Preposterous Poker Probabilities

If you really want to understand the game of poker, you need to understand the odds! Odds are the chances of you holding a winning hand. And while odds aren’t everything, knowing the numbers can certainly help you to hone your skills and to understand some of those seemingly crazy hands.

While it’s important to hold out for the right hand to play, in Texas Hold’em, your chances of getting a top starting hand are only 2.1%! This includes AA, AK suited, and picture pairs. To be exact, your chance of getting those coveted pocket rockets is 221 to one. It’s always great to get those hands, but you can’t wait forever! Something to be wary of, though, is playing just any suited cards. You might think that it raises your chances of winning greatly, but it’s really only by around 2.5%.

In a 52-card standard deck of cards, the odds of hitting a royal flush are 649,740 to 1! In Texas Hold’em, where hands are made by choosing the best five cards out of seven, the odds jump to 30,939 to 1. That’s still crazy high! The same odds hold true for Seven Card Stud. Even more than that, the chances of getting a SPECIFIC royal flush are 2,598,960 to 1. You’re FIVE TIMES more likely to get struck by lightning! Online poker is four times faster than live games, so you’ll see royal flushes more often, but the odds are still astronomical. If you manage to score a royal flush, count yourself lucky!

Speaking of the standard deck – If you were to shuffle a 52-card deck, how many different variations in the order of cards do you think you’d get? The answer is 52! (52 factorial), which is a MASSIVE number. 52! equals 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000. That’s over eighty unvigintillion! And on the subject of arranging a single standard deck of cards, while it’s not relevant to card games, that number is even HIGHER if you count whether the cards are right side up or not.

As mathematician Yannay Khaikin explains, “Any time you pick up a well shuffled deck, you are almost certainly holding an arrangement of cards that has never before existed and might not exist again.” There are more ways to arrange a single deck of playing cards than there are atoms on Earth.

The next time you score AA or that coveted royal flush, remember just how lucky you are! And take a moment to appreciate your next well-shuffled deck. You’ll probably never see that specific arrangement of cards again in your lifetime.