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# Probability of Four of a Kind (fraction)

MichaelBartmess.Probability of Four of a Kind (fraction)

The **Probability of Four of a Kind (fraction) **constant defines the probability of being dealt four-of-a-kind and is represented as a fraction. The** Four of a Kind **hand is a five card hand having four of five cards being the same value cards. For example:

- 4 of spades
- 4 of hearts
- 4 of diamonds
- 4 of clubs, and
- an 8 of spades

would be a **Four of a Kind **hand.

The number of possibilities of a** ****Four of a Kind** hand is the number of card values, `((13),(1))`; times the number of possible card values of the fifth card (the card that is not part of the four off a kind), `((12),(1))`; times the number of suits of that fifth card could be, `((4),(1))`. The total number of five card hands possible is computed as `((52),(5))` (see the constant defining number of five card hands), so this constant represent the ratio of number of possible **Four of a Kind** hands to the number of five card hands possible,`((52),(5))`.

**Additional Resources:**

The Poker Calculator provides all the equations, the calculations, to determine the probabilities of success and failure when playing Poker with a standard five card deck.

[**Card Games | Poker | Combinatorics | Probability | Chance**]

**Probability of Four of a Kind (fraction)**, references 1 equation/constant.

**Equations and Constants **

**Probability of Four of a Kind (fraction)**, is used in 12 equations/constants.

**Equations and Constants **

- Probability of Flush losing (fraction)
- Probability of Flush losing (percentage)
- Probability of Full House losing (fraction)
- Probability of Full House losing (percentage)
- Probability of One Pair losing (fraction)
- Probability of One Pair losing (percentage)
- Probability of Straight losing (fraction)
- Probability of Straight losing (percentage)
- Probability of Three of a kind losing (fraction)
- Probability of Three of a kind losing (percentage)
- Probability of Two Pair losing (fraction)
- Probability of Two Pair losing (percentage)
- more...