# My First Review!

Update, 10:27 pm: It turns out the book is available for sale right now! So go buy one right this very second! Don’t know what that June 4 date was all about…

And it’s a good one! The official release date for the Big Monty Hall Book (BMHB) is June 4, but some review copies have already gone out. One of those went to Peter Flom, who is a diarist for Daily Kos. You can find the full review here.

Flom writes:

I’ll mention right up front that the book was sent to me by Oxford University Press, it’s called the Monty Hall Problem, the author is Jason Rosenhouse, it’s due out in early July, and I liked it a lot.

Early June, not July. But I’m glad he liked the book.

This is one diary and the book is 200 pages. So, what else is in the book? There’s considerable detail about the origins of the problem and the huge outcry when vos Savant published the right answer. There’s extensive coverage of a lot of variations of the Monty Hall game (e.g. different probabilities, more doors etc). Much more important, though, this is a (mostly successful) attempt to teach a course in probability theory through the use of the MH problem.

Mostly? I’ll take it!

I think it has a couple audiences. First, if you are taking a formal probability course at university, this could be a good backup to your text. OTOH, if you are teaching such a course, you could use this as a main text (I’ve never seen a probability text that is this much fun to read). A course based on this book would cover a lot of the ground of a one-semester intro to probability course.

Probably few at daily Kos are in either of those groups. Among the general population, I think this book could be read in two ways: First, you could read chapters 1, 2, 6, 7, and 8, and either skip 3, 4, and 5 or skim them. (Chapter 4, in particular, will be heavy going). Second, if you want to learn probability theory, you could read the whole book. In this case, you’ll want to read it more like a text book.

I was really gratified to read this, since it conforms well to what I was envisioning when I wrote the book. There is a tradeoff between mathematical rigor and readiblity, but I wanted to have a fair amount of both. This is a math book, and I wasn’t afraid of having some equations and notation. But I also wanted plenty of material that a nonmathematician could read as well. So much of the book has no math at all, while in other places the math is fairly light. There are a few places where the math gets pretty dense, but they can be skipped on a first reading. Or a second one, for that matter.

I was also trying to show how a first course in probability theory could be taught using nothing more than variations on the Monty Hall problem, so I am glad Flom commented on that.

1. #1 SiMPel MYnd
May 14, 2009

OK, I’m officially confused.

The link to the Amazon page shows that it’s already available and in-stock. (Also, strangely, you can get a used copy starting north of \$90, but you can get a new copy for under \$20.)

So, what gives?

2. #2 Jason Rosenhouse
May 14, 2009

You’re right! It turns out the book is available right now. Thanks for the head’s up.

3. #3 Blake Stacey
May 14, 2009

I guess that means I need to get my review off the ground now! And here I thought I’d had the rest of the month.

4. #4 Libraryguy
May 14, 2009

Congratulations! Looks like a good book. I’ll have our library system buy a copy so everyone can read it.

5. #5 Takis Konstantopoulos
May 15, 2009

Some time ago I came across a certain “generalization” of the problem, published in this paper:

E. Engel and A. Venetoulias. “Let’s Make a Deal!”
Mathematical Scientist, 18, 73–84, 1993

You may alread know it of course….

6. #6 Jason Rosenhouse
May 15, 2009

Blake –

Libraryguy –

Thanks for the kind words.

Takis –

Yep, I know that paper. It’s mentioned in the book.

7. #7 Jud
May 15, 2009

Jason:

I have a Kindle, love it, and would really, really like to get almost all my reading material there (helps that books are cheaper on Kindle, too).

How much, if any, say do you have regarding whether your book becomes available on Kindle? Or do you happen to know whether there are plans to make it available in that form?

I’m reading the excerpt on Amazon now, and it’s much more entertaining than I thought it would be. (No aspersions on your writing abilities – I just thought to myself, “Probability math, yuck.” But I’m being drawn in by the couple of pages I’ve read, which for me is a reliable sign I’ll enjoy the entire book.) In fact, I promise to buy it if it comes out on Kindle. (There, a sure sale. That should persuade Oxford!)

8. #8 Bob
May 15, 2009

I didn’t see a chapter called the Full Monty in the ToC. I am disappointed.

9. #9 tomh
May 15, 2009

@ #7

According to the Amazon page, “If you are a publisher or author and hold the digital rights to a book, you can sell a digital version of it in our Kindle Store.” Then a “learn more” link. I’m also a Kindle fan.

10. #10 Jason Rosenhouse
May 15, 2009

Jud –

As far as I know it’s completely out of my hands whether an electronic version of the book is made available. I’ll ask my contacts at Oxford University Press about it. Glad you found the first few pages amusing!

11. #11 Bayesian Bouffant, FCD
May 15, 2009

(Also, strangely, you can get a used copy starting north of \$90, but you can get a new copy for under \$20.)
So, what gives?

I’d go with door #2, the new book for \$17.96.

12. #12 Bayesian Bouffant, FCD
May 15, 2009

You should encourage Flom to post a review at Amazon.com. No customer reviews up yet.

