Probability of Straight (percentage)

Not Reviewed
Constant / Last modified by AndrewS on 2016/11/08 17:28
`"Probability"_"Straight" = [((10),(1)) ((4),(1))^5 - ((10),(1))((4),(1))]" in " ((52),(5))`
Rating
ID
MichaelBartmess.Probability of Straight (percentage)
UUID
2b75fe46-bd25-11e3-9cd9-bc764e2038f2

The Probability of a Straight (percentage) defines the probability of being dealt a Straight and represent the probability as a percentage.  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))`.

ProbabilityofStraightpercentage-illustration.png

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.

[Card Games | Poker | Combinatorics | Probability | Chance]