Probability of Royal Flush (percentage)

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Constant / Last modified by AndrewS on 2016/11/08 17:26
`"Probability"_"Royal Flush" = ((4),(1)) " in " ((52),(5))`
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MichaelBartmess.Probability of Royal Flush (percentage)
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The Probability of a Royal Flush (percentage) constant defines the probability of being dealt a Royal Flush and represent the probability as a fractional percentage.  The Royal Flush is a five card hand having all in the same suit with these card values:

  • an Ace
  • a King
  • a Queen
  • a Jack, and
  • a 10

The number of Royal Flushes is exactly four, since there are one in each suit in a standard deck.   So there are four chances in the total number of five card hands that are possible.  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 is a ration of 4 to C(52,5).

ProbabilityofRoyalFlushpercentage-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.

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