Probability of Two Pair (fraction)

The Probability of a Two Pair (fraction) constant defines the probability of being dealt two pair and the probability is represented as a fraction.  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))`.

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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