Puzzle of the Week #96 - Self Working Trick

The following is a self-working card trick I invented a few years ago for my daughter to perform.

In the instructions below I have left out a crucial piece of information – what is the value of ‘x’? (Technically there are 3 possible answers, but I’m looking for the smallest of those).

 

Take a normal pack of 52 cards, well shuffled.

Discard the first ‘x’ cards.

Deal the remaining cards into 3 equal piles.

Ask the mark to choose one of the piles to discard.

Ask the mark to choose another pile. Show them the card on the bottom of that pile and then place that pile on top of the other remaining pile (so that the target card is roughly in the middle of the pile).

Deal all of the cards into two piles, left-right-left-right-etc.

Pick up the right pile and again deal them left-right-etc.

Continue until all but one of the cards is in the left pile. The card remaining in the right pile is the target card.