The Trick Collector

Before watching the performance it is recommended to read the clarification below first. Craig Petty from Magic TV has a tutorial explaining the how, not the why. The information below enables you to understand what goes on while all steps are executed. The video starts with 2 piles, each exactly 26 cards (52 in total, no jokers). Craig counts them while talking. The spectator selects a pile and takes an unknown number of cards out (14 in the performance). Thats the number in A ny C ard A t A ny N umber. Next the 26-14=12 are put back on the table. Then Craig asks the spectator to choose a card from his pile (26 cards). That is the selected A ny card (8 ♣ ) . When the card is taken back he controls it to the bottom (convincing control, vid5 and 9 here ) at position 26 ( this is the key to the secret ). Then the 26 cards are put on top of the 12 cards. Now there are 12+26=38 cards on the table, chosen card at position 26. The visual below shows the pile simplified, start order left...

Classic with 2 decks & secret. The logic is  ACAAN related. 4 suits x 13 =52 Performance and explanation visualized (VIDEO)  and the secret revealed (MATH) Suppose you start with 3 cards x, y and z. Then the 1st pile has 13-x+1 cards. The 2nd pile has 13-y+1 and the 3rd 13-z+1. So, the number of cards in the 3 piles is 13-x+1+13-y+1+13-z+1 = 42-(x+y+z) ⟺ The number of cards not in the 3 piles is 52-(42-(x+y+z) = 10 + (x+y+z) ⟺ When you put away 10 cards the remainder is x+y+z