THE MONTY HALL PROBLEM, Posted 19 April 2013

THE MONTY HALL PROBLEM: The Remarkable Story of Math's Most Contentious Brainteaser
JASON ROSENHOUSE
Oxford University Press
$35.95 hardcover, available now

Rating: 3.5 bumfuzzled stars of five

The Publisher Says: Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

My Review: I'd rate it higher if I understood it....

Twenty years ago, a brouhaha erupted in Parade magazine, of all unlikely places, about a probability problem, of all unexpected things. It's an exercise in applied probability mathematics. Here's the famous statement of the problem:

"Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?"

Okay, so the answer is, "Always switch." You'll win about 64% of the time if you always switch, vs 31% of the time if you DON'T switch. This has been demonstrated again and again and again and again since the problem surfaced in 1959 (under a different name). People are *still* arguing about it! People with advanced degrees in math are arguing against the mathematical proof! (Which reinforces my absence of respect for the mere possession of an advanced degree.)

This book contains formulae and equations, so the phobic should pass it by. Being barely numerate, I skipped anything that had italic x's or y's, curly brackets, extra-large parentheses, or other quick identifiers of mathspeak, and I did okay.

What did I learn? 1) Jason Rosenhouse has a sense of humor and a quick way with a zinger. 2) Always switch doors on "Let's Make a Deal." 3) Rein in my curiosity about subjects I don't grasp readily...getting books via InterLibrary Loan means one has to read them too quickly for comfort!

Should you read it? Probably not. It's not a subject of interest to most people. If it is of interest to you, make sure you have ample time to revisit the more baroque sections. And run run run like a bunny if you see the word "Bayesian!" That way mouth-breathing, drool-dripping, eye-crossing befuddlement lies!