What is the chance of getting a poker royal flush in 5 cards?

The royal flush is the top hand in poker. It is most accurately called a royal straight flush because it consists of a straight of the highest cards (Ace, King, Queen, Jack, 10) of all the same suit, which is the flush part. Being dealt a royal flush is an event that any poker will certainly remember because it is quite rare.

Just how rare is it? Let’s look at one method for calculating the probability of having a royal flush dealt in 5 cards. A mathematical method called the combination formula can be used to figure out the answer.

With this formula, as described in the book Practical Casino Math by Hannum and Cabot, you would compute how many combinations of 5-card hands can be produced with a 52-card deck. The answer is 2,598,960. Then divide that figure by 4 to represent the 4 suits of the 4 possible royal flushes.

The result is a probability of 1 in 649,740 that you will be dealt a royal flush in 5 cards. With such a staggeringly low probability of getting the highest hand ... more.

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