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A wonderful account of this is given in Ellenberg's "How Not to Be Wrong": https://en.wikipedia.org/wiki/How_Not_to_Be_Wrong

I highly recommend the book; it is a popular mathematics book, written by a real mathematician, discussing some real mathematics, with an engaging style.

Actually, I think this issue was brought up in the book "How Not to be Wrong" by Jordan Ellenberg, and the MIT students eliminated risk by taking advantage of a Steiner system. So I suppose it favors the intelligent, not necessarily the rich.

There is a fun chapter on this topic in Jordan Ellenberg's latest book "How not to be wrong".
It's called the "Baltimore stockbroker fraud".

I know that specific story from the book "How not to be wrong", by Jordan Ellenberg.
It was nice to read it from a different angle in this article

I highly recommend Ellenberg's "How Not To Be Wrong". Ellenberg is a first-class mathematician and general expositor, and his book illustrates the power (and the limitation, in an endearing way) of mathematics as a tool of thought.

on my reading list so far:
D. Huff et al - How to Lie with Statistics
J. Ellenberg - How Not to Be Wrong: The Power of Mathematical Thinking

IIRC Bill Gates recommended them.

There's a nice explanation of the game and the exploitation in the book How Not to Be Wrong: The Power of Mathematical Thinking.

#2 is called this: http://en.wikipedia.org/wiki/Buffon%27s_needle. This is also mentioned in Jordan Ellenberg's book How Not to Be Wrong, and has a similar passage with your explanation above. I mention the book as much because it's a great read.

My first exposure to this idea was in Jordan Ellenberg's fantastic book "How Not to Be Wrong: The Power of Mathematical Thinking". Here's a post from him that goes into the same example he uses in the book:

https://slate.com/human-interest/2014/06/berksons-fallacy-wh...

There are quite a few popular books on this topic, e.g. How Not to Be Wrong: The Power of Mathematical Thinking :

https://smile.amazon.com/How-Not-Be-Wrong-Mathematical/dp/01...

Jordan Ellenberg's "How not to be wrong". Recommended even for non teenagers.

I've just started reading How Not to Be Wrong: The Power of Mathematical Thinking by him. I enjoy these synchronicities.

This story (and the math behind it) is discussed at length in "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg. I highly recommend it, the other stories in it are equally enlightening.

Alternatively, they could do the math and figure out when the expected value exceeds the purchase price. That's how these games have been won in the past. It's explained a bit in the book, "How Not to Be Wrong: The Power of Mathematical Thinking" by Ellenberg, Jordan

I hated math before and I thought I was gonna hate it in my whole life. Not until I had to study GMAT and it changed my life forever. I watched the GMAT problem solving explanation on Khan Academy. I think it was pretty simple math and fun to learn. easy to understand for math haters. It was pretty awesome. To me, math is the new door to the new world. I started reading books about math and related field like Physics. (Thinking in numbers by Denial Tammet, How Not to Be Wrong by Jordan Ellenberg. Cosmic Numbers: The Numbers That Define Our Universe by James D. Stein, Richard Feynman and etc. I think you get this, stay curious, stay open to learn. Hope this help and good luck! :)

I've had a pretty similar experience. Get exercise, sleep, food and hydration under control, then (in my case) medication helps me make the most of that structure.

I actually just wrote a giant post [1] about what I've learned about managing ADHD so far. It focuses on the core stuff, but I want to follow it up with a breakdown of how books like Deep Work (e.g. Flow; Farsighted; Thinking, Fast and Slow; How Not to be Wrong) have made a difference for me.

[1] https://medium.com/@sashacollecutt/life-with-adhd-a61cae5a5b...

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) by Barbara Oakley

How Not to be Wrong: The Power of Mathematical Thinking by Jordan Ellenberg

I'm not sure but I heard Little Brother by Cory Doctorow covers ideas of privacy and information security?

I haven't read it myself yet but I heard great things about Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter.

There's some interesting analysis of the math behind Spot It! on stackoverflow [1].

That post mentions the Fano Plane, which, incidentally, I first read about in the book How Not to Be Wrong by Jordan Ellenberg, a mathematician quoted in the article about Set that started this thread. In the book, he uses the Fano Plane to explain how to pick numbers for a specific kind of lottery.

[1] http://stackoverflow.com/questions/6240113/what-are-the-math...

I used to commute in silence or listening to the radio for my daily Silicon Valley drive (237 Milpitas to Mountain View), and by the time I got to work, I'd be angry, frustrated, and cognitively spent.

Listening to audio books has allowed me to relax, enjoy the reading, and get to work excited about the day.

I treat the time as a chance to "read" those books which I wouldn't normally spend either my work hours nor my free time hours on. It's a chance to get informed on topics that are only slightly related to work, but expand your mind in ways that will make you a better thinker, and thus a better programmer.

The books I've found particularly good on audio are:

* Zen and the Art of Motorcycle Maintenance

* Thinking, Fast and Slow

* How Not to be Wrong

* Ready Player One

* Neuromancer

The Four Steps To The Epiphany - Steve Blank

Code by Charles Petzold

Artificial Life - Steven Levy

Time Reborn - Lee Smolin

The Singularity is Near - Ray Kurzweil

Surfaces and Essences - Douglas Hofstadter

How to Measure Anything - Douglas Hubbard

-- One of my favorites is How Not to Be Wrong by Jordan Ellenbreg

I have that on my list of "to read real soon now". Sounds fascinating.

