The 52 deck of cards

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Everyone of us has shuffled a deck of 52 cards once already. But did you also know that you created a sequence of cards that has never existed before in the history of mankind and never will with a probability of almost 100%? You don’t believe me, then read on.

Well, we can determine the possibilities of different card sequences of a 52 card deck pretty quickly using the faculty. You should also know that faculties rise exponentially and incredibly fast. Thus 70! is already larger than a Googol (that is a one with 100 zeros). Also 52! is so huge that the human mind can hardly comprehend this size. Our brain is simply not designed for such magnitudes. Strictly speaking, it results in:


Because of this size, you can almost surely state that if you shuffle a 52 deck of cards, you will create something unique. Most likely, no one has ever had exactly this sequence of cards, and no one will ever shuffle it.

What if I told you that there are more possibilities to shuffle a deck of 52 cards than there are atoms on Earth? … Did I say on Earth? I meant in the entire Milky Way! In the following, I’m trying to illustrate the vanishlingly small possibility to receive a certain sequence of cards when shuffling a deck of 52 cards.

Let’s assume that you started shuffling the deck of cards. Every second a new combination of cards. For the sake of simplicity, we also assume that you never shuffled a sequence twice, which would in reality happen more and more often, especially towards the end. Now imagine that every 1 billion years someone came and took one grain of sand from the earth. You shuffle until he has taken every grain of sand from every desert on earth. Then he comes every 1 billion years and gives you 1 cent. You continue shuffling. You shuffle and shuffle until you can purchase a sheet of paper for the ridiculously low price of 1 trillion euros. Now you continue shuffling, every second a new combination until you can afford to purchase a mountain of paper from the earth to the sun. Did I say one mountain of paper? I meant 2.6 trillion.

As you can see from the above example, it would take an incomprehensibly long time to shuffle the deck of cards with all its possibilities. Here comes another amazing calculation: Imagine that every person that has ever lived would have mixed a new sequence of cards every second of their life. We also assume that the age of each person amounts 100 years. In fact, the average life expectancy in the Stone Age is estimated to be just 10 years. However, let’s assume that the 108 billion people would have shuffled every second of their 100 years long lifes. How many possibilities do you think they would have reached? All of them? Half of it? One out of hundred? It were only one quindecillionth.

The next time you shuffle a deck of cards remember that you in all likelihood created something very unique.

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