Complex Numbers

It's In The Cards

"30-Day Blogging Challenge ON HIATUS"  [13+]:
28. Card Playing Day!
Do you like playing cards? Which card games do you prefer?

Long ago, I used to host a Poker Night at my place. Unlike many such events, this wasn't a boys' club, nor was it merely an excuse for my group of friends to get together. I mean, that's what we were doing, of course, but poker was the purpose of the evening; it was a casual, low-stakes game, but we were still serious about it.

Nor was it a tense Hold 'Em tournament, but good old-fashioned dealer's choice: draw or stud or one of the many variations thereof.

Things drifted apart after a while, so this stopped even before the pandemic made hosting poker games a difficult proposition, but I do miss the games.

I've played a few of the purpose-built card games, you know, like Cards Against Humanity and others that use different decks, and those can be fun too.

When I go out gambling, though, my game of choice is blackjack, not poker. Or, at least, it was when I could still go out gambling.

I realize this isn't a particularly clever or funny entry; I'm just not in the mood to do clever and/or funny right now. But I feel like I should do more than a plain prompt answer, so I thought I'd point out some things about a standard deck of cards.

There are more ways to arrange a deck of cards than there are atoms on Earth  

Consider how many card games must have taken place across the world since the beginning of humankind.

That's a stretch. Playing cards aren't much more than 1000 years old  , and the evolution to the modern, standard, French style deck of 52 cards arranged in four suits with aces, royalty, etc. took maybe 5-600 years, so we're not talking about "the beginning of humankind" but roughly "from about the time of Shakespeare."

It seems unbelievable, but there are somewhere in the range of 8x10⁶⁷ ways to sort a deck of cards. That’s an 8 followed by 67 zeros.

What they are describing there is the number of possible permutations of a pack of 52 cards. The number is written as 52!, which is read "fifty-two factorial," and is the result you get when you multiply all of the integers from 1 through 52: 1x2x3x4x5x...x50x51x52.

It is, as the article notes, a really stupendously huge number. Considering that the universe is, by comparison, only about 4x10¹⁷ seconds old, you can maybe start to see how people can say there has probably never been the same particular combination of shuffled cards in all of the history of cards.

Or, as the article puts it with even less clarity, 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 finding a repeat.

It is, however, the nature of humans to only notice when such shuffling produces "interesting" combinations of cards -- such as straights, flushes, or four-of-a-kind. When playing poker, we'll notice those (because they tend to be winning hands) far more often that the just as likely 6-10-3-K-8 of mixed suits, for example.

Cards are a good way to teach statistics and probability - but they're also handy tools for explaining the concept of entropy.

But mostly, I just miss playing poker.