# Monty Hall problem on MythBusters **URL:** \ **Category:** Cafe Society\ **Created:** [November 26, 2011, 7:06am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134 "2011-11-26T07:06:38Z")\ **Posts on this page:** 20\ **Page:** 10
**Author:** ![Malthus](https://avatars.discourse-cdn.com/v4/letter/m/85f322/32.png) [@Malthus](https://boards.straightdope.com/u/Malthus)\ **Post date:** [August 27, 2015, 7:34pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/181 "2015-08-27T19:34:03Z")
> [@cmMaze](#): > > Simplified - > The 2 Final choices appear to be 50%/50%, but at the odds of the FIRST guess (between 3) is still only 1/3 (33%) Perhaps the way to look at it is that the odds of your first guess being right never improve. They were 33% when you guessed, and they remain 33% when you are offered the choice to switch. The switch gives you odds of 66%. ---
**Author:** ![cmMaze](https://avatars.discourse-cdn.com/v4/letter/c/7ab992/32.png) [@cmMaze](https://boards.straightdope.com/u/cmMaze)\ **Post date:** [August 27, 2015, 7:36pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/182 "2015-08-27T19:36:18Z")
> [@Malthus](#): > > Perhaps the way to look at it is that the odds of your first guess being right never improve. They were 33% when you guessed, and they remain 33% when you are offered the choice to switch. The switch gives you odds of 66%. Exactly! 🆒 ---
**Author:** ![filmore](https://avatars.discourse-cdn.com/v4/letter/f/7993a0/32.png) [@filmore](https://boards.straightdope.com/u/filmore)\ **Post date:** [August 27, 2015, 7:59pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/183 "2015-08-27T19:59:57Z")
This problem comes up often on the net and real life. I think it’s hard for people to understand the true odds because 3 doors is pretty close to 2 doors. There’s not enough difference for it to be obvious it’s worth it to change. I think it’s easier to understand the problem if you consider a lot more doors than just 3. Imagine there are 100 doors. You initially pick door #10. The host then opens 98 doors to empty rooms and leaves door #52 closed. If the odds were still 50/50, then you would win half the time by keeping your first choice. But that’s not the case. You’ll only win 1/100 times if you keep your same door and you’ll win 99/100 times by switching doors. With a lot of doors, it’s easier for people to see that their first choice didn’t get any better and it’s much more likely the prize is behind the door that the host didn’t open. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [August 27, 2015, 8:16pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/184 "2015-08-27T20:16:53Z")
I think the easiest way to understand it is to realize that you are given the choice of one door or two doors. When you name one door you can have what is behind that door, or you can have what is behind both other doors. Since there is just one prize, clearly the prize will be behind one of the two doors twice as often as the one door. When you name a door to start with you are dividing the doors into two sets. A set with one door, and a set with the two other doors. Monty is giving you the chance to select either set, but first he opens one empty door in the set of two, and then he is asking if you want the third door. When you ‘switch’ all you are doing is saying you want what is behind both doors in the set of two, knowing one of them is empty, and knowing which one it is. Imagine if Monty started it all by saying you could pick two doors. You pick two. Obviously the prize is behind one of those two doors 66% of the time. Then he opens one of the doors that is empty and asks you if you want the unopened door that you picked, or the one door you didn’t pick in the beginning. Nothing has changed about your odds. The two doors you selected had the prize behind one of them 66% of the time and it still does. Now he’s asking you if you want to switch to the one door that had only a 33% chance of having the prize behind it since the beginning, or the unopened door that was part of the set of two with a 66% chance of having the prize. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 27, 2015, 11:51pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/185 "2015-08-27T23:51:46Z")
Both **Filmore** and **TriPolar** frame it nicely in their own respective ways. > [@Maserschmidt](#): > > Additional years of Klostermann observation have swayed me toward **SlackerInc’s** opinion… Has he said more stupid shit? ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [August 28, 2015, 4:35am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/186 "2015-08-28T04:35:40Z")
> [@Lord\_Feldon](#): > > I didn’t understand it (I accepted it, but I didn’t understand it), until I realized that switching _always_ reverses the outcome. Holy shit. I didn’t think I could think any new thoughts about the Monty Hall problem but you just gave me one. Thanks! ---
