The Monty Hall “problem”

I stumbled by chance on this book The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser on Amazon, or rather and more accurately Amazon suggested the book as connected to Burdzy’s The Search for Certainty. I first thought why would anyone need a whole book for explaining a simple conditioning argument (and the fallacy of conditioning on the wrong event) that I usually give as a problem to my second year undergraduates. But then I started reading the comments and found one that could not believe there was such a book because the answer was clearly 50-50! (Obviously, this comment was written by someone who had not read the book…) And I thus vaguely remembered a story about a highly respectable and respected statistician getting trapped by this puzzle… So maybe a book is in order. Maybe. But I find the argument of one of the commenters of the above disbelieving comment quite convincing: imagine there are 10,000 doors (instead of just 3), you pick one, the host opens 9,998 out of the 9,999 remaining ones and let you decide between switching  to the last remaining door and sticking to your original choice. Would you ever stick?!