This is an extremely simple trick I published in Cardopolis (1984) in which both your selected card and the spectator’s becomes reversed in the deck. Despite the simple means involved the effect is a stunner for laymen. It is directly based on Walter Gibson's Double Reverse which can be found in Annemann's Miracles of Card Magic. See the new Dover edition. It was David Bentley of Chester who first showed me the original effect many years ago.
METHOD: Give the deck to a spectator and ask him to shuffle it, cut it into two halves and give you one half of the deck. You then both shuffle your respective halves and whenever the spectator feels, the cards are sufficiently mixed he is to look at the bottom card of the packet and place it face down on the table in front of him.
By way of example you turn over your packet and point out that the card on the face of the packet is, let’s say the Ten of Spades. Now ask him to look at the bottom card of his packet, emphasising that he need not show you the card, and having memorised it he is to place it face-down on the table.
As soon as the spectator does this you perform a double lift from the face of the packet now face-up in your left hand. Deal the top face-down card on the table in front of you. This is an indifferent card and the Ten of Spades is face-down on top of the face-up packet.
Obviously this is illogical but the spectator, occupied with his own task, will not notice what you have done and will assume that the Ten of Spades is the card on the table. When you do it put more emphasis on the fact that you are making no attempt to see which card the spectator is putting on the table rather than what you are doing with your cards.
Now there are two cards face-down on the table. Pick up the spectator’s card and insert it apparently face-down into your face-down packet asking the spectator to do the same with your card and his packet.
Once more the spectator will be one step behind you and when he is busy inserting your card in his packet you flip your packet over by inserting the left thumb under the cards to lever them over. Your right hand covers the turning of the packet and then lifts takes the packet from the left hand and places it on the table.
When the spectator has completed the action you ask him to follow suit and put his cards on the table. You now place your cards on top of his. Then pick up the deck and cut one quarter of the cards from the bottom to the top.
Recap on what has happened. Two cards have been selected and lost in the deck. Your's was the Ten of Spades. Ask the spectator for the name of his selection. Spread the deck across the table and reveal that the two selected cards are now face-up in the face-down spread. It happens so quickly that it appears to be completely impossible.
NOTES: The differences between this routine and the original are that at no time do the cards actually go behind the back and more importantly the spectators do see your selected card at the beginning of the trick. It's very simple but very effective.