50 Books each year

Chapter 6, The Power of Mathematical Thinking, Jordan Ellenberg

July 15, 2020 Mijndert Burger Season 1 Episode 6
50 Books each year
Chapter 6, The Power of Mathematical Thinking, Jordan Ellenberg
Chapters
50 Books each year
Chapter 6, The Power of Mathematical Thinking, Jordan Ellenberg
Jul 15, 2020 Season 1 Episode 6
Mijndert Burger

In chapter number 6 of the podcast show ' 50 books each year ' Mijndert is reviewing; The Power of Mathematical Thinking, by Jordan Ellenberg. If you want to learn how to win the lottery and which lottery to play then this is the book for you. Mijndert will read the examples that Jordan is providing in the book and tell you how to make the calculations. Mijndert is also reviewing with Jordan how stockbrokers work and how banks push their index funds. Do you want to know what the mathematical way of thinking about this is? Join the show, subscribe! Because reading 50 books per year is amazing and teaches us a lot! Want Mijndert to read and review a book? Go to www.50bookseachyear.com or contact us info@50booksperyear.com

Show Notes Transcript

In chapter number 6 of the podcast show ' 50 books each year ' Mijndert is reviewing; The Power of Mathematical Thinking, by Jordan Ellenberg. If you want to learn how to win the lottery and which lottery to play then this is the book for you. Mijndert will read the examples that Jordan is providing in the book and tell you how to make the calculations. Mijndert is also reviewing with Jordan how stockbrokers work and how banks push their index funds. Do you want to know what the mathematical way of thinking about this is? Join the show, subscribe! Because reading 50 books per year is amazing and teaches us a lot! Want Mijndert to read and review a book? Go to www.50bookseachyear.com or contact us info@50booksperyear.com

0:01
Do you know how to win the lottery or when not to believe a stockbroker? Then listen to this chapter chapter number six.

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Hello, and welcome to 50 books each year, the podcast show where we read 50 books each year, so you don't have to. This is your host Mijndert Burger. Yes, and we are off chapter number six. And we are reviewing the book how not to be wrong the power of mathematical thinking by Jordan elenberg Jordan is a professor of mathematics at the University of Wisconsin Madison the book is 437 pages long without the acknowledgments and it talks about the mathematical problems and examples in real life. And like I said in the intro, the real life problem that we are going to tackle is how to win the lottery. I don't know about you, but I am an emotional person. I am in tune with my feelings.

1:00
I know what I feel when a few and how to respond to it and how to ventilate it. And yes, this also means I was and emphasis on the was playing the lottery as well.

1:13
But when I saw this book and it's a New York Times bestseller, when I saw this book, how not to be wrong the power of mathematical mathematical thinking, I was like, I am not thinking this way. mathematical thinking is not my daily routine. I need to learn from this. This is a perfect book to review on 50 books each year, because I want to learn from this How can I put the things from this book into my daily life and that is what Jordan elenberg did. Thank you so much, Jordan for this book. It is published originally in 2014. That does not make this an old book because mathematics Of course, it changes over time, but it is so relevant what is in this book, and lotteries in my case are always relevant.

2:00
So let's talk about it. Let's dive into it right away, how to win the lottery. And to start off, we're going to start with a an example. You have a lottery and you buy a ticket of $2. Now with the tickets, you have a one in 200 chance of winning $300.

2:21
Now, if you would pay this lottery 1000 times, statistically, you would win five times. Now, of course, of course, lotteries are random. Winning is random, but statistically speaking, you have a chance about five times a week. So you would win 1500 dollar.

2:42
This sounds like an amazing amount of money 1500 dollar in your pocket, but you have to remember, you invested 1000 times times $2. So you invested $2,000 so you lost you lost actually $500 Now, this also accumulate

3:00
To your $2 tickets is worth $1 50 per ticket. Now in mathematics, they call this the expected value, or the average value. And Jordan says the expected value is actually a wrong kind of term. We don't use it because it's not correct anymore. We use the term average value. So Jordan will go with that average value for this ticket was 1.5 dollar.