If you're a fan of "How not to be wrong" (http://www.jordanellenberg.com/how-not-to-be-wrong )—and, if you're not, then go read it and you probably will be—then it may be worth noting that this article is by the same author. It is an excellent and accessible exposition that doesn't shy away from pointing to more technical resources for those who are interested.

The top 4 this year for me:

How Not to Be Wrong: The Power of Mathematical Thinking

Algorithms to Live By: The Computer Science of Human Decisions

How to Change Your Mind: What the New Science of Psychedelics Teaches Us about Consciousness, Dying, Addiction, Depression, and Transcendence

Moral Tribes: Emotion, Reason, and the Gap Between Us and Them

Phenomenal books. I have a longer list of recommendations I've collected over the decades: http://yboris.com/reading/

The book How Not to Be Wrong: The Power of Mathematical Thinking[1] by Jordan Ellenberg has a segment on this with similar examples (minus the programming bits), tying it in to human psychology and, with surprising insight, the behavior of slime molds. Would definitely recommend reading if you find these kinds of topics interesting.

[1]: http://amzn.to/2kHiROT

Let me propose another theory. In the awesome book "How not to be wrong" ellenberg walks through a scenario with dishonest roulette machines as a way to explain Bayesian Inference and shows how powerful your priori are in interpreting new evidence that you are shown. If you hold a non neutral viewpoint on something, natural variations of a neutral truth will take an extremely long time to adjust your view of reality.

It just so happens that most highly educated people get their initial priori set from the institutes of learning that have increasingly become sounding chambers for liberal ideologies. So its no surprise that it takes a preponderance of evidence to migrate those views back towards a neutral reality ( if in fact reality is neutral ). A similar situation can be established for rural and uneducated people. They get their priori set from their parents and peers who have a very distinct view of government and governance. All the other talk I see of reasons for the homogenization of the educated class into a specific political view just reads like chest thumping to me.

My above comment has started its slow descent into negative karma, and there's probably nothing I can do about it -- what's the point of karma if not to spend it from time to time anyway.

I'm currently reading "How Not to Be Wrong" by mathematician Jordan Ellenberg; here's what he has to say about his calling:

"Pure mathematics can be a kind of convent, a quiet place safely cut off from the pernicious influences of the world's messiness and inconsistency. I grew up inside those walls. Other math kids I knew were tempted by applications to physics, or genomics, or the black art of hedge fund management, but I wanted no such rumspringa. As a graduate student, I dedicated myself to number theory, what Gauss called "the queen of mathematics," the purest of the pure subjects, the sealed garden at the center of the convent, where we contemplated the same questions about numbers and equations that troubled the Greeks and have gotten hardly less vexing in the twenty-five hundred years since.

"At first I worked on number theory with a classical flavor, proving facts about sums of fourth powers of whole numbers that I could, if pressed, explain to my family at Thanksgiving, even if I couldn't explain how I proved what I proved. But before long I got enticed into even more abstract realms, investigating problems where the basic actors— "residually modular Galois representations," "cohomology of moduli schemes," "dynamical systems on homogeneous spaces," things like that—were impossible to talk about outside the archipelago of seminar halls and faculty lounges that stretches from Oxford to Princeton to Kyoto to Paris to Madison, Wisconsin, where I'm a professor now. When I tell you this stuff is thrilling, and meaningful, and beautiful, and that I'll never get tired of thinking about it, you may just have to believe me, because it takes a long education just to get to the point where the objects of study rear into view."

Maths appeal rests in it being a "sealed garden at the center of the convent". One should do math because this sealed garden brings you peace, because you belong there.

This reminds me of one of the chapters from "How Not to Be Wrong: The Power of Mathematical Thinking" by Jordan Ellenberg (highly recommended). He describes how "stock brokers" would send out a "free stock prediction" to thousands of email addresses. The prediction would be a simple up/down prediction for a specific stock. The prediction was randomly chosen. But these "brokers" would send an equal number of up and down predictions, ensuring that they got a correct prediction for half of their recipients. They would then throw away half of the emails (the wrong half), and repeat with the remaining half. After ten predictions, there would still be a small number of people remaining for whom they'd sent only correct predictions to (10 in a row, which seems really impressive if you can't see the full picture). They would then contact these few people and offer to keep selling them predictions for a fee.

Stories like this (And Paul the Octopus, who I see was mentioned already) are exactly the same thing. Thousands of people are trying to using deep learning (i.e. stats), or other crazy methods as in this article, to make predictions. Of course every now and then one of them is going to work better than expected. This would be the case even if people were simply using random numbers. But we ignore all the ones that fail and give heaps of attention to the Pauls.

I also find reading multiple books in parallel really helpful. In this way, you can read multiple kinds of books.

For example, I am currently reading a "mathematical book"- Jordan Ellenberg's 'How Not to Be Wrong', a big fat novel in my native language, and Rumi's poetry in English.

It get's tiring to read serious non-fiction for multiple hours but there is still appetite for reading left. You should switch to a fiction then. And read poetry and book like Meditations by Aurelias now and then, maybe not even linearly.

I have found this combination to work for me really well.