When someone is not playing with a full deck he is either mentally, psychologically or intellectually deficient.
The deck referenced in not playing with a full deck is a deck of cards. There is a popular story that the origin of this phrase dates back to the 1500s, when a tax was levied against decks of cards. People would get around the tax by purchasing decks of 51 cards instead of 52 cards, thereby not playing with a full deck.
He may be an intelligent person, but some of the things he does gives the impression that he is not playing with a full deck.