Average value of one card, aces low at one

Question

Draw one card at random from a standard 52-card deck. Number cards 2 through 10 are worth their face value, each face card (jack, queen, king) is worth 10, and each ace is worth 1.

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

Accepted Answer

Expected value here is the total of all card scores divided by 52. Every suit scores the same, so 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 10 each add 30. - The ace is worth only 1. One suit totals 54 + 30 + 1 = 85 points. Four suits give: 4 	imes 85 = 340 	ext{ total points.} Divide by 52 cards: EV = \frac{340}{52} = \frac{85}{13} \approx 6.54. The only change from the aces-high version is that each ace dropped from 11 to 1, a loss of 10 points per ace across four aces, which is 40 fewer points in th…

Average value of one card, aces low at one

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