**Author:** ![Frylock](https://avatars.discourse-cdn.com/v4/letter/f/ce7236/32.png) [@Frylock](https://boards.straightdope.com/u/Frylock)\ **Post date:** [August 28, 2015, 4:43am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/187 "2015-08-28T04:43:09Z")
> [@cmMaze](#): > > Exactly! 🆒 Exactly as has been explained much more clearly several times already in the thread. Your own statement is full of ambiguities and other ill-defined terms. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 28, 2015, 4:48am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/188 "2015-08-28T04:48:26Z")
I would go further and say that the post that reopened this thread was flat out wrong, mathematically speaking. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 28, 2015, 4:58am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/189 "2015-08-28T04:58:15Z")
Going back and looking at the post where I brought up Klosterman, I must say I think my explanation of the Monty Hall problem was pretty good, even if I do say so myself: [http://boards.straightdope.com/sdmb/showpost.php?p=14775744&postcount=161](http://boards.straightdope.com/sdmb/showpost.php?p=14775744&postcount=161) ---
**Author:** ![Rigamarole](https://avatars.discourse-cdn.com/v4/letter/r/77aa72/32.png) [@Rigamarole](https://boards.straightdope.com/u/Rigamarole)\ **Post date:** [August 28, 2015, 6:06am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/190 "2015-08-28T06:06:10Z")
> [@cmMaze](#): > > - 3 Doors, Pick 1 = 1/3 Chance AND 1/3 Probability > > - 1 Door Removed = 50% Chance -MINUS- the 1/3 PROBABILITY you got it RIGHT the FIRST time! > > Therefore it IS a 50%-50% CHANCE of getting it right, but LESS of a PROBABILITY you got it right on the first guess. (by 1/3) > > – > > Clarify the terms, and there is no need for the hypothetical variations of probability and chance. Why would you bump a 3-4 year old thread with this nonsensical dreck? The problem has already been very well covered and it’s very simply put: 1/3 chance of getting it right if you stay, 2/3 chance of getting it if you switch. There’s no more to it than that. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 28, 2015, 6:12am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/191 "2015-08-28T06:12:37Z")
A lot of people need a little more than that, because they don’t see \*why \*that’s true. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 28, 2015, 6:19am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/192 "2015-08-28T06:19:35Z")
How about this more concise version: If you think you picked the right door the first time when there were three to choose from, stay. If you think it’s more likely than not that you picked the wrong door, switch. ---
**Author:** ![Rigamarole](https://avatars.discourse-cdn.com/v4/letter/r/77aa72/32.png) [@Rigamarole](https://boards.straightdope.com/u/Rigamarole)\ **Post date:** [August 28, 2015, 6:30am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/193 "2015-08-28T06:30:41Z")
> [@SlackerInc](#): > > A lot of people need a little more than that, because they don’t see \*why \*that’s true. Sure, but that’s the part that’s been very well covered already. He just bumped the thread with all this meaningless gibberish that attempts to complicate the matter more than need be. ---
**Author:** ![SlackerInc](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/slackerinc/32/275_2.png) [@SlackerInc](https://boards.straightdope.com/u/SlackerInc)\ **Post date:** [August 28, 2015, 7:30am UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/194 "2015-08-28T07:30:49Z")
True enough! And, ironically, claims to “clarify” the matter. :smack: ---
**Author:** ![cmMaze](https://avatars.discourse-cdn.com/v4/letter/c/7ab992/32.png) [@cmMaze](https://boards.straightdope.com/u/cmMaze)\ **Post date:** [August 28, 2015, 1:20pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/195 "2015-08-28T13:20:46Z")
It was immediately followed by the simplified version - The 2 Final choices appear to be 50%/50%, but at the odds of the FIRST guess (between 3) is still only 1/3 (33%) Perhaps you didn’t read the rest? It was obvious the first message didn’t break it down into understandable terms, but the concept was basic. The followup should have made that more clear for you. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [August 28, 2015, 1:34pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/196 "2015-08-28T13:34:49Z")
> [@cmMaze](#): > > It was immediately followed by the simplified version - The 2 Final choices appear to be 50%/50%, but at the odds of the FIRST guess (between 3) is still only 1/3 (33%) That’s just a restatement of the solution, and it used terms that weren’t rigorously defined. Choices between two selections always “appear to be 50%/50%” if you don’t understand math. A key point is the odds presented originally (1 in 3) don’t change when MH reveals the goat because no new information is given. Your simplified version doesn’t help explain the logic of the problem, and it serves to confuse things missing the important points. Everyone responding here understands the probabilities of the original problem. This old and well worn thread was really about explaining to people who didn’t understand and your post really doesn’t advance the discussion in any meaningful way. ---
