"The dealer is known to deal cards from a deck that is comprised of 10 standard card decks. This means that there are 40 of each rank of card and 520 total cards. The dealer plays a game where he shuffles all 10 decks together randomly, and then he starts turning over cards from the top of the deck. Once he turns over 5 kings, the game is over. You win the game if you are closest to how many cards total (including the final king) the dealer turns over before the game ends. How many cards would you guess to maximize your chances?"
My solution is as follows: it is equally likely for a King to appear anywhere in the deck as well as any other card, so we can use a symmetry argument. There are 480 cards that aren't a King, meaning that there are in expectation 480/41 cards in between Kings. Therefore, the answer is 480/41*5 + 5 (to add in the extra 5 kings) ~ 63.5, so we choose 63. The answer is 53, and they do not use symmetry. Why is my answer incorrect?
The answer description is attached in this screenshot.
