Comments on: The game show problem http://earlyretirementextreme.com/the-game-show-problem.html Becoming debt-free is the first step to building a better world. Financial independence is the second. Doing what YOU want is the third. Thu, 09 Feb 2012 00:07:08 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: Moneyedup http://earlyretirementextreme.com/the-game-show-problem.html/comment-page-1#comment-15838 Moneyedup Mon, 30 Aug 2010 03:19:48 +0000 http://earlyretirementextreme.com/?p=904#comment-15838 I remember this problem being at the beginning of the movie 21 (great film by the way). Why would you change your door? I would say, go with your guy instinct, and stick with the first door you pick. I think that graphics are needed to illustrate this problem better, so thanks to linking to the wiki page with this problem. I remember this problem being at the beginning of the movie 21 (great film by the way). Why would you change your door? I would say, go with your guy instinct, and stick with the first door you pick. I think that graphics are needed to illustrate this problem better, so thanks to linking to the wiki page with this problem.

]]> By: Jacob http://earlyretirementextreme.com/the-game-show-problem.html/comment-page-1#comment-2810 Jacob Fri, 21 Nov 2008 00:47:19 +0000 http://earlyretirementextreme.com/?p=904#comment-2810 @elliot - Yeah, I got inspired by the "21" movie although I knew the problem before that as the tiger example. I found the wiki page today and also learned that it was known as the Monty Hall problem. I agree the wiki explains it better (with pictures even). In the four door case ... the prior probability of winning is 1/4 and the prior probability of losing is 3/4 ... conditioned on the probability that the host selectively shows a goat after you arbitrarily pick a door, the probability of winning by switching is 3/8 and the probability of losing by switching is 5/8. The fact that the prior probability of not switching and the conditional probability of switching add up in the three door case is coincidental. Well, technically not quite coincidental .. in the three door case, you will be forcing the game show host's hand in 2 out of 3 case (if your door hides a goat). This leaves 1 out of 3 which equals your initial probability. In the four door case the host is never forced. @elliot – Yeah, I got inspired by the “21″ movie although I knew the problem before that as the tiger example. I found the wiki page today and also learned that it was known as the Monty Hall problem. I agree the wiki explains it better (with pictures even).

In the four door case … the prior probability of winning is 1/4 and the prior probability of losing is 3/4 … conditioned on the probability that the host selectively shows a goat after you arbitrarily pick a door, the probability of winning by switching is 3/8 and the probability of losing by switching is 5/8.

The fact that the prior probability of not switching and the conditional probability of switching add up in the three door case is coincidental. Well, technically not quite coincidental .. in the three door case, you will be forcing the game show host’s hand in 2 out of 3 case (if your door hides a goat). This leaves 1 out of 3 which equals your initial probability.
In the four door case the host is never forced.

]]> By: Teh Chad http://earlyretirementextreme.com/the-game-show-problem.html/comment-page-1#comment-2808 Teh Chad Thu, 20 Nov 2008 19:28:54 +0000 http://earlyretirementextreme.com/?p=904#comment-2808 I really enjoyed seeing this in the beginning of the movie 21. It's rainman stuff for the masses! I really enjoyed seeing this in the beginning of the movie 21. It’s rainman stuff for the masses!

]]> By: farmwife http://earlyretirementextreme.com/the-game-show-problem.html/comment-page-1#comment-2807 farmwife Thu, 20 Nov 2008 19:04:24 +0000 http://earlyretirementextreme.com/?p=904#comment-2807 Depending on the goat -- is this a national champion who is going to make me babies I can sell for $2500? :) I certainly wouldn't want a car. Not much used to me. A new pickup would be nice, but probably not worth the extra $ it would take to insure and license it. So yeah, gimme the goat. As far as probability.... my interest waned about 2 lines in :) Depending on the goat — is this a national champion who is going to make me babies I can sell for $2500?

:)

I certainly wouldn’t want a car. Not much used to me. A new pickup would be nice, but probably not worth the extra $ it would take to insure and license it.

So yeah, gimme the goat. As far as probability…. my interest waned about 2 lines in :)

]]> By: elliott http://earlyretirementextreme.com/the-game-show-problem.html/comment-page-1#comment-2806 elliott Thu, 20 Nov 2008 18:12:16 +0000 http://earlyretirementextreme.com/?p=904#comment-2806 A nice attempt at explaining the Monty Hall Problem, but could be more clear. In the first part, you never directly state that switching is preferred with a 2/3 probability (but you do hint at it). Your final example is wrong though. Simply, the total probability does not add up to one. If P(switch)=3/8 and P(not switch)=1/4, then P(switch)+P(not switch) = 5/8. Where are the phantom 3/8 of probability hiding? http://en.wikipedia.org/wiki/Monty_Hall_problem#Solution A nice attempt at explaining the Monty Hall Problem, but could be more clear.

In the first part, you never directly state that switching is preferred with a 2/3 probability (but you do hint at it).

Your final example is wrong though. Simply, the total probability does not add up to one. If P(switch)=3/8 and P(not switch)=1/4, then P(switch)+P(not switch) = 5/8. Where are the phantom 3/8 of probability hiding?

http://en.wikipedia.org/wiki/Monty_Hall_problem#Solution

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