{"id":10,"date":"2018-09-16T14:30:42","date_gmt":"2018-09-16T22:30:42","guid":{"rendered":"http:\/\/han-web.com\/blog\/?p=7"},"modified":"2018-10-26T16:51:26","modified_gmt":"2018-10-27T00:51:26","slug":"the-drunkards-walk-and-the-most-counter-intuitive-math-problem","status":"publish","type":"post","link":"http:\/\/www.han.co\/blog\/?p=10","title":{"rendered":"The Drunkard’s Walk and the most counter-intuitive math problem"},"content":{"rendered":"

I don’t think there’s a more counter-intuitive math problem than the Monty Hall problem.<\/p>\n

It’s based loosely on the TV show Let’s Make a Deal<\/em>, but was made popular after a Parade <\/em>magazine columnist was <\/span>berated, by literally thousands of Ph.D.s and mathematicians, for her correct <\/em>answer.<\/p>\n

Here’s the problem:<\/p>\n

Suppose the contestants on a game show are given the choice of three doors: Behind one door is a car; behind the others, goats. After a contestant picks a door, the host, who knows what’s behind all the doors, opens one of the unchosen doors, which reveals a goat. He then says to the contestant, “Do you want to switch to the other unopened door?” <\/em><\/p>\n

Is it to the contestant’s advantage to make the switch?<\/em><\/p><\/blockquote>\n

The answer and reasoning for it is best described by Wikipedia here<\/a>. I think the decision tree diagram explains it most clearly. The most mind-boggling aspect of the answer is that it’s a 2-to-1 advantage!<\/p>\n

I completely forgot about this problem until I was reading The Drunkard’s Walk: How Randomness Rules Our Lives<\/em><\/a> written by Leonard Mlodinow, who also co-authored A Briefer History of Time <\/em>with Stephen Hawking. Mlodinow’s new book contains this and other “real-life” probability and statistics problems (How a mathematician won a small fortune by playing roulette; Use of the Prosecutor’s Fallacy in the O.J. Simpson trial; Why firing Merril Lynch’s CEO for losing on subprime investments doesn’t make sense) interspersed with\u00c2\u00a0a surprisingly interesting history of famous mathematicians.<\/p>\n

I think it’s a fantastic book to read if you’re on a math kick, but a boring one to read if you’re having one of those days where you just don’t feel like calculating your waiter’s tip in your head.<\/p>\n","protected":false},"excerpt":{"rendered":"

I don’t think there’s a more counter-intuitive math problem than the Monty Hall problem. It’s based loosely on the TV show Let’s Make a Deal, but was made popular after a Parade magazine columnist was berated, by literally thousands of Ph.D.s and mathematicians, for her correct answer. Here’s the problem: Suppose the contestants on a […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-10","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=\/wp\/v2\/posts\/10","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=10"}],"version-history":[{"count":0,"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=\/wp\/v2\/posts\/10\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=10"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=10"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.han.co\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=10"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}