# Probability of One Pair (percentage)

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Constant / Last modified by AndrewS on 2016/11/08 17:23
"Probability"_"One Pair" = [((13),(1)) * ((4),(2)) * ((12),(3)) * ((4),(1))^3]" in " ((52),(5))
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The Probability of One Pair (percentage) constant defines the probability of being dealt just one pair and the probability is represented as a percentage.  The One Pair hand is a five card hand a single pairs of cards of the same card value and the remaining card having different values.  For example: 4 of spades, 4 of hearts, 10 of diamonds, jack of clubs, and an 8 of spades would be a One Pair hand.

The number of possibilities of a One Pair hand is the number card values, ((13),(1)); times the number of combinations of two suits being chose from four suits, ((4),(2)); times the number of choices of the remaining three cards that are not the same value as the pairs, ((12),(3)); times the number of choices of the suit of the cards that are no the pair, ((4),(1))^3.  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 One Pair hands to the number of five card hands possible,((52),(5)).

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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