13. #13 Jud
May 15, 2009

Regarding the problem that is the subject of the book and its counterintuitive nature, I had a sort of “light-bulb moment” reading through the reviews and comments at Daily Kos. Of course there is danger in trying to derive reliable information from such sources, but for the edification (amusement? consternation?) of Jason and others, let me just go through my train of thought.

What brought me intuitive comfort in the result was the thought that at the start of the process (choose from among three doors, hiding a car and two goats), whichever door you select, you have a 1-in-3 chance of having selected the door with the car, a 2-in-3 chance that it is not behind the door you selected, and those facts never change throughout what follows.

When Monty throws open one of the doors you didn’t pick to show you a goat, rejiggering the odds to 1-in-2, which is what folks intuitively seem to do, would be correct only if time travel were a reality. That is, at the time you made your original choice, this additional information was in your future, and couldn’t travel back in time to increase your odds to 1-in-2.

To see this more clearly, start with 2 doors instead of 3. After Monty throws open the door you didn’t select, if you get a second chance your probability of picking the correct door increases to certainty. But you didn’t have that information originally, so it doesn’t alter the fact that you had a 1-in-2 shot rather than a sure winner with the original selection.

Thinking the same way regarding the 3-door scenario, the fact that there was a 2-in-3 chance the car would be behind a door you didn’t originally pick is unchanged by the fact that Monty is now showing you what’s behind one of the originally unselected doors.

14. #14 MarkusR
May 15, 2009

“But I switched the door and I still didn’t win!”

Just wondering, are there any who are vehemently against the accepted solution?

15. #15 Bayesian Bouffant, FCD
May 15, 2009

From the Update at the Flom review:

I even wrote to (Marylin vos Savant). She got the answer correct, but really botched the explanation…

Certainly not the only time she’s done that. I recall another probability question she asked about male vs. female children. She is either not good at explaining things, or not good at seeing what it is about the question which confuses people.

16. #16 fernando
May 15, 2009

Jason: I have not read yet your book but I have a way to explain that I think it is the easiest way.
Imagine another problem. Monty asks: “Do you want to change the door that you chose for the other two doors?” The probability of winning the car in this case is 66%. The person accepts. So Monty, knowing where the car is and to create suspense in the audience, opens a door with the goat and then opens the other.
But the only difference between those two problems is that on Monty Hall problem he first opens the door and ask later.

17. #17 Blaine
May 15, 2009

Haven’t read the book. Might pick it up. I always wondered what all the fuss was over this problem. Each door has 1/3 prob. Choosing a door partitions the probability space into two regions with objective probabilities of 1/3 and 2/3 respectively. Gaining subjective knowledge about the contents of one of the two doors in the 2/3 prob partitition does not change the objective probs. The region with two doors still has a 2/3 prob of containing the right door. So moving to that region is the best move since you now know subjectively which door in the 2/3 region NOT to choose. Doesn’t anyone study measure theory anymore?

18. #18 Sara
May 16, 2009

Oh, this is so awesome :). I was *waiting* for this book to come out.

19. #19 Soren
May 17, 2009

Another intuitive way of convincing yourself that it is in your best interest to change doors is to imagine a game with 1000 doors.

here you have a 1/1000 chance of picking the right door.

Monty now opens 998 doors with no car behind them.

Now in the 3 door game peoples intuition tells them its a 50/50 chance, but in the 1000 door game it is obvious that you would be a fool not to change doors.

20. #20 heddle
May 18, 2009

Jason,

Congratulations!

21. #21 Jon
May 20, 2009

Can I nit-pick on the opening for 1.1 in the book, where you talk about math as the “sole academic subject about which people brag of their ineptitude”?

Whenever someone finds out I teach English, that person almost invariably calls on one of a two (and sometimes both) stock responses. Many will joke, “I better watch my grammar!” Others feel absolutely comfortable telling me how much they hated English in school.

Maybe it’s some social law – if not, can we call it Jon’s Law? – that whenever someone learns that you teach a certain academic subject, he or she will feel fully compelled and comfortable telling you how he or she once disliked the subject and did not perform well in it at school.

I have the book in my wish list!

22. #22 Leni
May 25, 2009

Congrats on the nice review, Jason. It’s sounds like a great book! I look forward to reading it one of these days. Statistics is something I’ve long wished to understand better.

23. #23 Dave C
June 2, 2009

Congrats on getting this published, Jason! While I don’t consider myself to be too bad at math, I have never learned that much about probabilities, and I have found the MHP to be deeply perplexing when I’ve encountered it in the past. I’ll definitely have to read this at some point to get a better grasp on it.

24. #24 Dave C
June 2, 2009

Also, since I’m a poor college student who can’t afford to buy this right now, I suggested to my university’s library that they buy it. 🙂

25. #25 film izle
June 9, 2009

Certainly not the only time she’s done that. I recall another probability question she asked about male vs. female children. She is either not good at explaining things, or not good at seeing what it is about the question which confuses people.