Medium

Probability

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 $\textbf{maximize your chances}$? Note that this is different than the expected value.

Notes

Hint