Over-under shuffle cycle length for 14 cards

A simple shuffle works like this: hold the deck face down and deal the cards one at a time from the left hand to the right, placing the 2nd card on top of the 1st, the 3rd underneath, the 4th on top, and so on, alternating until every card is moved. Repeating this shuffle on an even-sized deck eventually restores the original order; for instance $4$ cards return after $3$ shuffles, and decks of $2,4,8,16,32,64$ cards return after $2,3,4,5,6,7$ shuffles. How many shuffles bring a $14$-card deck back to its starting order?

$14$. Writing the shuffle as a permutation of the $14$ positions, it turns out to be a single $14$-cycle, so its order is $14$. A direct simulation confirms the deck first returns to its original order after $14$ shuffles.