I was just shown this card trick.
Let me attempt to explain: You begin by shuffling a standard 52 card deck.
After it is shuffled decently enough for your audience, lay down the first card face up, and then count up from the value of that card to 13. For example, I draw a 9, I then draw 4 more face up cards (9 + 4 = 13) and add these cards to the pile. You continue this until you are out of cards or you can no longer count up to 13.
At this point you put all these piles but 3 arbitrary piles together. Of the 3 remaining piles, turn over the top card of two piles. From the discarded cards from earlier (the other piles plus the remainder) you remove 10 cards plus the value of each of two face up cards. For example, if the two face up cards are 4 and 9, I remove 10 + 4 + 9 = 23 cards from my hand.
The number of cards left in your hand will be the value of the face down card of the third pile.
What exactly is the math behind this trick? I haven't been able to find a single explanation for this trick. Thanks!