May 20, 2026 · 42 min · 10 segments
A friend's story leads Pete and Noah to dive into the high-stakes world of poker to settle a debate: does a flush really beat a straight? Using the tools of combinatorics and probability, our hosts…
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I think we should start by just reminding listeners of what a poker deck is, and what is poker?
All right.
Poker is a game that's played with a standard deck of 52 cards.
Those cards are divided up into four suits, clubs, diamonds, spades, and hearts, and within each suit, you have 13 ranks, starting with the ace, going all the way up through two, three, four, five, six, to 10, and then jack, queen, king at the top.
Those are the picture cards or the face cards.
That's right, and of course, the ace is interesting because, as you mentioned, it sometimes comes below a two and has the role of one, but at other times, it's beyond the king, right? It's whatever the uppermost card is.
We'll get to that sort of dual role of ace in a bit, but essentially, 52 cards in this deck, also just a standard deck of playing cards.
Now, poker has a lot of variations, but I think the version we wanna focus on here is something like five-card stud.
Tell me about it, stud.
[rock music]
Right, and the game of five-card stud is basically played where the dealer shuffles the 52 cards together so they're all randomly shuffled up, deals out five cards to each playerAnd then after a round of betting or two, players compare their hands to see who has the, quote-unquote, "highest hand." And depending on what cards you're holding in your hand, you might have a hand that's very common, in which case, good luck.
Or you might have one of the rarer hands, like a flush or a straight or a full house, in which case you have a better chance of winning.
And these hands are ranked by how hard they are to get.
The harder a certain hand is to get, the more other hands it's going to beat.
What's interesting to me is that when I was a kid, I did not understand, nobody told me this, that there was this mathematical probability calculation l- lurking in the background that determined the ordering of the hands, which one is worth more than another.
It is.
So I guess one of the first things we need to figure out is how many different hands are even possible from a deck of 52 cards, right?
If we had 52 cards and the dealer shuffles them, now of course there's lots and lots of different ways that a deck could be shuffled, right?
I think we should start by just reminding listeners of what a poker deck is, and what is poker?
All right.
Poker is a game that's played with a standard deck of 52 cards.
Those cards are divided up into four suits, clubs, diamonds, spades, and hearts, and within each suit, you have 13 ranks, starting with the ace, going all the way up through two, three, four, five, six, to 10, and then jack, queen, king at the top.
Those are the picture cards or the face cards.
That's right, and of course, the ace is interesting because, as you mentioned, it sometimes comes below a two and has the role of one, but at other times, it's beyond the king, right? It's whatever the uppermost card is.
We'll get to that sort of dual role of ace in a bit, but essentially, 52 cards in this deck, also just a standard deck of playing cards.
Now, poker has a lot of variations, but I think the version we wanna focus on here is something like five-card stud.
Tell me about it, stud.
[rock music]
Right, and the game of five-card stud is basically played where the dealer shuffles the 52 cards together so they're all randomly shuffled up, deals out five cards to each playerAnd then after a round of betting or two, players compare their hands to see who has the, quote-unquote, "highest hand." And depending on what cards you're holding in your hand, you might have a hand that's very common, in which case, good luck.
Or you might have one of the rarer hands, like a flush or a straight or a full house, in which case you have a better chance of winning.
And these hands are ranked by how hard they are to get.
The harder a certain hand is to get, the more other hands it's going to beat.
What's interesting to me is that when I was a kid, I did not understand, nobody told me this, that there was this mathematical probability calculation l- lurking in the background that determined the ordering of the hands, which one is worth more than another.
It is.
So I guess one of the first things we need to figure out is how many different hands are even possible from a deck of 52 cards, right?
If we had 52 cards and the dealer shuffles them, now of course there's lots and lots of different ways that a deck could be shuffled, right?
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