If you're playing poker, the hand you'd most like to see is a royal flush. If you don't know, a royal flush is ten, jack, queen, king and ace, all of the same suit. (spades, clubs, hearts or diamonds) and it's the best possible hand in poker.

But what are your chances of making a royal flush in spades, in say, Texas Hold'em?

If math interests you, you may find this part interesting, if not, I put some really cool royal flush clip art with special effects, below.

To start, you first need to know that there are 311,875,200 ways of being dealt five cards from a 52 card deck. But, since the order that the cards come out doesn't matter, that number shrinks to 2,598,960 possible distinct hands. So the odds of you getting a royal flush in one suit are 1 in 2,598,960 or .0000004. Or put a different way, not good.

Another way to arrive at the .0000004 answer is to figure the chance of getting any of the five cards you need to make a royal flush from the entire deck of 52 cards. Then the chance of getting any of the remaining 4 cards from the remaining 51 cards left in the deck and so on.

5/52 = .096
4/51 = .078
3/50 = .06
2/49 = .041
1/48 = .021

Now multiply all of the decimal equivalents (.096 x .078 x .06 x .041 x .021) to arrive at the chance of getting a royal flush in one particular suit, .0000004.

Of course, in Texas Hold'em, a royal flush in one suit is just as good as any other suit and since there are four suits, your odds are four times better. This means that instead of a 1 in 2,598,960 chance to make a royal flush in one suit, you have a 1 in 649,740 to make a royal flush in any of the four suits or 000002. Or put another way, not much better.

With those odds, if you're ever fortunate enough to have a royal flush in a game, it's too good a hand not to show.

You’re free to use this poker clip art on your personal or commercial site as long as you do not use them for sale or to form your own free collection of clip art.

Enjoy!