Before Becoming A Card Shark, You Need To Know This Method - Part 2

Alice, Bob, and Charlie are all sorting standard poker decks.

Alice looks through the deck until she finds the ace of hearts, then sets it aside and starts over. Now she looks for the two of hearts until she finds it, then sets it aside. She continues in this way until she's put the cards in order.

Bob first sorts the cards into piles by suit (4 piles) and only then sorts them into their final order.

Charlie decides to sort the cards into piles by number instead of by suit before the final sort (13 piles).

The actions they take in sorting the cards take the following amounts of time:

  • moving a card to a pile: n14 \frac{n-1}{4} seconds, where nn is the number of piles we are sorting into,
  • looking at a card to decide what to do: 0.5 seconds,
  • any other "actions" should be considered to take no time.

If they were given 1000 1000 randomly shuffled decks to sort, in what order would we expect them to finish?

Image Credit: Richard Heaven

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