3:27
So this is not a good lottery to invest in, of course, you can have a chance that you buy one ticket, and you have the jackpot of 300. But those chances are really slim. And if you play the long game, then this is not a good lottery for you.

3:46
Now,

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this is only a one in 200 chance, so let's make it a more realistic lottery. Let's go with six kind of numbers and 9.3 million tickets. Let's do this and I'm going to explain

4:00
To you, so bear with me. If you would match all six numbers, you have one in 9.3 million chance to variable jackpots. If you have five, it's one in 39,000 for $4,000 force one 800 for 153 is one and 47 for $5. And if you have to correct, you have a one in 6.8 chance and you get a free ticket. Now, do you remember the numbers? Probably not. But they're in Jordans way of explaining explaining the whole situation of lotteries. It's in the book as well. But if you would calculate this in a mathematical kind of way, and you would play big

4:43
the average value of this ticket

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is 97.8 cents. That is not a lot. You would lose big in this lottery. Even though you would have variable jackpots, which is

5:00
Clearly more than the $4,000, you could win with five of the six numbers correct.

5:07
The average value of this ticket is 97.8 cents. Now let's get over this. What do you have to do? You have to calculate here, what the chances are of winning it.

5:23
And what you will win with it, you will make that into a sum. And for for every identifier for every correct number of balls or numbers, you would make a calculation by itself. So for the beginning, it would be if you would have all six numbers, then let's say the jackpot is 1 million. So you have to divide 1 million by 9.3 million because that's the amount of tickets there is. Now, put this number that you calculated here to decide and add to it. The next

6:00
one to five corrects, that is the word price of $4,000. You divided by the chance that you have to one in 39 sorry 93,000

6:12
put this number to decide and edit to the first one and continue to do this. So also the 150 divided by the chance of one at 800 and so on and so on. If you would calculate this, you would get the average value of 97.8 cents. That is not a lot. This is a luxury where you are losing. Now, here in Europe, there is a lottery euro million and it is published by Jordan that this lottery has returned an average value of 40 cents only 40 cents while you pay 2.5 euro

7:00
Yes, exactly. Maybe you're not good at mathematical thinking as as well. But I calculated it that six point 25 times the loss. This is a lot of money. That's a lot of money that you're pushing towards the lottery. And it's not coming in your way.

7:17
Stop playing these bad lotteries. Of course, Jordan is not pushing you to play the lottery, calculate what is in it and how to beat the system. But he's explaining how lotteries work, and what the mathematical way of thinking is when you're playing these lotteries. Because this is just statistics, chance,

7:43
and even geometry, but we'll get into that too.

7:48
So, Jordan loves to explain a lottery in Massachusetts from 2005. Now, they had initially no jackpots and they didn't

8:00
Nobody was playing the game anymore or nobody was winning the jackpot. So you try to reinvent it and they came up with a roll down system. So for every time the jackpot or every couple of times a jackpot didn't go or didn't go to a buyer, then there was a roll down and the jackpot would go to the lower tiers of tickets. Fantastic system. Now, when we calculate the numbers for this if you would have five matches, so the maximum is five bowls, five matches, it is a one in 9393.

8:44
If you would have five matches, it is a one at 39,000 chance for $50,000. If you have four matches, it's a one in 800

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you would win $2,385

9:00
If you would have three matches, it's a 147 of $60.

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calculated again, so do the chances, the amount of money that you're that you're possibly the amount of money that you might win, divided by the chance, for example, the $50,000 divided by

9:21
93,000.

