[High School - Calculus/Algebra/General Math] Card Shuffling Problem

[aTzUeLo1191]

Today our Calc teacher gave us a practice quiz for the upcoming year. On the quiz were a couple of trick problems that seemed hard but once you found out how to do them, they were much simpler. One of the problems, however, has given me a headache because I have been thinking throughout the day what the answer could be.

The question: if you shuffle a deck of cards perfectly starting with the left hand on top (meaning the first shuffle will be A,A,2,2,3,3,4,4 and so on), how many times will you have to shuffle it to return to its original position?

I did a few perfect shuffles, and I kept track of the 2nd card, the 2 of Spades. After a while, I noticed that the distance it travels throughout the deck keeps doubling - after 0 shuffles, its the 2nd card, after 1 shuffle its the 3rd card, after 2 shuffles, its the 5th card, and so on.

Now comes the tricky part. Because my numbers go past 52 and keep getting larger, its obviously not going to come back to the 2nd position. Will I know that the card has reached its original position when its place in the deck is a multiple of 52 plus 2 because its the 2nd card, or is it plus another number? Or, is my math totally wrong and I need to start from scratch? Please, any help (without giving me the answer, I want to find it myself for future problems) would be much appreciated.