Ill-Gotten Gains selection order

[BC]

If I cast Ill-Gotten Gains, is there a specific order in which it will resolve.  To be more precise, my opponent and I simultaneously discard our hands, then do I (the active player) select the three cards I want to return to my hand followed by my opponent doing the same?  Does he get to see the cards I selected before he chooses his cards, or is it completely blinded until all cards have been selected?

[bomholmm]

The active player selects his cards first and the other player does get to see them before choosing theirs.

[Anusien]

In a duel, if both players are ever asked to perform an action simultaneously, the Active Player performs the action, then the Non-Active Player performs the action.  This is part of the APNAP (Active Player, Non-Active Player) Rule.