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))`
MichaelBartmess.Probability of Straight (fraction)

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))`.


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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