## Great Monty Hall problem site

Jeremy Jones has created an outstanding interactive site, "Stay or Switch," just to help people understand the Monty Hall problem.

I got this email from Jeremy last night and was inspired to check out his site.

Dear Sol,

I love your blog (got a kick out of the "Fields arranged by Purity" comic). I've also been excited about math since middle school. I love teaching it and I got really interested in teaching/explaining complicated concepts using simple animations. So I picked what I thought was one of the most hard-to-explain problems, the Monty Hall Problem, and made a game simulation and multiple animated explanations. I recently published a website devoted to the problem. It's www.stayorswitch.com. I'd love to know what you think of the site.

All the best,

Jeremy

I was blown away by the effort Jeremy has made to explain a classic but unintuitive problem. The graphics and animation are professional quality, And, the explanation of the problem using 100 goats is the best one I've seen. Awesome job, Jeremy!

Folks, please spread the word and encourage Jeremy to make more of these awesome math animations!

Jeremy JonesAugust 4th, 2011 - 07:02

Thanks for the support, Sol! Hopefully there are more videos to come in the near future.

Paul SalomonAugust 4th, 2011 - 16:50

Great problem. Great site. Here’s a little story about what happened when I asked this question to some fifth graders. I get an unsatisfying answer. You’ll see what I mean.

http://wp.me/p1IW16-38

DeniseAugust 5th, 2011 - 16:50

Nice site, as far as it goes. I’ve added a link to it in my Monty Hall article.

Unfortunately, the problem as usually stated is ill-posed, and this site suffers from the same illness. The standard analysis works only if the game show host knows where the car is AND if he has to open a door and offer you a chance to switch. If either of these is not true (that is, if the host is ignorant OR if he has freedom), then the odds of getting the car by switching my be quite different.

Wikipedia offers a good analysis of the possible alternate scenarios.

DeniseAugust 5th, 2011 - 16:52

Oops: “…

maybe quite different.”Jeremy JonesAugust 5th, 2011 - 20:37

Thanks Denise. You’re right about posing the problem. In the explanation video I make sure to make the point that the host knows where the car is and always reveals a goat. In the game on the site, I don’t make the point because I figured that after about 2 plays someone would realize that the host obviously opens a door to reveal a goat each time (because you never see any cars). You’re right though that it makes all the difference in the world.

Win SmithAugust 11th, 2011 - 06:39

That is an excellent way to explain and explore the problem. Thank you for the link. I’ve linked to it (and this site) as well:

http://welltemperedspreadsheet.wordpress.com/2011/08/10/play-the-monty-hall-game/

I think this problem raises some issues about the utility concept in economics that I will discuss in a future post on my blog.