Half-mages are either the strongest or the weakest people of a civilization. To be a half-mage is to have either all of the strengths of a normal mage or all of the weaknesses.
One does not typically know that he or she is a half-mage until puberty. At that point, either powers emerge or weaknesses become apparent.
It has been common throughout the centuries to send weakness half-mages on dangerous missions or have them fight each other to the death. Power half-mages have typically been used as long-range soldiers, or in some cases front-line commanders with a considerable bodyguard.