Average value of one card, aces high at eleven

Question

Draw one card at random from a standard 52-card deck. Score it like this: number cards 2 through 10 are worth their face value, each face card (jack, queen, king) is worth 10, and each ace is worth 11.

What is the average point value of the card you draw?

Accepted Answer

Expected value is the average score over all 52 equally likely cards. A clean way to get it: add up the scores of all 52 cards, then divide by 52. Every suit is identical in value, so I will total one suit and multiply by four. In one suit: - The number cards 2 through 10 sum to 2+3+4+5+6+7+8+9+10 = 54. - The three face cards are worth 10 each, adding 30. - The ace is worth 11. One suit totals 54 + 30 + 11 = 95 points. Four suits give: 4 	imes 95 = 380 	ext{ total points across the deck.} Divide by the 52 cards: EV = \frac{380}{52} = \frac{95}{13} \approx 7.31. So a random card is worth abo…

Average value of one card, aces high at eleven

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