# The Indicator from Planet Money - Probability, Gambling, And Death

## The concept of probability may feel intuitive today, but for much of human history, that wasn't the case. Jacob Goldstein tells the origin story of probability.

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NPR

00:00:11

I want this indicator from Planet Money. I'm Cardiff Garcia or one of the hosts of our sibling podcast Planet Money and you are back on the indicator now to tell us another one of the stories in your fantastic new book money, the true story of a made-up thing and today's topic is the invention of probability Theory so probability of the uncertain future, but you know, if you just step back it is also sort of a way of thinking about the world is the way that feels intuitive, you know, if you go look at 5:38 to see their estimate of the chance that Joe Biden or Donald Trump is going to win the election as I do many times today weather app on your phone to see what are the chances it's going to rain tomorrow. These are probabilistic predictions does feel natural. Like obviously we can try to make these kinds of predictions, but for most of human history actually people did not

00:01:07

I think this way they got the future was basically unknowable that it was controlled by God or the gods or by fate or Mother Nature or whatever. And so this idea that has come to feel natural that we can think about the future in this probabilistic way is something that people basically invented or at least discovered something about this that I kind of love is that we sort of thing of probability as it's kind of wonky mathey very high falutin but respectable thing but probability Theory actually has its roots not and universities are in Higher Learning but in gambling and in death so good. Let's do both of those. Let's go gambling and death will start with gambling cuz the gamblers came first and so there is in fact this one moment this one exchange of letters. We can point to as the moment when probability theory was born there. Is this exchange of letters in 16.

00:02:07

54 between these two French math geniuses. For Ma and Blaise Pascal Who besides being a mathematician was a big Gambler and they were trying to figure out a problem that gamblers have been thinking about for a few hundred years by this moment. It was called the problem of the points and to explain this problem Jacob you and I are going to do a simulation you and I are going to bet on a series of three coin flips were going to be $100 big big money's best two-out-of-three coin flips. I've got a quarter here and I'm calling Tales you've got head here comes the flip.

00:02:45

Okay, and it came up Tails? All right, excellent. So you're up 1 to nothing, correct? But now you know what we we got to keep going with the show. We can't keep flipping the coin. We're going to stop the game before it's done. Okay. So now we stopped the game before the end. And the question is how do we split the pot? So this is what form on and Pascal were trying and they figured it out there solution was first we got to look at every possible outcome of our coin flips and figure out who wins in each one. We've already had that first with the came up Tails. So I only need one more flip to come up tails to win out of the next two flips. And so there are actually three different combinations were I can win and then for me I will only win if heads comes up on both of the next to flip. So there's only one combination of the remaining flips where I with so therefore possible combinations,

00:03:45

Three where you win and one where I win you have a 3 out of 4 chance of winning 75% I have a one-in-four chance of winning 25% So that's got one for my decide the fair way to split that got that hundred dollars that we bet. It's $75 for you and $25 for me. That is the solution to the problem of the points sing like this kind of an obvious and simple math problem. Like that was not hard, let down right little bit of a letdown. I actually know I actually think the obviousness to us of this problem is sort of the point here, right? Like before these guys figure this out. This was just not the way people thought about the world, you know, they thought of the future as unknowable not as something you could tell kulick and because they figured it out and because probability spread from gambling to so many other parts of the world. It has become sort of second nature to ask it has become obvious in this way.

00:04:45

Also, I can see the appeal of thinking that the gods had faded me to win this time instead of it. Just being probability. We are then going to talk about how probability moved on from gambling from debauchery to something a little bit more morbid to death.

00:05:06

This message comes from NPR sponsor one signal Publishers presenting hoax Brian stelter's instant New York Times best-selling book about the relationship between Fox News and Donald Trump. The New York Times calls hoax a thorough exploration of the relationship between Trump and his favorite Channel hoax by Brian stelter available. Now wherever books are sold. So the guy who gets us gets probability Theory into death is Edmund Halley. This is the 1690s. Now two decades later. How late is British? He's already by this point helped his pal Isaac Newton published the principia a he has not yet figured out the comment thing that's coming Halley's Comet. This is the problem is actually trying to solve at this moment is how to price annuities. Why not a comment annuities were talking about here is a kind of financial product it still exists today and he was

