I have played poker many times, and during our Thursday poker evenings, I have never got a royal flush. That got me thinking, what are the odds of actually getting the illusive Royal Flush?

Royal Flush
Royal Flush – Adobe Stock

As seen above, a royal flush is a straight of Ten, Jack, Queen, King and Ace, all of the same suit. There are 13 different cards in a deck, each having 4 suits making a total of 52 cards. Being only 52 cards, you would assume the odds aren’t that difficult to get 5 of the same to make a royal flush? But odds and combinations when examined up close end up multiplying exponentially!

Deck of Cards
Deck of Cards – Adobe Stock

According to Thoughtco, using some not so simple math, there is a 1 in 649,740 chance of being dealt a Royal Flush! Put in another way, you have a 0.00015% chance of getting the Royal Hand. Hearing these big numbers makes it hard to understand so let’s put it this way.

If I played poker every Thursday and say I get dealt 100 hands for the whole nights game. It would take me 6497.40 games for me to go through all combinations of cards once to get 1 Royal Flush. That’s 6497 weeks which is almost 125 years! No wonder I haven’t got one yet. If you are interested in the math behind it all, see below.

Royal Flush Illuminated – Adobe Stock

The Math Behind it all…

First we need to calculate how many possible combinations of cards there are. For this we use the combination equation known as C(Total number of cards, Number of cards in hand), which is C(52,5) = 2,598,960.

Now we need to divide this by the total number of possible Royal Flushes. Because it is a definite set of cards being Ten, Jack, Queen, King and Ace, you can only get one possible combination per suit. Because there are four suits, this totals four possible Royal Flushes.

Total possible combinations/possible Royal Flushes (2,598,960/4) = 649,740.

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