This is a very powerful two-spectator coincidence effect, where one spectator selects (and loses) a card under very fair conditions, and then a second spectator impossibly locates the card. I will teach two versions, one in which the second spectator can't look at the card they reverse under the table and one in which they can. (The effect description and conditions below are for the former version.)
Imagine:
The magician introduces a deck of cards - he spreads it face-up to display that all the cards are different. He then hands the deck over to one of the spectators and asks them to thoroughly shuffle the deck. They can shuffle in any way that they want.
The magician then says, "I want you to make a free choice of any card in the shuffled deck. Simply spread the deck face-down across the table and slide out any card - that will be your selection. Don't show it to anyone; only look at it yourself. Then, replace the card anywhere inside the spread and square up the spread.
The spectator does as instructed. Once done, the magician instructs them to thoroughly shuffle the deck again so that even they don't know where their card ends up. They can shuffle in any way that they choose, and as they shuffle, the magician looks away so that he can't possibly shuffle track.
After the shuffling is complete, the magician turns back around and asks the spectator to hand the deck over to the second spectator. The second spectator is then instructed to bring the deck under the table and to reverse any card sight unseen. They are to reach into the deck, pull out any card, turn it face-up (without looking at it) and slide it somewhere into the middle of the face-down deck.
After they've done that, the magician takes back the deck as he says, "You [the first spectator] selected any card at random, which you then freely shuffled into the deck. After that, you [the second spectator] took the deck under the table and blindly reversed a card. You could have reversed any card." The magician then has one of the spectators spread the deck face-up across the table, revealing one face-down card in the middle of the spread.
At this point, the magician turns to the first spectator and asks them to entertain the idea that, by some miracle, the second spectator selected the same card as them. Of course, they're very skeptical of this proposition. They name their card out loud for the first time, after which one of the spectators turns over the sole face-down card for the impossible reveal. (There are no other hidden face-down cards in the deck - the spectators can immediately examine the deck to verify this.)
Some important conditions of note:
