And overall, I'd give the article a thumbs up. The most important thing in an article like that is to get people's attention, get their interest, and get them thinking about deeper questions. It's a good article for that. But it's also a bit like a Fred Reinfeld book. If it gets your interest and you keep going, you may have to unlearn some of it later.

Actually our brains do not understand probability. There are volumes of work on that topic. In one of the later sections of Thinking, fast and slow Kahneman distinguishes between "humans" and "econs" to emphasize this point.

The book has a lot of pages in it, but it is written so the average high schooler should be able to handle it. It is a narrative story that provides a nice summary of the 4 - 6 decades worth of work on topics related to the cracked article.

Read the book and you can avoid the hyperbole, although you will still get a truthful summary of the basic notions of how human thinking does, or does not, work. After reading the book there is still room for deepening and sharpening your knowledge, if you wish. But the underlying scholarship is sound--Kahneman did win a Nobel prize for his contribution to the work reported in the book so he arguably knows a thing or two about the topic.

By that do you mean it doesn't come naturally to us? Because it can be studied and learned, just like any other subject.

Speaking of probability, the first thing that brings to mind is a contestant on Groucho Marx's show in the 50's, who had made a pretty big wad of cash in Vegas by studying their roulette wheels over a period of months to see which numbers were coming up more often. I'm sure they rotate the equipement and have other preventative measures in place now to prevent such things now. My dad has written a program in Visual Basic to do pretty much the same thing with the balls in Powerball, though as far as I know, he's never actually played it. I don't think it would work anyway, they probably swap that equipment out too, but I guess the point of the exercise was just to write the program.

I came out a winner in Vegas myself last year. In wandering through the casinos, I found three blinking machines in which the last user had left disgusted without cashing out. I made 28¢ that way, which doesn't sound like much until you stop to think how few come out even that much ahead. I didn't put anything into the machines myself, and the reason why I didn't is precisely because I did understand probability.

Probabilistic thinking is highly unnatural and even those with training often muck it up.

"Linda" is a classic story where a woman is described and the subject is asked whether it is more likely that she is a bank teller or a feminist who is a bank teller.

Probabilistically she is more likely to be a bank teller than a feminist who is a bank teller. But most people, even those with a firm grasp on probability will choose "feminist bank teller."

The Monty Hall problem got a lot of attention when Von Savant gave the correct answer to the problem and she was bombarded with criticism by folks, some very well trained, saying she was wrong.

Even with training the human brain doesn't manage probabilities very well.

The quality of the roulette wheels is under constant surveillance by the casinos for exactly the reason that an unbalanced wheel can give the observant player the edge. These days they have sensors checking for balance.

Dice and cards, which are subject to damage or physical manipulation are routinely swapped out every so often just to avoid giving players an edge.

I don't know specifically what the Powerball folks do, but I am certain they monitor for equipment discrepancies and perhaps replace equipment as a matter of routine. If not, your father's plan would work.

For a good example of that, see Charles Kalme's November 1975 article about Fischer's match conditions, in which he tosses out data willy-nilly when it doesn't fit the conclusion he wants to reach, and posits off-the-wall axioms, such as that there's a fixed "draw expectation" that's completely dependent on match rules, and is unaffected by parity levels, era, the individual players or anything else. Through some monumental data fudging, he managed to convince himself that a First-to-10-Wins Fischer-Karpov match wouldn't have lasted longer than 23 games, because that's how long such matches lasted in the 19th century. And he was a highly trained mathematician, and making errors that I with my mere Bachelor's Degree could spot. People can understand this stuff, but it does seem very easy to forget in difficult moments.

Exactly! It is sometimes amazing how far we will contort reality to reach the conclusion we want to reach. And we cannot help ourselves.

Dan Ariely (behavioral economist who writes for the general public on poor human thinking skills) has a story he tells on himself. He found a website where you enter relevant information--computer processes your answers and tells you what sort of car is right for you.

He fills out the form and the program says "Ford Taurus." Ariely doesn't like that answer so he goes back and changes a few answers, again and again, until the program tells him "Mazda Miata."

Kahneman tells some less dramatic stories on himself as well.

In a guest lecture I gave yesterday we segued into probability and ended up talking about cognitive biases, our tendency to fool ourselves, why the scientific methodology helps us avoid some of these biases. It was a fun class with an active discussion, and we were all laughing, smiling and learning at the same time.

The Von Savant incident is enlightening when you see the comments criticizing her. People flaunting degrees/skill in the maths so they're confident they are right, yet are wrong. It is a really counter-intuitive situation and even though I now know why she's right, I still want to reject her answer.

Was just thinking of getting Thinking Fast and Slow Kindle edition, but it is nearly 20 dollars! I'll go for the interlibrary loan instead. Thanks for the book tip.

General science interest--what would happen if you could throw a baseball at 90% the speed of light toward home plate? hint: it doesn't end well for anyone.

It would be a called strike?