Probability of One Pair (fraction)

The Probability of One Pair (fraction) constant defines the probability of being dealt just one pair and the probability is represented as a fraction.  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 not 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))`.

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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