Probability of Four of a Kind (fraction)

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Constant / Last modified by AndrewS on 2016/11/08 17:15
"Probability"_"Four-of-a-Kind" = [((13),(1)) * ((12),(1)) * ((4),(1))]" in " ((52),(5))
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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.

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