# Gameshow probability problem/riddle **URL:** \ **Category:** General Discussion\ **Created:** [March 5, 2010, 6:24am UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986 "2010-03-05T06:24:32Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 6:24am UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/1 "2010-03-05T06:24:32Z")
I don’t know why but I was thinking about this great logic/probability problem today. Many have probably heard this before but I’m going to post it anyway. I think it’s a great problem and fun to use to confuse the hell out of people. Try not to Google for the answer because 1) it’s easy to find and 2) knowing the answer is only a fraction of what value is in this problem to begin with. I absolutely did not get it right the first time I heard it and furthermore people with PHDs were writing vehement arguments about why the originally proposed solution (by Savant) was incorrect. This was after they heard the alleged solution! But of course they were wrong. OK, here it goes. > [@](#): > > You’re contestant on a game show and the host presents you with 3 doors. Behind 2 of those doors is a goat and behind the remaining door is a car. There are a few out there who might find great pleasure in one of those goats but let’s say for the sake of argument that in this game your goal is to win that car. So you pick a door, but before the gameshow host instructs his hot assistant to open that door he stops short and says he’ll give you an option. The gameshow host then opens one of the 2 remaining doors to reveal a GOAT behind it and says to you that you now have the option to 1) stay with the door you have currently selected or 2) switch to the other unopened door. What’s your move and why? Feel free to argue, comment, answer at will. If you know the answer and understand the reason behind it already please hold off until a number of gbfans get a chance to try it out. Please, please, please don’t spoil it by just going to wikipedia and pasting the answer/proof. ---
**Author:** ![kingpin](https://forum.gbfans.com/user_avatar/forum.gbfans.com/kingpin/32/188026_2.png) [@kingpin](https://forum.gbfans.com/u/kingpin)\ **Post date:** [March 5, 2010, 11:05am UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/2 "2010-03-05T11:05:12Z")
Saw this one on _Numb3rs_. ---
**Author:** ![hooker](https://forum.gbfans.com/user_avatar/forum.gbfans.com/hooker/32/5929_2.png) [@hooker](https://forum.gbfans.com/u/hooker)\ **Post date:** [March 5, 2010, 1:30pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/3 "2010-03-05T13:30:11Z")
This is also a line from Kevin Spacey in the movie “21.” ---
**Author:** ![Ron\_Daniels](https://forum.gbfans.com/user_avatar/forum.gbfans.com/ron_daniels/32/12_2.png) [@Ron\_Daniels](https://forum.gbfans.com/u/Ron_Daniels)\ **Post date:** [March 5, 2010, 2:34pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/4 "2010-03-05T14:34:00Z")
If you understand methodology and probability, it’s really simple. ---
**Author:** ![m\_burkit](https://forum.gbfans.com/user_avatar/forum.gbfans.com/m_burkit/32/187890_2.png) [@m\_burkit](https://forum.gbfans.com/u/m_burkit)\ **Post date:** [March 5, 2010, 2:35pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/5 "2010-03-05T14:35:30Z")
It depends. One of my biggest issues with this question and similar questions is they do not adequately describe the host’s behavior during this scenario. Most people will argue the mathematical probabilities for their answers to this, but since the host of the show is presenting the scenario to the contestant, I raise the question of motivation. Why would they present the choice? What makes better TV? Someone that wins a car, or someone that would have won a car but changes their decision to a goat? And what costs the studio more money, a goat or a car? When presented with this problem purely as a mathematical probability question, I’d switch my choice, because there is no human element in the equation. I won’t explain why though until others give their choices and explanations. If this was really happening, I’d probably stick with what I originally chose, but once again, it depends on the behaviors of the host and perceived motivation behind the scenario in the first place. That’s my answer. ---
**Author:** ![jackdoud](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/j/6a8cbe/32.png) [@jackdoud](https://forum.gbfans.com/u/jackdoud)\ **Post date:** [March 5, 2010, 2:37pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/6 "2010-03-05T14:37:01Z")
How is there a wrong answer to this? It’s not a factual question so there is no right or wrong. Unless the capitalization is intentional and the opened door actually revealed a GOAT ie: a Pontiac GTO so both the remaining doors have an animal behind them. Either way the “question” is deliberately obtuse, I don’t get the point. ---
