Probability of Royal Flush (fraction)

The Probability of a Royal Flush (fraction) constant defines the probability of drawing a Royal Flush and represent the probability as a fraction.  The Royal Flush is a five card hand having all in the same suit with the following 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)

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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