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Have three spectators each chose a card at random from a shuffled deck. Ask each to look at their card and memorize it, but not share the value with the other spectators.
Deal a pile of ten cards on the table, Now, deal a pile of fifteen cards to the right of the pile of ten and then another pile of fifteen cards to the right of this one. Lastly, you should have nine cards left in your hand. Drop them as a pack to the far right of the rest of the packs. Deal all cards face down. Ask the first spectator to put their card, face down, on top of the pile of ten. Ask them to cut as many cards as they want from the middle pack of fifteen and place them on top of their chosen card.
Repeat this with the second spectator, asking them to put their card on top of the first pack of fifteen cards you dealt, and then cut as many cards as they want off the other pack of fifteen and place them on top of their selected card. Ask the last spectator to put their card on top of the second pack of fifteen and cut as many cards as they want off the pack of nine and drop them of top of their selected card, just as the other spectators did..
Pick up what remains of the pack of nine and put it on top of the pack next to it. Put this pack on top of the pack next to it and repeat until all the cards are in one stack. Pick up the stack and, holding it face down, casually move the top four cards to the bottom of the deck. Remind the spectators that you had no control over how many cards they cut off the packs.
Now, deal a card face up on the table and another next to it face down. Ask the spectators to call out when they see their card. Continue to deal cards, one face up on the face up pile and another face down on the face down pile. If no one saw their card, (and they shouldn't have) pick up the face up cards and move them to one side. Pick up the face down cards and repeat the same procedure... a face up card and then a face down card. Eventually, you will be left holding only three cards face down, and guess what? They are the three chosen cards. This is self-working, although it doesn't seem quite possible because of the random way the cards were cut by the spectators.