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Playing card summary

March 28, 2014

When studying probability, most textbooks have questions using playing cards as the objects of interest.

Some students come from (family or cultural) backgrounds which means they have no experience of cards, which means that solving problems with playing cards is itself a problem for them.

So, here is a simple summary of the standard structure of a deck of cards.

Colour

Black

Red

Suit

Spades

Clubs

Diamonds

Hearts

Rank

(See note)

A

A♠

A♣

A♦

A♥

Number cards

2

2♠

2♣

2♦

2♥

3

3♠

3♣

3♦

3♥

4

4♠

4♣

4♦

4♥

5

5♠

5♣

5♦

5♥

6

6♠

6♣

6♦

6♥

7

7♠

7♣

7♦

7♥

8

8♠

8♣

8♦

8♥

9

9♠

9♣

9♦

9♥

10

10♠

10♣

10♦

10♥

Face
cards

J

J♠

J♣

J♦

J♥

Q

Q♠

Q♣

Q♦

Q♥

K

K♠

K♣

K♦

K♥

Note: Most people (and many but not all textbooks) classify Aces (A) as number cards (equivalent to 1). One textbook classified Aces as face cards (which seems silly to me – there’s no face).

So, in a pack, there are
– 52 cards (we have excluded two common extra cards, called Jokers)
– 26 red cards and 26 black cards.
– 4 suits – spades, clubs, diamonds and hearts.
– 13 cards ‘ranks’ – A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (Jack), Q (Queen) and K (King).
– 3 face cards (J, Q and K) in each suit, making 12 face cards in the whole pack.

The table above lists cards in what is commonly taken as ascending order, with each row containing cards of higher rank than previous rows. Some card games use Aces as the highest card, but this order is not used in textbooks I’ve seen.

For example,
– you have a probability of 2/52 that a randomly selected card from a full pack is a red 10.
– if you select an 8 card, the probability of someone selecting a higher ranked card (from the remaining 51 cards) is 20/51.

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