Question

this one too http://trickiestofall.blogspot.com/2011/07/card-game.html

Answer 1

CARD GAME
Alice ---- "Here's the deal. You give me $10. Then I will deal four cards (from a regular 52 card deck), chosen randomly, face down. You get to look at #1 first and decide whether to keep it. If not, look at #2 and decide whether to keep that one. If not look at #3, and decide. If you don't take that, then #4 is your choice. If your chosen value is n, I will pay you $n. Then we can reshuffle the entire deck, you give me another $10, and we can play again, and again, and again."



Bob ------ "Hmmm....I need a good strategy to beat you at this game, but I think I can do it."



Help Bob out with a strategy that will win. Note that the cards all have face value with the following exceptions: Ace=1, Jack = 11, Queen = 12, and King = 13.

Answer 2

If it is a 8 or above keep it because there are 28 possible cards below your value and 23 cards of equal or greater value so chances are you will lose money by going to the next card.

Answer 3

This applies even if you draw two cards lower than an 8 and then you draw an 8 because there will be 26 cards below your value but 23 above.

Answer 4

Note that the amount you initially paid has no bearing because once you pay your goal is to get the maximum possible money back even if it is less than $10. Also, If you draw a 7 you should still draw again because there are 24 values below verses 27 of equal or greater value.