9:24
Add dose for every tear, and you will come on a staggering return an average value of $5 53. Now you would only pay $2. So this is more than double, more than double. on a large scale, you could win with this lottery. Oh and Jordan laughs So explain how students from MIT being smart as they are, or figuring this out. And we're making ma me. Now how did you figure this out? One of the students had to write

10:00
Or had wanted to write an essay about return of lotteries. And when he did the comparison of lotteries, he found out that windfall, the state owned lottery in Massachusetts, was having this return. So he found his buddies, all the students

10:21
invested all the money they could, and they were making money on the roll down days. Because if you can double your money, every time, you are doing good. Now, of course, they were not the only ones figuring this out. Indians there were three big groups of people that were playing the game, but the three groups, each for their own had an average of 15% return. Now this is a kind of return you cannot get anywhere. So they were making me forever.

11:00
Every time they invested $100, they got 115 back. This is winning it. And this is only due to mathematical thinking. And this is insane. Jordan explains in the book exactly how to make the calculation. If you didn't follow it, I get it. I had to read it three, four times because they are wanting to have it correctly. And even if I'm reading it to you right now, I can imagine that it's very difficult to understand, but you have to read the book, you have to buy it. Understand for yourself, how can you calculate your local lottery or the lotteries that you might be able to buy and see if it has a good average value per ticket?

11:45
Now, to give you a scale of what was going on in Massachusetts, they were buying tickets by the thousands.

11:53
And it wasn't pure luck. Because if we think about a lottery, we think you buy a ticket and the ticket is the same kind of

12:00
value is the next ticket, you have an average value. And luck will give you the win or not the jackpot or not. But this is not the case.

12:11
The students from MIT figured out a way that they had to buy tickets, and it was coming from geometry.

12:20
Yes, geometry, the mathematical fields, where you have lines, curves, and all those kind of things. And that is how they find out which tickets to buy, and which not. Now, this is also being talked about in the book. So if you want to know how to win the lottery, or how to calculate the average value of the lottery, you have to buy this book. Now. I know what you're thinking, this might be a one time deal. No, it's not it happened before. You might also be thinking like why did the state have has this have this kind of lottery the state

13:00
was making money. They didn't care that the same people were making the money from the lottery because they were making 80 cents per ticket anyway.

13:11
So there you go, just stables make making money and they were making people happy. Nobody cared. Everybody was happy. And this is how it went down in the United States. The windfall

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jackpots Massachusetts, look it up. Jordan is talking about it. It is amazing, and I hope it inspires you to calculate what the numbers are for your lottery. Now, for the next part of the show, I want to talk about stockbrokers why they are important, why they are not important when to believe them when not to believe them. But first, let me ask you this.

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This is a new podcast, and it would help out to show a lot if you would subscribe to the channel. leave a review on Apple podcast or Spotify.

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And push the algorithm to promote this show.

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Thank you very much for considering and but that being said,

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and now, back to the show.

14:16
Yes, because the other thing, people are having a lot of dreams about becoming rich with stocks, so maybe nuts, the lottery, maybe stocks are your thing. Now, there is a famous story going on of a Baltimore stock broker. And Jordan is actually describing this in his book. Now, he has also said in the book, that he's not sure if this story is true or not, but it gives you the mathematical insights you need. When you see numbers from banks, stockbrokers, or any of the people that will try to sell you stocks. Here we go, and I'm quoting this from the book.

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One day you receive

15:00
an unsolicited newsletter from a stockbroker in Baltimore, containing a tip that a certain stock is due to a big rise, a beat a week passes. And just as the Baltimore stock broker predicted, the stock goes up. The next week, you get a new edition of the newsletter and this time, the tip is about a stock whose price to broker things is going to fall.

15:22
And indeed, the stock craters 10 weeks go by each one bringing a new issue of the mysterious newsletter with a new prediction. And each time the prediction comes true.

15:35
Now, of course, this is

15:38
unlikable, it was the end of the god this is unlikable. Of course, if you get a stockbroker, every week, you get a newsletter and every week the stock broker is right. You're thinking to yourself, Damn, this woman or this guy is good. Maybe I should invest here. And just when we're talking about when would you invest after newsletter one

16:00
newsletter three 510.

