Victor shuffles a standard 54-card deck, then flips over cards one at a time onto a pile, stopping after the first ace. However, if he ever reveals a joker he discards the entire pile, including the joker, and starts a new pile; for example, if the sequence of cards is 2-3-\text{Joker}-A, the pile ends with one card in it. Find the expected number of cards in the end pile.