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 4:57pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/7 "2010-03-05T16:57:05Z")
> [@jackdoud](#): > > How is there a wrong answer to this? It’s not a factual question so there is no right or wrong. > > Unless the capitalization is intentional and the opened door actually revealed a GOAT ie: a Pontiac GTO so both the remaining doors have an animal behind them. > > Either way the “question” is deliberately obtuse, I don’t get the point. There is a right/wrong answer to this - I mean, we’re talking probabilities not absolutes so regardless of the decision made I will say it’s not 0.0 or 1.0 probability, it is somewhere in between. Let me clarify, this is not a trick question. I’m not playing with words. A goat/GOAT/GoAt is an animal, which for all intents and purposes is an undesirable outcome for the contestant. 3 doors, 3 objects. 2 of the objects are goats. 1 object is a car. here’s one sample scenario DOOR 1, DOOR 2, DOOR 3 goat, goat, car Mburkit, sure if it was a scenario where the contestant was a poker player or something, could read people, and subsequently the host, then that could certainly play in, agreed. But again, this is a simple probability problem and there are no hidden probabilities involved. There’s only one correct answer based on the inputs. I think that’s where you landed after your comments, but just wanted to clarify that. ---
**Author:** ![jackdoud](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/j/6a8cbe/32.png) [@jackdoud](https://forum.gbfans.com/u/jackdoud)\ **Post date:** [March 5, 2010, 5:44pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/8 "2010-03-05T17:44:11Z")
> [@mikegbfan2009](#): > > But again, this is a simple probability problem and there are no hidden probabilities involved. There’s only one correct answer based on the inputs. I think that’s where you landed after your comments, but just wanted to clarify that. So the question should have been stated as “According to probability is it better for the contestant to keep the initial door picked or change their choice to the other door”. THAT is an actual question then. Just saying “would you change and why/not” makes it seem like a cheesey high-school english test essay question instead of the mathmatics problem it is. ---
**Author:** ![aj-quick](https://forum.gbfans.com/user_avatar/forum.gbfans.com/aj-quick/32/188008_2.png) [@aj-quick](https://forum.gbfans.com/u/aj-quick)\ **Post date:** [March 5, 2010, 6:04pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/9 "2010-03-05T18:04:18Z")
[![](https://discdn.gbfans.com/original/3X/8/7/87259838921eb7e6c4001f93ec44295ab47fab8f.jpeg ""21" explains the Monty Hall problem") ](https://www.youtube.com/watch?v=cXqDIFUB7YU) > **[Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem)** > > The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in (and solved by) Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990: Suppose you're on a game show, and yo... ---
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 6:21pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/10 "2010-03-05T18:21:46Z")
> [@AJ Quick](#): > > [https://www.youtube.com/watch?v=cXqDIFUB7YU](https://www.youtube.com/watch?v=cXqDIFUB7YU) > > [Monty Hall problem - Wikipedia](http://en.wikipedia.org/wiki/Monty_Hall_problem) I know, it’s like the second result that show up in Google if you type in “gameshow” and “probability.” At any rate if anyone is interested in working it out, hold off on watching the vid. > [@mikegbfan2009](#): > > Many have probably heard this before but I’m going to post it anyway. I think it’s a great problem and fun to use to confuse the hell out of people. Try not to Google for the answer because 1) it’s easy to find and 2) knowing the answer is only a fraction of what value is in this problem to begin with… Please, please, please don’t spoil it by just going to wikipedia and pasting the answer/proof. ---
**Author:** ![aj-quick](https://forum.gbfans.com/user_avatar/forum.gbfans.com/aj-quick/32/188008_2.png) [@aj-quick](https://forum.gbfans.com/u/aj-quick)\ **Post date:** [March 5, 2010, 6:24pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/11 "2010-03-05T18:24:27Z")
I’m gonna post Schrödinger’s cat. ---
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 6:24pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/12 "2010-03-05T18:24:47Z")