16:03
Who knows? But let's get the mathematical out of the way. Because if you would have a 50% chance of having the correct answer every 10 weeks, if you would calculate this, you have a one in 1024 chance this will happen. So this will be a fantastic stockbroker, of course. But

16:27
this is not the case. Of course, there is no way in bleep that this can be true.

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And this is how it works. And we'll quote again, from the book.

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Things look different when you tell the story from the Baltimore stockbrokers point of view.

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Here's what you didn't see the first time. The first week, you weren't the only one who got the broker's newsletter he sent out 10,240

16:58
but the newsletters weren't or

17:00
The same half of them were like yours predicting the rice in the stock. The other is predicting exactly the opposite. So, the 5120 people who got adult prediction from the stockbroker never heard of him again. But you and the 5119 other people who got the your version of the newsletter, got another tip the next week.

17:26
Have those 500 to 5102 20 newsletters have say what your sets and have the opposites and so on, and so on.

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By week 10, there's 10 lucky people

17:43
who will get 10 good predictions in a row. Now, let us end the quote here.

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This is just how it works with big numbers and statistics. This is mathematical thinking in its purest form.

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The biggest

18:00
Get a group of numbers, and you would be able to trim it down. You don't care about the individual number. person number A can be also person number BC, but that person gets 10 good predictions. Now, if you get 10 good predictions in your mailbox, it is very hard to resist the thought of investing, whatever you got, if it's 100 euro, it's 100. If it's $10,000, it's $10,000.

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But whatever you have, it's very hard not to invest because this person knows what he or she is talking about. And when are you going to need this

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because you're probably not going to get the newsletters in your letterbox. This is not how it works these days. But what happens nowadays is something we call incubator funds. incubator funds are funds from banks, and we all get

19:00
newsletters, emails or apps or things from banks or stockbrokers, about investing in finance. And they already predict even though when the fund is new, they predict that the fund made

19:19
revenue of 70% or 60% 5040. What is your number, but somehow a new fund

19:30
is already making a certain percentage of profit. Now, how does this work? banks are not stupid. Just as the Baltimore stockbroker.

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They diversified their chances. They have so many incubator funds,

19:50
that they will kill their babies, the ones that are not performing good, they will kill and the ones that are performing good in the last year, they will advertise

20:00
Now,

20:01
this is the real thing. And this is why you will see the message on every bank advertisements. That's the history of it is not a prediction of the future. But they are able to show that lovely shiny number that different made a 70% return in the last year. And this is how they did it. They had multiple of incubator funds, and they have multiple of babies that they killed. And they had a few shiny numbers that they pushed towards you. And you are investing in it because you see these big numbers and you think these guys and these girls, these people know what they are talking about, I should invest here.

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Now this makes you think

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this makes you think about the choices that you're making in your life. Where are you

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putting your money, is it the lottery? Is it the stock markets? Jordan elenberg has an answer from a mathematical point of view, when to trust when not to trust? And what questions to ask.

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And this is what amazing in his book because Jordan is able to make these big, big, big, big mathematical, difficult mathematical things into everyday, easy solutions and easy examples. And this is amazing because he's also talking about Flogger, atoms logarithms. What the hell are those you will find in the book. He's also talking about voting mechanisms.

21:44
Why a two party system like for example in the United States is a difficult thing to work with, if you're talking about my minority or majority groups. Now, of course I can already hear you think like that.

22:00
51% is 51% then you have a majority group, right? That is not how it works. And Jordan is explaining that in his book. So if you want to learn from Jordan how to put mathematical thinking in your everyday life, this is a book that you have to buy. I loved it, I would give it a four out of five though, because I'm not a mathematical person. And I had to read his book in seven days. It was difficult for me, but I plough through it. And I'm very proud of it. And I actually enjoyed the book a lot because it taught me a lot, a lot of mathematical views of the world and you are actually changing your views with the things that Jordan is writing his book. Thank you very much for listening. And with that being said,

22:48
subscribe to the podcast. 50 books each year, go to www dot 50 books each year.com for all of our social media channels and join the story

Transcribed by https://otter.ai