Average value of one card, faces twelve and aces fifteen

Question

Draw one card at random from a standard 52-card deck. Number cards 2 through 10 score their face value, each face card (jack, queen, king) scores 12, and each ace scores 15.

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

Accepted Answer

Expected value is the deck's total score divided by 52. Since all four suits score identically, total one suit and multiply by four. In one suit: - Number cards 2 through 10 sum to 2+3+4+5+6+7+8+9+10 = 54. - Three face cards at 12 each add 3 	imes 12 = 36. - The ace scores 15. One suit totals 54 + 36 + 15 = 105 points. Four suits give: 4 	imes 105 = 420 	ext{ total points.} Divide by 52 cards: EV = \frac{420}{52} = \frac{105}{13} \approx 8.08. The premiums on the special cards (faces at 12 instead of 10, aces at 15 instead of low) push the average up to about 8.1 points. Takeaway. Raising …

Average value of one card, faces twelve and aces fifteen

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