> [@jackdoud](#): > > > [@mikegbfan2009](#): > > > > But again, this is a simple probability problem and there are no hidden probabilities involved. There’s only one correct answer based on the inputs. I think that’s where you landed after your comments, but just wanted to clarify that. > > So the question should have been stated as “According to probability is it better for the contestant to keep the initial door picked or change their choice to the other door”. THAT is an actual question then. Just saying “would you change and why/not” makes it seem like a cheesey high-school english test essay question instead of the mathmatics problem it is. Part of the problem is to identify it as a probability problem. ---
**Author:** ![jackdoud](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/j/6a8cbe/32.png) [@jackdoud](https://forum.gbfans.com/u/jackdoud)\ **Post date:** [March 5, 2010, 6:31pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/13 "2010-03-05T18:31:15Z")
> [@mikegbfan2009](#): > > Part of the problem is to identify it as a probability problem. So then is it supposed to be a logic problem, a math problem or games theory? Purposefully asking an obtuse question obscures any conclusions you could draw from the answers. ---
**Author:** ![Tadao](https://forum.gbfans.com/user_avatar/forum.gbfans.com/tadao/32/6068_2.png) [@Tadao](https://forum.gbfans.com/u/Tadao)\ **Post date:** [March 5, 2010, 6:34pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/14 "2010-03-05T18:34:53Z")
Once the goat is revealed to be behind one of the unpicked doors, it is removed from the math problem. If you choose to include it, the original math problem becomes null and void. ---
**Author:** ![aj-quick](https://forum.gbfans.com/user_avatar/forum.gbfans.com/aj-quick/32/188008_2.png) [@aj-quick](https://forum.gbfans.com/u/aj-quick)\ **Post date:** [March 5, 2010, 6:37pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/15 "2010-03-05T18:37:35Z")
What is the probability if I want to get the goat? Like I live in Romainia or something. ---
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 8:11pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/16 "2010-03-05T20:11:30Z")
> [@AJ Quick](#): > > What is the probability if I want to get the goat? Like I live in Romainia or something. Mmmm, milk. ---
**Author:** ![jackdoud](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/j/6a8cbe/32.png) [@jackdoud](https://forum.gbfans.com/u/jackdoud)\ **Post date:** [March 5, 2010, 8:39pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/17 "2010-03-05T20:39:44Z")
> [@mikegbfan2009](#): > > Mmmm, milk. Woah woah woah! You never said it was a female goat… ---
**Author:** ![mikegbfan2009](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/m/6a8cbe/32.png) [@mikegbfan2009](https://forum.gbfans.com/u/mikegbfan2009)\ **Post date:** [March 5, 2010, 9:24pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/18 "2010-03-05T21:24:32Z")
> [@jackdoud](#): > > > [@mikegbfan2009](#): > > > > Mmmm, milk. > > Woah woah woah! You never said it was a female goat… Only one is… ---
**Author:** ![phantom50](https://forum.gbfans.com/letter_avatar_proxy/v4/letter/p/43a26b/32.png) [@phantom50](https://forum.gbfans.com/u/phantom50)\ **Post date:** [March 5, 2010, 9:35pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/19 "2010-03-05T21:35:06Z")
Choose wisely. [flash=512,296][http://www.hulu.com/embed/FHMxZHgc9kf0u1DAnuVATQ/0/i26[/flash]](http://www.hulu.com/embed/FHMxZHgc9kf0u1DAnuVATQ/0/i26%5B/flash%5D) Brock phantom50 ---
**Author:** ![Foom\_Man](https://forum.gbfans.com/user_avatar/forum.gbfans.com/foom_man/32/106_2.png) [@Foom\_Man](https://forum.gbfans.com/u/Foom_Man)\ **Post date:** [March 5, 2010, 9:35pm UTC](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986/20 "2010-03-05T21:35:34Z")
I still fail to understand just why the odds are not simply one:two. The game show analogy for the math is misleading. At the end of the day (in the game show scenario) you still have two doors with one car. That, inherently, means there’s a 50% chance of success or failure. The clip from “21” does a ■■■■-poor job of actually explaining the logic behind the “correct” decision. The math is basically 1/3 choice (your initial decision) divided by 1/2 (what you are left with)= 2/3. The math fails to tell me just why picking one over the other results in a 2/3 benefit- **why doesn’t staying with my initial decision give me a 2/3 chance of success?** By eliminating door #3 from being the correct choice you are removing it from being the correct choice… so there are only 2 correct choices. 1:2 [Next page](https://forum.gbfans.com/t/gameshow-probability-problem-riddle/28986.md?page=2)