David Berglas has been performing a card trick for decades that has been known as the Holy Grail of magic tricks. No, it’s not his famous trick of vanishing a grand piano in a crowded ballroom while the pianist was playing it:
His most amazing trick is a type of ACAAN: Any Card At Any Number. ACAAN tricks consist of a spectator who is asked to name any card in a deck — let’s say the nine of clubs. Another is asked to name any number between one and 52 — let’s say 31. The cards are dealt face up, one by one. The 31st card revealed is, of course, the nine of clubs and the audience is astounded.
There are dozens of ways to achieve this affect, but Berglas does something nobody else has been able to do. For decades he has performed this trick by placing the cards on a table and he didn’t handle them again until after the revelation. All other known techniques require the magician to touch the deck in some way. This trick is so stupendous and so flawless that it seems to demonstrate the seemingly impossible.
Berglas has revealed almost all of his tricks except this one. He even claims that he doesn’t even think he can teach it since it would be like trying to teach someone how to improvise in jazz. It’s a reminder of just how wonderful and full of surprise the world can be.
Update: if you want to see some possible solutions, The Common Magician gives a really good discussion on techniques.