**Author:** ![aldiboronti](https://avatars.discourse-cdn.com/v4/letter/a/9fc348/32.png) [@aldiboronti](https://boards.straightdope.com/u/aldiboronti)\ **Post date:** [August 28, 2015, 2:48pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/197 "2015-08-28T14:48:15Z")
> [@Martian Bigfoot](#): > > For me, at least, the the problem is easier to visualize if it’s scaled up: Imagine a really rubbish game show where instead of three doors, there are 100 doors. You choose one, and then Monty says: “I’ll make this easy for you, because this is the worst game show ever. I’ll now open 98 of the remaining doors, where there is no prize. Only one of them remains closed. You can keep your door, or switch to my door instead.” > > Now, think. There are really only two sets of doors: The one door you picked, and the set of doors you didn’t pick. With 100 doors instead of three, your chance of picking the right door on your first pick was just one percent. The chance of the prize being behind a door \*somewhere \*in the set of the doors you didn’t pick, is 99 percent. > > When Monty asks if you want to switch, he’s really asking: “Do you want to keep the door that you initially picked, or switch to the full set of doors that you didn’t? I’ve already opened 98 of those doors, so if the prize was anywhere in this set from the get go, and you switch, you’ll win, guaranteed.” > > In other words, if you picked the right door to begin with, you win if you keep your door. If you picked the wrong door to begin with, you’ll win if you switch. But your chances of picking the right one at the start was only one percent! > > In this case, the answer should be a no-brainer. Doh, switch every time! You’ll get a 99 percent chance of winning! > > Now, in the actual Monty Hall problem, the situation is _exactly the same, just with different numbers._ Your chance of picking the right door to begin with was 1/3. The chance of picking the wrong one was 2/3. Switching gives you a 2/3 chance of winning. That’s precisely the method I used to finally grasp it a couple of years back. I just could not see it before scaling up; it then became crystal clear. ---
**Author:** ![cmMaze](https://avatars.discourse-cdn.com/v4/letter/c/7ab992/32.png) [@cmMaze](https://boards.straightdope.com/u/cmMaze)\ **Post date:** [August 28, 2015, 5:14pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/198 "2015-08-28T17:14:17Z")
> [@Telemark](#): > > That’s just a restatement of the solution…key point is the odds presented originally (1 in 3) don’t change… That’s exactly what I said. I was trying find a very simple way to explain this to someone who didn’t already understand the concept. And, why the odds of sticking are only 33% vs 66% and not 50%/50%, as they may appear to be. There were so many discussions, it wasn’t easy to follow all 4pages of detailed examples. Sorry if my post wasn’t good enough for you. Just pass it by. 😉 ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [August 28, 2015, 6:00pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/199 "2015-08-28T18:00:33Z")
> [@cmMaze](#): > > it wasn’t easy to follow all 4 pages of detailed examples. 4 pages?! How about at least 20 threads going back over 15 years. Enjoy some light reading. 🙂 > **[Monty Hall Open's a door.....](https://boards.straightdope.com/sdmb/showthread.php?t=90)** > > Cecil; Your assumptions were almost on the mark, but not quite… Here is the original question again: Suppose you’re on a game show and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say... > **[A couple of Monty Hall variations....](https://boards.straightdope.com/sdmb/showthread.php?t=137419)** > > I’ve got a couple variations on the Monty Hall problem that are interesting. The first, which I came up with, seems to be easy to solve, but I wanted to run it by y’all. The second, which was pointed out to me by a guy on another message board, is... > **[Monty Hall Problem](https://boards.straightdope.com/sdmb/showthread.php?t=2095)** > > In the words of Cecil, he “screwed this one up” on the first reply. Interestingly, the prominent mathematician Paul Erdos gave a similar answer to this question; the contestant should be indifferent to switching as the odds are still 50-50. From the... > **[Explain the Monty Hall problem to me?](https://boards.straightdope.com/sdmb/showthread.php?t=329774)** > > You’re on the game show Let’s Make a Deal. You are shown three doors, and each has a prize behind it. One has a new car and the other two have “zonks.” If you choose the correct door, you get the car. You choose door #1. Monty Hall then reveals... > **[Monty Hall](https://boards.straightdope.com/sdmb/showthread.php?t=383461)** > > http://www.straightdope.com/classics/a3\_189.html I’m fascinated by this one. The analogy is used, to describe the probability, that it’s like Monty’s offering you Door #2 AND Door #3, or just Door #1. But if he’s opening Door #3 anyway, isn’t... > **[Monty Hall \[edited title\]](https://boards.straightdope.com/sdmb/showthread.php?t=366732)** > > Just a quick comment regarding the three doors, goat and car explanation. I suppose there is no right answer as if Monty knows what is behind each door it is up to him if he bluffs you or not. I presume if u picked a door with a goat he would open... > **[Monty Hall Question](https://boards.straightdope.com/sdmb/showthread.php?t=357158)** > > The current column