Probability of Full House (fraction)

The Probability of a Full House (fraction) constant defines the probability of being dealt a Full House and is represented as a fraction.  The Full House hand is a five card hand having three of five cards being the same value cards and the remaining two card being of the another same value card.  For example:

• 4 of spades
• 4 of hearts
• 4 of diamonds
• Jack of clubs, and
• an Jack of spades

would be a Full House.

The number of possibilities of a Full House hands is the number of card values, `((13),(1))`; times the number of combinations of three suits chosen from four suits, `((4),(3))`; times the times the number of card values different from the card value of the three like cards, `((12),(1))`; times the number of combinations of two suits chosen from four suits, `((4),(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 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.

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