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# Probability of Three of a Kind (fraction)

MichaelBartmess.Probability of Three of a Kind (fraction)

The **Probability of a Three of a Kind (fraction)** constant defines the probability of being dealt three-of-a-kind and the probability is represented as a fraction. The** Three of a Kind **hand is a five card hand having three of five cards being the same value cards and the remaining two cards not being the same value as each other. For example:

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

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

The number of possibilities of a** Three of a Kind** hand is the number of card values, `((13),(1))`; times the number of combinations of three suits being chose from four suits, `((4),(3))`; times the number of combinations of choosing two cards that are not the same value as the three of the same value, `((12),(2))`; times the number of choices of the two un-like cards done twice, `((4),(1))^2`. 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 **Three 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 Three of a Kind (fraction)**, references 1 equation/constant.

**Equations and Constants **

**Probability of Three of a Kind (fraction)**, is used in 6 equations/constants.

**Equations and Constants **