the short end” of anything came to mean the inferior part, and soon this was combined with “stick” to yield the current cliché. See also
wrong end of the stick.