In theory every time you sufficiently shuffle a deck of cards you are making history by creating a new unique order of cards that has never existed.
The reason for this is because there are 52 factorial (52!) possible card combinations in a standard deck of 52 cards. That means when you figure the total card combinations you have 52 options for the first card, 51 options for the second card, 50 for the third, etc. The factorial math works out like a long multiplication problem: 52x51x50 etc.
So how many possible card combinations are there when you shuffle a deck of playing cards? Well, 52! comes out to:
Of course if you assume cards from the factory are already usually in a specific order then that particular combination has been created many times in the past, but each time you shuffle you get farther and farther from that original order and into unique orders. It takes about 7 shuffles before the deck of cards is ordered in a new unique way never before achieved in history.
What does that number even mean?
52! is a hard number to grasp. A word for this number would approximately be 80 unvigintillion or 8×1067. It is significantly larger than the number of stars in the visible universe, 1067 card combinations versus 1023 stars in the universe. If all the approximately 6 billion people on Earth began shuffling a deck of playing cards one time per second for the next 100 billion years we would not even come close to fulfilling all possible card combinations.
- 52! (link is external). WolframAlpha.
- Overview: This page displays the math result of 52! and is where I got the word unvigintillion.
- Astronomers count the stars (link is external). Andrew Craig.
- Overview: This article talks about a researcher’s estimate of the number of stars in the visible universe. It is significantly less than 52!.
- Making History by Card Shuffling (link is external). Su, Francis E., et al.
- Overview: Explanation of the probability and the fact that it takes about 7 shuffles before the cards are truly randomized and shuffles start becoming unique.
- Image Credit: parade.com