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# Probability of Flush (fraction)

MichaelBartmess.Probability of Flush (fraction)

The **Probability of a Flush** **(fraction)** constant defines the probability of being dealt a **Flush** as a fraction. The **Flush **is a five card hand having all in the same suit and the card values do not have to be in consecutive order. An example of a **Flush** would be the following five cards all of the same suit

- a 2
- a 3
- a Queen
- a 7
- a 10

The number of **Flushes** possible is the product of the number of five card choices in the 13 card values, `((13), (5))` times the number of suits, `((4), (1))`; minus the product of the number of royal flushes `((4), (1))` times the number of straight flushes`((10), (1))`. So the chances of being dealt a **Flush** (excluding royal flush and straight flush) is the ratio of the number of **Flushes** to the total number of five card hands that are possible. The total number of five card hands possible is computed as `((52), (5))` (see the constant defining number of five card hands).

**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 Flush (fraction)**, references 1 equation/constant.

**Equations and Constants **

**Probability of Flush (fraction)**, is used in 8 equations/constants.

**Equations and Constants **

- 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...