Take a deck of cards and shuffle it with reckless abandon. Cut, riffle, and cut again—the more chaotic, the better. Now, gaze upon the resulting arrangement, an unpredictable set of cards. This precise sequence of cards will never be seen again.
If you had been shuffling this deck non-stop since the big bang, dealing a fresh hand every second, you would still be lightyears away from replicating this exact combination. Leap forward to a distant future, where the sun has exhausted its fuel and the earth is a distant memory. You are left alone, floating in a spacecraft, still shuffling with obsessive regularity, yet the probability of duplicating his hand remains very small.
What is 52 factorial?
In simple terms, a factorial represents the number of possible combinations with a set of integers. It is calculated by multiplying all positive integers up to a given number.
For a standard deck of 52 cards, we are dealing with 52 factorials (52!) This means multiplying all integers from 1 to 52:
52! = 1x 2 x 3 x 4 x 5 x 6 x 7 x 8 x… x 50 x 51 x 52
The result of this is a staggering number.
52!=80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000
It contains 68 digits.
This figure represents the number of possible unique combinations within a 52-card deck.
To put it in perspective, if you shuffled the deck every second, it would take you over 1.4 x 10^50 years to go through all the possible combinations. The estimated age of the universe is 1.38 x 10^10 years, meaning you would need to shuffle billions of times the current age of the universe to reach just a fraction of the possible combination.
Poker and 52!
If you are challenged to play a hand of poker every billion years until you get a royal flush, which has odds of 1 in 649,740. Once you get a royal flush, buy a lottery ticket and win the jackpot, which has odds of 1 in 45,057,474.
Then throw a single grain of sand into the Grand Canyon. Repeat this process until the Grand Canyon is full. To know the full picture, I will give you information that the Grand Canyon has a volume of approximately 4.17 trillion cubic meters.
Let us assume a grain of sand occupies about 0.0625 cubic millimeters. To fill the Grand Canyon, you would need approximately 6.67 x 10^22 grains of sand. Dealing a hand of poker every billion years, it would take approximately 4.15 x 10^22 billion years to fill the Grand Canyon, assuming you get a royal flush and win the lottery every time.
52! Around the equator
Start by choosing your favorite location along the equator. Imagine walking around the earth at a pace of one step every billion years. The earth’s equatorial circumference is approximately 40,075,017 meters. Bring a deck of playing cards with you so you can play countless hands of solitaire during your journey.
After completing the walk around the globe, remove a drop of water from the ocean each time. The Pacific Ocean holds about 707.6 million cubic kilometers of water. Continue this process until the ocean is completely empty. Then lay down one sheet of paper on the ground, fill the ocean back up, and start the process again, adding one sheet of paper each time you empty the ocean.
Keep doing this until the stack of paper reaches the distance from the earth to the sun. You will notice that the timer still shows 8.063 x 10^67 seconds remaining. The distance from the Earth to the sun, or one astronomical unit, is 149,597,870.691 kilometers. Even if you repeat this process a thousand times, the stack of paper won’t be tall enough. There will still be over 5.385 x 10^67 seconds left, meaning you will have completed just about one-third of the task.
Conclusion
You thought it might be easier than this, didn’t you? The chances of getting the same set of cards. Or have you ever thought about it? Now you know what a 52 factorial is; it is a 68-digit number. That is the chance of you getting the same set of cards, which could be a mind-blowing fact if you think about it.
Read More: Are Blackjack Odds Better With More Players?
