Math magic : shuffling cards

I've been watching a lot of YouTube videos about maths, especially Vsauce. I highly recommend it, it's fascinating and fun and simple to understand. This is entirely from one of his videos : https://youtu.be/ObiqJzfyACM
  1. Do you know that every time you shuffle a deck of 52 cards, chances are you have put those playing cards into an order that they have never been in, in the entire history of cards!
  2. The number of different ways 52 cards can be arranged is 52 factorial
    Which means : 52x51x50x49x48x47x46x45x44.........
  3. It is a HUGE number!!!!! Don't make the math, here it is :
    80658175170943878591660636856403766975289505440883277824000000000000
  4. In fact, even if the cards were rearranged every seconds since the beginning of the earth, you still wouldn't have come close to assembling every arrangement possible!
  5. Because 52 factorial is more than 8x10 to the 67th
    The universe is only 10 to the 18th seconds old...!
  6. Even that doesn't paint the whole picture of how big 52 factorial is :
  7. Imagine sitting a timer to countdown 52 factorials seconds
  8. Stand on the equator and wait 1 billion years
  9. After a billion years have passed, take a single step forward and then wait another billion years before taking a second step.
  10. So once you have walked all the way around the earth take a single drop of water out of the Pacific Ocean
  11. now continue walking at a rate of 1 step every billion years removing one drop after every journey around the entire earth.
  12. By the time the Pacific ocean is completely empty put a single sheet of paper on the ground.
  13. Refill the ocean and keep going until the stack of paper reach the sun.
  14. At that point there will still be 8x10 to the 67th seconds left on the timer!
  15. You have barely made a dent!
  16. If you start all over again and do that thing a thousand more times, you will only be a third of the way done!
  17. The creator of this story has a great idea to pass the rest of the time left if you're bored :
  18. Deal yourself Five cards every billion years, when you finally deal yourself a royal flush, buy a lottery ticket. Every time the ticket wins the lottery, throw a single grain of sand in the Grand Canyon.
  19. As soon as the grand canyon is completely full of sand, remove one ounce of rock from Mount Everest at every winning lottery ticket until it's leveled.
  20. Now do the five card/royal flush/lottery ticket/Grand Canyon/mount Everest thing 256 more times...
  21. And then, and only then, will your timer have reached zero!
  22. That is how big the possibilities of order in a deck of cards is!
  23. The tiny deck of cards
  24. I love maths
  25. It's better than magic, because it's real !
    And not real simultaneously!