Brain Teasers | Card Game

 Question:

A casino offers a card game using a normal deck of 52 cards. The rule is that you turn over two cards each time. For each pair, if both are black, they go to the dealer’s pile; if both are red, they go to your pile; if one black and one red, they are discarded. The process is repeated until you two go through all the 52 cards. If you have more cards in your pile. you win $100 otherwise (including ties) you get nothing. The casino allows you to negotiate the price you want to pay for the game. How much would you be willing to pay to play this game?

Solution:

No matter how the cards are arranged there will always be an equal number of cards in your pile and the dealer’s pile.

Reason: If you pick one black and one red card then the pair will get discarded, so an equal number of black and red will get discarded. As a result, the number of black and red cards left for you and the dealer is always the same.

Even though it is a tie the dealer will win, hence the dealer will always win the game.

So, one should not pay anything to play this game.

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