00:06:06

It works when I buy an annuity. I pay a lump sum of money up front, but they are $100,000 and then in exchange I get a payment every year until I die with my peace a $5,000 a year and obviously whether or not this is a good deal depends entirely on how long I live like if I buy an annuity and then drop dead the very next day that is a horrible deal for me. I do a hundred thousand dollars and I didn't get anything back. But if I buy an annuity and I live for another 60 years that is a pretty sweet deal. So how he was interested in annuities because the British government was big in the annuities business at the time the British government sold annuities, but here is the wild part the rates on the annuities were the same no matter the age of the buyer. So if you were 20 years old and likely to live for decades or 80 years old and not likely to live for decades you got the same deal from the government. So what how he does his

00:07:06

She gets this record of births and deaths from this one town that just happens to keep really good records of these things. And then he does a bunch of math uses this new, you know, probability Theory and he publishes paper laying out How likely people are to die in a given span of time and he finds you know, somebody who just turned 20 has a 1% chance of dying in the next year 50 year old has a 3% chance of dying in the next year given us and we were once like here's a quote on man of thirty May reasonably expect to live between 27 and 28 years to realize that all these life expectancies and then he turns to annuity. She says the government should sell annuities at a price where the buyer gets back the money they pay upfront if they live for the average amount of years reasonable enough. So, you know a 20 year old should get paid less each year than an 80 year old. Do I take it the government then did exactly that right?

00:08:06

What is that a fixed price regardless of age and I think this speaks to really just how different this probabilistic way of thinking was, you know, it seems so obvious to us in part because since how is time probability has spread to so many different things, you know, what's in finances and medicine is Insurance in weather apps and election predictions, but when it happened it was really this giant intellectually in human thought and so it took a while to sink in. Thanks so much man. Thanks very much man. The book is money the true story of a made-up thing.

00:08:40

7:30 indicator was produced by Darren would in fact check by Shawn. Saldania our editors Patty Hearst and the indicator is a production of NPR.

00:08:57

After months of campaigning, we are finally on the cusp of knowing what happens next in the White House and in the halls of Congress, the NPR politics podcast will be there with you every day with the latest results and we'll tell you what you need to know in these uncertain times.

NPR

00:00:11

I want this indicator from Planet Money. I'm Cardiff Garcia or one of the hosts of our sibling podcast Planet Money and you are back on the indicator now to tell us another one of the stories in your fantastic new book money, the true story of a made-up thing and today's topic is the invention of probability Theory so probability of the uncertain future, but you know, if you just step back it is also sort of a way of thinking about the world is the way that feels intuitive, you know, if you go look at 5:38 to see their estimate of the chance that Joe Biden or Donald Trump is going to win the election as I do many times today weather app on your phone to see what are the chances it's going to rain tomorrow. These are probabilistic predictions does feel natural. Like obviously we can try to make these kinds of predictions, but for most of human history actually people did not

00:01:07

I think this way they got the future was basically unknowable that it was controlled by God or the gods or by fate or Mother Nature or whatever. And so this idea that has come to feel natural that we can think about the future in this probabilistic way is something that people basically invented or at least discovered something about this that I kind of love is that we sort of thing of probability as it's kind of wonky mathey very high falutin but respectable thing but probability Theory actually has its roots not and universities are in Higher Learning but in gambling and in death so good. Let's do both of those. Let's go gambling and death will start with gambling cuz the gamblers came first and so there is in fact this one moment this one exchange of letters. We can point to as the moment when probability theory was born there. Is this exchange of letters in 16.

00:02:07

54 between these two French math geniuses. For Ma and Blaise Pascal Who besides being a mathematician was a big Gambler and they were trying to figure out a problem that gamblers have been thinking about for a few hundred years by this moment. It was called the problem of the points and to explain this problem Jacob you and I are going to do a simulation you and I are going to bet on a series of three coin flips were going to be $100 big big money's best two-out-of-three coin flips. I've got a quarter here and I'm calling Tales you've got head here comes the flip.

