Interesting fact about card shuffling...

Every now and then it happens to me that I stumble upon something obvious yet something that didn't occurred to me. This time it was this post. It's about shuffling cards, I and many others did it so many times. Yes, I knew that there are many combinations, but with a little bit of analysis it turns out that there are so many combinations that every shuffle is very likely unique in a history of card shuffling. That conclusion is what made my say Wow! Even more impressive is when you say that particular ordering of cards is uniqe in human history. Admittedly, that is a bit out of proportions since modern cards, accoring to the post, appeared in Europe somewhere around 14th century And, according to Wikipedia, they were invented in China, somewhere in 9th century. But even if the cards were with humans from the day one (however we interpret that), it wouldn't be enough time to try all the combinations!

The total number of combinations with a deck of 52 cards is 52!. This is exactly:

52! = 80658175170943878571660636856403766975289505440883277824000000000000

or approximately 8.0658X10⁶⁷. It is a huge number, even though substantially less than number of atoms in visible universe (10⁸⁰) :). Ok, and with overestimation of number of shuffles done in history of playing cards we end up with a number that is by 40 orders of mangitude smaller, i.e. somewhere around 1.546X10²⁰ (note that I think that in the original post there is an error in the calculation).

And for the end I have an interesting rhetoric question: Can I patent a certain card combination as an invention? :) Obviously, I can not give decisive proof that no one else invented that particular combination, but this shows that it is highly likely so! :)