You pick a card at random from an ordinary deck of 52 cards. If the card is a diamond, you get some points; if not, you lose 2 points. What value for the diamonds would make the game fair?

A fair game has an expected score of 0. There are 13 diamonds and 39 non-diamonds, so the expected score is (13/52) × value + (39/52) × (−2). Setting this equal to 0 gives value = 6 points. Therefore, 6 points makes the game fair.

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