I should admit that I don’t generally use the Monty Hall problem with students, as I am not convinced anyone is enlightened by having it explained. But I have had fun teasing people with it, from my girlfriend 35 years ago, to a senior QC at a dinner. However, my first thought was: how can anyone write a whole book on this? Well, Jason Rosenhouse has, and it’s surprisingly good.
Why surprisingly? Skipping ahead:
The book is chatty and welcoming, and the author’s enthusiasm is infectious. There is, however, a rather uneven use of mathematics, with binomial coefficients introduced without definition on page 11, and fairly basic ideas of probability coming much later. I am not sure of the intended audience: serious enthusiasts may find it too basic, while beginners will grind to an exhausted halt well before the end.
To be honest, after 194 pages of Monty Hall I still am not inclined to use the problem in my efforts to inspire people about the joys of probability, statistics and risk. But I am impressed at how much material can be hung onto a single problem, and the author has my sincere admiration for being such a dedicated, if not obsessive, exponent.
Yeah, it was difficult sometimes to decide how much formal mathematics to include. It was my hope that in most cases people could “read around” the more technical mathematics while still following the gist of the story. It is for others to decide if I succeeded. I must say, though, that while I have shown the book to quite a few “serious enthusiasts,” so far no one has accused me of making it too basic!