I draw a card from a standard 52-card deck. If I draw an Ace, I win 1 dollar. If I draw a 2 through 10, I win a number of dollars equal to the value of the card. If I draw a face card (Jack, Queen, or King), I win 20 dollars. If I draw a club, my winnings are doubled, and if I draw a spade, my winnings are tripled. (For example, if I draw the 8 of clubs , then I win 16 dollars.) What would be a fair price to pay to play the game? Express your answer as a dollar value rounded to the nearest cent.
+23251 If you draw a diamond, the cards are worth: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 20, 20
If you draw a heart, the cards are worth: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 20, 20
If you draw a club, the cards are worth: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 40, 40, 40
If you draw a spade, the cards are worth: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 60, 60, 60
Adding these together, you get: 115 + 115 + 230 + 345
The total of all the card are 595.
Since there are 52 cards, the average value is 595 / 52 or 11.44230... or 11 23/52
which is the fair price.
Rounded to the nearest penny: 11.44 (which actually gives the player a slight advantage).
