ADJ Clubroom Noticeboard

Dealing with a full deck of atoms.

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March 1, 2023In Physical, Head, Sight3 Minutes

Did you know there are more ways to arrange a deck of cards than there are atoms on Earth?

It seems unbelievable, but there are somewhere in the range of 8×1067 ways to sort a deck of cards. That’s an 8 followed by 67 zeros. To put that in perspective, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before they would get even one billionth of the way to find a repeat.

This is the nature of probabilities with such great numbers. Though a long-time blackjack dealer might feel like they have shuffled thousands of cards in their lifetime, against a number this big, their rearrangements are irrelevant.

There are simply too many ways to arrange 52 cards for any randomly organised set of cards to have repeated itself.

Holding the Universe in the palm of your hand

This literally exciting calculation is denoted by an exclamation mark and is called a factorial.  As a rule, factorials multiply the number of things in a set by consecutively smaller numbers until 1. Since there are 4 cards in our mini-deck, there are 4 factorial or 4! numbers of ways it can be arranged, which equals 24. While this might not seem like a particularly large number, by the time you get to 52! (or 52x51x50 … ) you get a number with 68 total digits – an integer much larger than all the atoms estimated to be on Earth. Your can explore more about this concept and other resources from the team at Mcgill Univesity here. 

You are going to go and find a pack of cards now aren’t you?

If this fact has triggered your mind to think about your next card game then here is an interesting fact that you can surprise and delight your friends and family with; not all shuffling techniques are created equal.  The most popular/common method can take up to 10,000 complete shuffles to create a truly random order, while one technique can do this in just seven. Watch Professor Persi Diaconis of Standford Univesity explain why.