What Is a Standard Deck of Cards?

Four kings from deck of playing cards
One king from each of the four suits. Jeanene Scott/The Image Bank/Getty Images

A standard deck of cards is a common sample space used for examples in probability.  A deck of cards is a concrete.  In addition, a deck of cards possesses a variety of features to be examined in a deck of cards. This sample space is simple to understand, but yet can be utilized for a number of different kinds of calculations.

It is helpful to list of all of the characteristics that make a standard deck of cards such a rich sample space.

While anyone who plays cards has encountered these traits, it is easy to overlook some features of a deck of cards.  Some students who are not as familiar with a deck of cards may need to have these features explained to them.

Features of a Standard Deck of Cards

The deck of cards that is being described by the name "standard deck" is also known as French deck. This name points to the deck's origins in history.  There are a number of important features to be pointed out for this type of deck. The main items that are necessary to know for probability problems are the following:

  • There are a total of 52 cards in a deck.
  • There are 13 ranks of cards. These ranks include the numbers 2 through 10, jack, queen, king and ace. This ordering of the rank is called “ace high.”
  • In some situations ace ranks above king (ace high).   In other situations the ace ranks below the 2 (ace low).  Sometimes an ace can be both high and low.
  • There are four suits: hearts, diamonds, spades and clubs.  Thus there are 13 hearts, 13 diamonds, 13 spades and 13 clubs.
  • The diamonds and hearts are printed in red. The spades and clubs are printed in black.  So there are 26 red cards and 26 black cards.
  • Each rank has four cards in it (one for each of the four suits).  This means there are four nines, four tens and so on.
  • The jacks, queens and kings are all considered face cards. Thus there are three face cards for each suit and a total of 12 face cards in the deck.
  • The deck does not include any jokers.

Example

The above information comes in handy when it’s time to calculate probabilities with a standard deck of cards. We will look at a series of examples. All of these questions require that we have a good working knowledge of the composition of a standard deck of cards.

What is the probability that a face card is drawn?  Since there are 12 face cards and 52 cards total in the deck, the probability of drawing a face card is 12/52.

What is the probability that we draw a red card?  There are 26 red cards out of 52, and so the probability is 26/52.

What is the probability that we draw a two or a spade?  There are 13 spades and four twos.  However, one of these cards (the two of spades) has been double counted.  The result is that there are 16 distinct cards that are either a spade or a two.  The probability of drawing such a card is 16/52.

More complicated probability problems require knowledge about a deck of cards as well.  One type of this problem is  determining the likelihood of being dealt certain poker hands, such as a royal flush.