Probability of Three of a Kind (fraction)

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Constant / Last modified by AndrewS on 2016/11/08 17:31
"Probability"_"Threer-of-a-Kind" = [((13),(1)) * ((4),(3)) * ((12),(2)) * ((4),(1))^2]" in " ((52),(5))
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MichaelBartmess.Probability of Three of a Kind (fraction)
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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))). 