Whats in a Deck of Cards.

in steemstem •  5 months ago

Deceptive Complexity

We all know that simple deck of playing card 52 cards or 54 if you include jokers, that's four suits clubs, diamonds, spades, and hearts with three face cards and ten numbered cards per suit.

To tell the truth, I think its cool as to be able to use the tags #steemstem, and #cryptography when talking about playing cards The reason I can do this will be clear in my next post.

So just how complicated is that "Go Fish" stack.

Brief History.

Ok, once I start looking at history I tend to struggle to be brief.

As I said we all know that 54 card deck of playing cards, some have made or lost fortunes on the turn of a card but for most of us maybe we played simple games with friends and family like a bridge, poker, go fish but just how long have we enjoyed the humble playing card(pre-smart phones).

The oldest surviving complete deck of playing cards is estimated to have been made somewhere between 1470 and 1500 but the origins may stretch back much further than that.

As with much of history very we people are in agreement with all the facts and when it comes to cards its more of the same but here is one of the most common theories on the invention of playing cards I could find.


This should be no surprise, we are talking about the culture that invented paper in around 100bc and woodblock printing somewhere around 400ad so being the first to invent a game printed on paper cards is not much of a stretch. Historical documents mention playing cards in china somewhere around 700-900ad since then the general idea is that from there they spread to surrounding areas eventually making their way to Egypt and then into Europe.

As the game spread it branched into the familiar playing cards we know, the Tarot used for divination and fortune-telling and Mantegna Tarocchi which shares a lot of similarities with a tarot deck but is suggested to have been an educational tool.

How Freaking complicated.

I'm no maths guy and there is a very real chance that I will make an error during my explanation of the complexity in a deck of cards so please bear with me.

Let's start simple its just common sense that if you have 1 item there is only one way to arrange it and that is you have two items only two but things get complicated very very fast as the number of items increases lets have a quick look.

3 items = 6 combimnations
4 items = 24 combinations
5 itesm = 120 combinations
6 items = 720 combinations

The numbers grow incredibly rapidly, in order to discover the number of combinations that could be made from a set of items we find the factorial in maths talk that means the product of all non-negativee numbers equal to or less than the number of items.

For example if we want to calculate the combinations for a set of 6 the calculation would look like this.

6! = 6 x 5 x 4 x 3 x 2 x 1= 720

Now just how many combinations of a deck of 52 cards are there? Lets remove the jokers as keep the deck at 52 cards your welcome to go ahead and calculate it manualy. you know 52 x 51 x 50 x 49... etc or you can open up the calculator on your desktop or phone set it to scientific and type 52followed by n! if you want to take the easy way.

The answer might not look impresive and you might be forgiven for thinking that your calculator has broken but trust me its rediculious.

8.0658175170943878571660636856404e+67 combinations

Thats roughly 80,658,175,170,943,878,571,660,636,856,404,000,000,000,000,000,000,000,000,000,000,000,000 possible ways to arange a deck of 52 cards.

In Perspective.

Now we have a number that is just to big to comprehend, to really grasp how many combinations that equates to lets play more maths.

7 billion = The rough population of the world.
31,536,000 = The seconds in a year.
52! = The factorial of a deck of cards

52! / (7,000,000,000 x 31,536,000)

If the entire world was shuffeling a deck of cards and producing a unique combination every second of the year it your would get 220,752,000,000,000,000 done and dusted.

That only leaves.

365,379,136,637,239,429,638,964,253,354,010,000,000,000,000,000,000 more years to get through.

A little more perspective.

It almost doesn't matter what examples you use to explain just how astrominicaly large this number is


Some super smart science guys estimate the age of the universe at around 13.7 billion if our magic card shuffeling population started at the dawn of time the process would would go on long past the water boiling of the Earths oceans as the sun goes red giant and eventualy goes cold some 5 billion years from now, it would go on long enough to see every light in the sky wink out and leaving the universe dark and still have plenty of combinations to get through.

All from just a simple deck of cards.

Kind regards


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I love your post

Isn't this a whole pile of fun facts!! Do you and your wife play cards much? Have a great day!


not really The next post that I'm writing is how to use a deck of cards to encrypt and decrypt a secret message once I started looking into cards I found out how complex they really are.

and I love the idea that every time you properly shuffel a deck your holding a combination that no one else has ever held before


Seriously interesting! It seems you've really enjoyed delving into this topic. I never considered how many combinations there could be in a deck of cards! Where I am from we played cards a lot i don't now but do enjoy some games when we gi visit our grandmothers!

What a great post Peter! I grew up playing cards and still do ... old school, but this is something I'd never thought about before now :) I love all your examples just to show how astronomically huge that number actually is. And the photo of the oldest complete deck ... so awesome!

Thanks for sharing :)