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Draw one card from a standard 52-card deck. Assign values: A=1, 2-10 face value, J/Q/K=10. What is the expected card value?
| Card(s) | Value | Count | Probability | Value × P |
|---|---|---|---|---|
| Ace (A) | 1 | 4 | ||
| 2 | 2 | 4 | ||
| 3 | 3 | 4 | ||
| 4 | 4 | 4 | ||
| 5 | 5 | 4 | ||
| 6 | 6 | 4 | ||
| 7 | 7 | 4 | ||
| 8 | 8 | 4 | ||
| 9 | 9 | 4 | ||
| 10 | 10 | 4 | ||
| J, Q, K (face) | 10 | 12 |
Number cards (A through 10): Each appears 4 times.
12 face cards (J, Q, K), each worth 10:
The expected value of a randomly drawn card is about 6.54.
If Ace counts as 11 instead of 1 (like in blackjack for soft hands):
The expected value (6.54) is higher than the median card value (6) because the face cards all count as 10, pulling the average up. This asymmetry is important in card games like blackjack.