Whenever a player chooses one or more targets, each player reveals the top card of their library. The player who reveals the card with the highest converted mana cost may change the target or targets. If two or more cards are tied for highest cost, the target or targets remain unchanged. Changing targets this way doesn't trigger abilities of permanents named Psychic Battle.
10/4/2004 You can change all, some, or none of the targets.
10/4/2004 You can’t change the number of targets, choose an illegal target, or make something get targeted more than once.
10/4/2004 An empty library will have no card to reveal, so a player with an empty library has no card to compare. The effect looks for the highest cost card of the cards that actually are revealed.
4/18/2017 The converted mana cost of a split card is determined by the combined mana cost of its two halves.