# Probability of Straight (fraction)

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Constant / Last modified by AndrewS on 2016/11/08 17:27
"Probability"_"Straight" = [((10),(1)) ((4),(1))^5 - ((10),(1))((4),(1))]" in " ((52),(5))
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The Probability of a Straight (fraction) constant defines the probability of being dealt a Straight and represent the probability as a fraction.  The Straight is a five card hand having five cards of successive values but in mixed suits (in at least two suits).  For example, 4, 5, 6, 7, 8 of three different suits would be a Straight or 8, 9,10, Jack, Queen of two suits.

The number of Straights is the product of the number of starting choices for the five card sequence of values, ((10),(1)) times the number of choices of suits for each of the five cards((10),(1))^5; minus the possible straights that are of all the same suit ((10),(1))((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 represents a ratio of number of possible Straights, excluding same suit straights, to the number of five card hands possible,((52),(5)).