It's a nice trick...
Back when I was into magic (long ago) that trick was known as "The Invisible Deck".
The reason it is called that, is because of the original "patter", which was geared
around an invisible deck of playing cards. It went like this:
Here I have an invisible deck of playing cards in my hands. Please take it, and hold it.
OK, open the deck, select any card and remember what card it was. OK? Now turn
the card over, and put the card in the deck backwards (or upside down). Now put the
cards back in the box.
Then the magician takes out another (real) boxed deck of cards from his pocket, and
asks what card did you select? The person tells him the card, (which doesn't matter, it
can be any card) and when the magician opens up the real box of cards, and fans them
out, the card that the person selected is indeed reversed also!
In case you can't find the trick, or wish to make a few decks, search out a product called
"roughing fluid". It will allow you to make such a deck from a regular deck of cards, and
also make many other similar tricks.