What Are the Odds of Poker Hands?

In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.

Poker hand probabilities are based on the concept of combination. A combination is a selection of items from a set, without regard to the order in which they were selected.

For example, a poker hand can be described as a combination of cards. The number of ways to choose 5 cards from a deck of 52 cards is .

52C5 = 2,598,960

This means that there are approximately 2.6 million ways to choose 5 cards from a deck of 52 cards. The probability of being dealt any particular hand then is simply the number of ways that hand can be chosen divided by the total number of possible hands:

PRO TIP:When playing poker, it is important to be aware of what the odds are for each hand. Knowing the odds can help you make informed decisions and potentially increase your chances of winning. For example, a royal flush is the most rare hand and has a probability of 0.000154% of occurring. On the other hand, a pair is much more common and has a probability of 42.26%.

P(hand) = no. ways to choose hand / total no. of possible hands

For example, the probability of being dealt a flush (a hand with all five cards of the same suit) is

4C5 / 52C5 = 0.001982 or approximately 0.2%.