00:02:45

Okay, and it came up Tails? All right, excellent. So you're up 1 to nothing, correct? But now you know what we we got to keep going with the show. We can't keep flipping the coin. We're going to stop the game before it's done. Okay. So now we stopped the game before the end. And the question is how do we split the pot? So this is what form on and Pascal were trying and they figured it out there solution was first we got to look at every possible outcome of our coin flips and figure out who wins in each one. We've already had that first with the came up Tails. So I only need one more flip to come up tails to win out of the next two flips. And so there are actually three different combinations were I can win and then for me I will only win if heads comes up on both of the next to flip. So there's only one combination of the remaining flips where I with so therefore possible combinations,

00:03:45

Three where you win and one where I win you have a 3 out of 4 chance of winning 75% I have a one-in-four chance of winning 25% So that's got one for my decide the fair way to split that got that hundred dollars that we bet. It's $75 for you and $25 for me. That is the solution to the problem of the points sing like this kind of an obvious and simple math problem. Like that was not hard, let down right little bit of a letdown. I actually know I actually think the obviousness to us of this problem is sort of the point here, right? Like before these guys figure this out. This was just not the way people thought about the world, you know, they thought of the future as unknowable not as something you could tell kulick and because they figured it out and because probability spread from gambling to so many other parts of the world. It has become sort of second nature to ask it has become obvious in this way.

00:04:45

Also, I can see the appeal of thinking that the gods had faded me to win this time instead of it. Just being probability. We are then going to talk about how probability moved on from gambling from debauchery to something a little bit more morbid to death.

00:05:06

This message comes from NPR sponsor one signal Publishers presenting hoax Brian stelter's instant New York Times best-selling book about the relationship between Fox News and Donald Trump. The New York Times calls hoax a thorough exploration of the relationship between Trump and his favorite Channel hoax by Brian stelter available. Now wherever books are sold. So the guy who gets us gets probability Theory into death is Edmund Halley. This is the 1690s. Now two decades later. How late is British? He's already by this point helped his pal Isaac Newton published the principia a he has not yet figured out the comment thing that's coming Halley's Comet. This is the problem is actually trying to solve at this moment is how to price annuities. Why not a comment annuities were talking about here is a kind of financial product it still exists today and he was

00:06:06

It works when I buy an annuity. I pay a lump sum of money up front, but they are $100,000 and then in exchange I get a payment every year until I die with my peace a $5,000 a year and obviously whether or not this is a good deal depends entirely on how long I live like if I buy an annuity and then drop dead the very next day that is a horrible deal for me. I do a hundred thousand dollars and I didn't get anything back. But if I buy an annuity and I live for another 60 years that is a pretty sweet deal. So how he was interested in annuities because the British government was big in the annuities business at the time the British government sold annuities, but here is the wild part the rates on the annuities were the same no matter the age of the buyer. So if you were 20 years old and likely to live for decades or 80 years old and not likely to live for decades you got the same deal from the government. So what how he does his

00:07:06

She gets this record of births and deaths from this one town that just happens to keep really good records of these things. And then he does a bunch of math uses this new, you know, probability Theory and he publishes paper laying out How likely people are to die in a given span of time and he finds you know, somebody who just turned 20 has a 1% chance of dying in the next year 50 year old has a 3% chance of dying in the next year given us and we were once like here's a quote on man of thirty May reasonably expect to live between 27 and 28 years to realize that all these life expectancies and then he turns to annuity. She says the government should sell annuities at a price where the buyer gets back the money they pay upfront if they live for the average amount of years reasonable enough. So, you know a 20 year old should get paid less each year than an 80 year old. Do I take it the government then did exactly that right?

00:08:06

What is that a fixed price regardless of age and I think this speaks to really just how different this probabilistic way of thinking was, you know, it seems so obvious to us in part because since how is time probability has spread to so many different things, you know, what's in finances and medicine is Insurance in weather apps and election predictions, but when it happened it was really this giant intellectually in human thought and so it took a while to sink in. Thanks so much man. Thanks very much man. The book is money the true story of a made-up thing.

00:08:40

7:30 indicator was produced by Darren would in fact check by Shawn. Saldania our editors Patty Hearst and the indicator is a production of NPR.

00:08:57

After months of campaigning, we are finally on the cusp of knowing what happens next in the White House and in the halls of Congress, the NPR politics podcast will be there with you every day with the latest results and we'll tell you what you need to know in these uncertain times.