Infinity in Your Hand

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Infinity in Your Hand

Look at this number:

This is the number of ways in which a deck of 52 cards can be shuffled, a number with 68 digits in it. That’s approximately 8 x 10^67, in mathematical notation. In mathematical terms, it is expressed as the factorial of 52, written as 52! It means 52 x 51 x 50 x …. 4 x 3 x 2 x 1.

It’s easy to look at these representations and imagine that this isn’t a very large number. It is, in fact, a number so large that even astronomical terms are smaller that it!

Here’s a lovely visualisation by Scott Czepiel on

“Let’s try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We’re going to see how much fun we can have before the timer counts down all the way.

“Start by picking your favourite spot on the equator. You’re going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. The equatorial circumference of the Earth is 40,075,017 meters.”

Czepiel wisely, and possibly tongue-in-cheek, suggests: “Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps,” because once you complete that round-the-world trip, you find he’s barely got you started.

“After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. The Pacific Ocean contains 707.6 million cubic kilometres of water. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.

“Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063 x 10^67 more seconds to go. 1 Astronomical Unit, the distance from the Earth to the Sun, is defined as 149,597,870.691 kilometers. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385 x 10^67 seconds remaining. You’re just about a third of the way done.”

That’s going to get pretty boring, so to help you pass the time, Czepiel suggests you take up poker, something also suggests. You will be looking for the ultimate winning hand, right? The royal flush. It occurs in one out of every 649,740 hands.

Czepiel continues the mad game with this little added excitement: “Every billion years deal yourself a 5-card poker hand. Each time you get a royal flush, buy yourself a lottery ticket. If that ticket wins the jackpot, throw a grain of sand into the Grand Canyon. Keep going and when you’ve filled up the canyon with sand, remove one ounce of rock from Mt. Everest. Now empty the canyon and start all over again. When you’ve levelled Mt. Everest, look at the timer, you still have 5.364 x 10^67 seconds remaining. Mt. Everest weighs about 357 trillion pounds. You barely made a dent. If you were to repeat this 255 times, you would still be looking at 3.024 x 10^64 seconds. The timer would finally reach zero sometime during your 256th attempt.”

That shouldn’t take too long, should it now? Unfortunately, as Czepiel breaks it to us sadly: “Of course, in reality, none of this could ever happen. The truth is, the Pacific Ocean will boil off as the Sun becomes a red giant before you could even take your fifth step in your first trek around the world. Somewhat more of an obstacle, however, is the fact that all the stars in the universe will eventually burn out leaving space a dark, ever-expanding void inhabited by a few scattered elementary particles drifting a tiny fraction of a degree above absolute zero.” He says that the exact details are still a bit fuzzy, but according to some estimates of the end of the Universe, all this could happen “before you would’ve had a chance to reduce the vast Pacific by the amount of a few backyard swimming pools.”

As you can see, this is what makes most card games fascinating. You really do have a set of possibilities that are as close to infinity as a human can reach. And you can hold that deck in one hand.

Come on, play poker now! is certified to guarantee as random a deal of the deck of cards as possible by no less than iTech. Aim to hold infinity in one hand.

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