What is in a standard deck
A standard deck has 52 cards. They split into four suits (spades, hearts, diamonds and clubs), and each suit holds 13 ranks: ace, 2 through 10, jack, queen and king. Two suits are black and two are red, so 26 cards of each colour. Every combination of rank and suit appears exactly once, which means there are no duplicates and no card is more likely to turn up than another.
That last point is the key. A well-shuffled deck is a closed, fully known set of outcomes. Unlike a die roll or a spin of a wheel, you can list every possible card in advance, and the proportions never change unless cards leave the deck. Almost every probability question about cards is a counting question about this one list.
Some games change the list. Many use one or two jokers, some remove cards to make a shorter deck, and some combine several decks into a shoe. Everything below assumes the plain 52-card version, and the same reasoning adapts to the others once you recount.
Single-card probabilities
With 52 equally likely cards, the chance of a specific card is 1 in 52, or about 1.9%. Larger groups are just fractions of the deck:
| Event | Cards that count | Probability |
|---|---|---|
| A specific suit (say hearts) | 13 | 13/52 = 1/4 |
| A specific rank (say aces) | 4 | 4/52 = 1/13 |
| A red card | 26 | 26/52 = 1/2 |
| A face card (jack, queen, king) | 12 | 12/52 = 3/13, about 23.1% |
| A ten-valued card in blackjack (10, J, Q, K) | 16 | 16/52 = 4/13, about 30.8% |
These are the building blocks. Notice how the same deck can give different answers depending on how a game groups cards. Blackjack counts four ranks as worth ten, so 16 of 52 cards behave alike, while in poker those same cards are all different ranks. The deck is fixed; the question is what the rules ask.
Why the odds change as cards leave
Cards are usually dealt without replacement, so the deck shrinks and its make-up shifts. If you draw one ace, three aces remain among 51 cards. The chance that the next card is also an ace is 3/51, about 5.9%, rather than 4/52, about 7.7%. If the first card was not an ace, the next card is an ace with probability 4/51, about 7.8%.
This is the core difference between cards and, say, repeated coin flips. A coin has no memory, but a deck effectively does: each card dealt is information about what is left. Events like these are dependent events, and the idea of conditional probability, which asks how the odds change once you know something, fits naturally. The same shift is what makes any tracking of dealt cards worth discussing in blackjack, though it does not make outcomes certain.
One useful symmetry runs the other way. Before you look at anything, the second card of a shuffled deck is just as likely to be an ace as the first: 4/52. You can check it: the chance of ace then ace is (4/52) x (3/51) = 12/2652, and the chance of non-ace then ace is (48/52) x (4/51) = 192/2652. Together that is 204/2652, which simplifies to 1/13, the same as 4/52. Position in the deck does not matter unless you have seen cards.
Counting hands
Questions about whole hands need counting methods rather than single fractions. The order in which cards arrive often does not matter for the hand you end up holding, so the relevant tool is combinations. The number of different five-card hands is 2,598,960. The number of different 13-card hands, as dealt in bridge, is 635,013,559,600. Both come from the combinations formula, covered in more detail in material on permutations combinations and on factorial notation.
Five-card poker hands are the classic example. Each of the 2,598,960 hands is equally likely, so the probability of any category is the number of hands in it divided by that total. For instance, there are 624 ways to hold four of a kind, so the chance is 624/2,598,960, about 0.024%, or roughly 1 in 4,165. The full table of categories belongs to its own article on poker hand odds; the point here is that a few lines of counting produce exact figures.
A simple example of useful shortcuts is the chance of at least one ace in a five-card hand. Counting every hand with an ace is awkward, so count the hands with no ace instead: there are 48 non-aces, giving 1,712,304 five-card hands without one. Subtracting that share from everything gives about 34.1% for at least one ace. This trick is called complement counting, and it appears constantly in card problems.
Orderings and shuffling
A different question is how many ways the whole deck can be arranged. The answer is 52 factorial (52!), about 8.07 x 10^67. That figure is far beyond anything that can be listed or played through, which is why it is often said that a thoroughly shuffled deck is almost certainly in an order that has never occurred before. That statement is a statement about the size of the number, not a claim about any specific shuffle method, and how well a real shuffle approaches a uniformly random order is a separate question with its own research.
What the deck can and cannot tell you
Knowing the composition of the deck lets you work out exact probabilities for hands, draws and combinations. It does not predict the next card in a shuffled deck, and it does not remove the structural cost built into games where the house takes an edge. In casino games, a house edge means the expected result over many plays is a loss for the player, however well the card arithmetic is understood. Past hands do not change the odds of future shuffled decks.
Card probability is best treated as a way of understanding why certain hands are rare and others common, and of seeing how information changes odds. If gambling is part of your interest and it stops being enjoyable or starts to cause problems, a local support service can offer confidential help.