# Card game: How much will you pay to gamble?

You turn over the cards 2 at a time, if they are both red, you keep the cards, if they are both black I keep the cards. If one is red and the other is black then neither you nor I get a card. If you have more cards then I you win \$100 otherwise you win nothing. What is the maximum amount you are willing to pay to play this game?

• How big is the deck? – Gerry Myerson Feb 15 '14 at 5:47
• 52 cards - a regular deck – Random Feb 15 '14 at 5:49
• OK, maybe you should edit that information into the question. But maybe one way to approach the problem is to solve it first for a 2-card deck, then 4-card, 6-card, looking for a pattern or a recursion. – Gerry Myerson Feb 15 '14 at 5:50
• okk. Thanks! Can you give me an example? My math skills are rather poor.. – Random Feb 15 '14 at 5:51
• Actually, the question I should have asked was, how many red cards in the deck, and how many black? If the numbers are the same, then for each time there are 2 red cards turned over, there must be a time when two black cards are turned over, so you never win, and shouldn't pay anything. – Gerry Myerson Feb 15 '14 at 5:55