A Battle of Wits

As an additional cost to cast this spell, exile two cards from your hand face down.
Name two separate cards. One of the names must be a card exiled from your hand this way, and the other cannot be.
An opponent of your choice then chooses one of the exiled cards, then both are revealed.
If the chosen card was a named card, that player loses the game, if not, you lose the game instead.