A casino offers a game using a normal deck of cards, which contains 52 cards. Every turn, two cards are drawn. If both cards are black, the cards go to your pile. If both cards are red, the cards go to the dealer's pile. If both cards have a different color, the cards go to the discard pile. These turns are repeated until all 52 cards are drawn. If you have more cards than the dealer, you win 100 dollars, otherwise you lose. How much would you be willing to play this game?

The 52 cards contain 26 red cards and 26 black cards. It does not matter how the game evolves, at the end you will always end up with the same number of cards as the dealer. The discard pile will have the same number of red and black cards. Therefore, your pile should have the same number of black cards as the dealer has red cards. Not less, not more. Therefore, the dealer will always win.

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