Probability of Straight Flush (fraction)

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"Probability"_"Straight Flush" = [((10),(1)) ((4),(1)) - ((4),(1))]" in " ((52),(5))
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The Probability of a Straight Flush (fraction) constant defines the probability of being dealt a Straight Flush and represent the probability as a fraction.  The Straight Flush is a five card hand having five successive value cards all in the same suit exactly.  For example, 4, 5, 6, 7, 8 all of hearts would be a Straight Flush or 8, 9,10, Jack, Queen all of spades.  This probability excludes the four Royal Flushes which are a special case of a Straight Flush.

The number of Straight Flushes is the number of starting choices times the number of choices of suits minus the four possible Royal Flushes.  The total number of five card hands possible is computed as C(52,5) (see the constant defining number of five card hands), so this represent the ratio of number of possible Straight Flushes to the number of five card hands possible,C(52,5).