Having a unit/card Masked as it comes into play

Is there any way to make it so a player can pick a unit/card from a list and it comes into play Masked (so as the other player does not know what unit/card you chose)?

Of course, you have to choose the option in the deck: Draw:always face down (or similar, i dont remember now)

I’ve tried doing it with a deck as you suggest and it works okay, but the problem I’m having now is that I need to be able to have an arbitrary number of copies of a card and right now whenever I pick one from the deck it disappears from it. Cloning is a bad idea because it would tell the opponent that you are playing multiples of the same card.