Probability of Two Pair (percentage)

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Constant / Last modified by AndrewS on 2016/11/08 17:34
"Probability"_"Two Pair" = [((13),(2)) * ((4),(2))^2 * ((11),(1)) * ((4),(1))]" in " ((52),(5))
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MichaelBartmess.Probability of Two Pair (percentage)
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The Probability of a Two Pair (percentage) constant defines the probability of being dealt two pair and the probability is represented as a percentage.  The Two Pair hand is a five card hand having two pairs of cards with each pair having the same card value and the remaining card having a different value than either pair.  For example: 4 of spades, 4 of hearts, 10 of diamonds, 10 of clubs, and an 8 of spades would be a Two Pair hand.

The number of possibilities of a Two Pair hand is the number of combinations of two card values, ((13),(2)); times the number of combinations of two suits being chose from four suits applied twice, ((4),(2))^2; times the number of choices of the remaning cards that is not the same value as the two pairs, ((11),(1)); times the number of choices of the suit of the single card, ((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 Two Pair hands to the number of five card hands possible,((52),(5)). 