contains a link to the earlier Monty Hall Question, which I have some concerns with. Two questions in particular seem to be twisted to support incorrect answers. The way I see it is that the odds they also have a son are 1/2. It... > **[Pigeons beat Monty Hall problem](https://boards.straightdope.com/sdmb/showthread.php?t=555198)** > > I hate to start yet another Monty Hall thread (see Unca Cecil’s column), but this is really a new tangent. Apparently humans – and this applies across cultures – have very good reasons for not intuitively understanding the Monty Hall problem. ... > **[Boys and Girls, there's lies, damn lies, and statistics. From the Monty Hall...](https://boards.straightdope.com/sdmb/showthread.php?t=548215)** > > Okay so in a discussion with a friend both Monty Hall problem and the two siblings with a specified gender of one came up. Specifically discussed in: On “Let’s Make a Deal,” you pick Door #1. Monty opens Door #2 — no prize. Do you stay with Door #1... > **[Monty Hall Problem Revisited Again Again!](https://boards.straightdope.com/sdmb/showthread.php?t=499621)** > > I played out all possible cases and outcomes and I find that the odds are even that the contestant will win if they switch or stay. I believe that the error in the accepted solution presents itself in the case where the contestant selects the door... > **[Must Comment on Monty Hall sub riddle/logic trick](https://boards.straightdope.com/sdmb/showthread.php?t=403560)** > > this is a sub riddle on the the monty hall page which has so far not met any opposition, ill paraphrase: “Two children are coming over your house for some reason. The first child walks in the door, she is a female. What is the probability that the... > **[Pigeons are better at Monty Hall than humans](https://boards.straightdope.com/sdmb/showthread.php?t=620601)** > > I confess the classic Monty Hall problem has always befuddled me. Yes I have read the proofs of how it works and I accept them and even understand them but it remains counter-intuitive to me (at least, I feel you only have a 50/50 chance when... > **[Experimental design: Monty Hall](https://boards.straightdope.com/sdmb/showthread.php?t=603295)** > > Regarding the infamous Monty Hall problem: I’ve sketched out all the possible answers on paper, and still can’t see how switching doors would have any effect. Rather than revel in ignorance, I’ve decided to take Cecil’s advice and play the game... > **[Let's Make A Deal 2/23 - Monty Hall Problem or No ?](https://boards.straightdope.com/sdmb/showthread.php?t=598195)** > > Not sure if this should go here, in the Cafe, or elsewhere. Mods please move. Wayne Brady just offered a contestant the classic Monty Hall Problem, Or did he? Three “Boarding Passes” were offered to two contestants. Each contestant took one. They... > **[If Monty Hall were more devious... (puzzle)](https://boards.straightdope.com/sdmb/showthread.php?t=576177)** > > So, this gameshow host informs you that, in his possession, he has two boxes, each of which can be either red, green, or blue. He also tells you that at least one of the two is green, and contains a prize. Then, he gives you the following choice: You... > **[Monty Hall problem on MythBusters](https://boards.straightdope.com/sdmb/showthread.php?t=632687)** > > The recent episode of MythBusters featured four fan-submitted myths, one of which was perennial Dope fave The Monty Hall problem. I was impressed with the way they handled it. They divided it into two problems: first, that there is a strong... > **[Monty Hall: does it matter if the host knows?](https://boards.straightdope.com/sdmb/showthread.php?t=740515)** > > I know and understand that in the original Monty Hall problem, you have about a 67% chance to win the car behind one of the three doors (the other two have goats) when you pick a door and always switch IF Monty always picks a goat. That is all well... > **[Deal or No Deal and the Monty Hall problem](https://boards.straightdope.com/sdmb/showthread.php?t=721450)** > > The Monty Hall problem (as famously debated here and elsewhere) is the counter-intuitive situation when having made a random choice, additional information is given that seems to alter the odds that one guessed correctly when in fact it does not. I... > **[quick 'monty hall problem' question...](https://boards.straightdope.com/sdmb/showthread.php?t=709047)** > > (quick… well, okay maybe not) you guys probably know all about this so please excuse the newbie. but there’s something I’d like someone to explain to me if possible, because I still can’t really get my head around it. Using the scenario of 3... [http://boards.straightdope.com/sdmb/showthread.php?t=704074](http://boards.straightdope.com/sdmb/showthread.php?t=704074) [http://boards.straightdope.com/sdmb/showthread.php?t=527671](http://boards.straightdope.com/sdmb/showthread.php?t=527671) ---
**Author:** ![Gedd](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/gedd/32/4938_2.png) [@Gedd](https://boards.straightdope.com/u/Gedd)\ **Post date:** [August 28, 2015, 8:13pm UTC](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134/200 "2015-08-28T20:13:10Z")
Was there a new breaththrough in mathematical theory? [Reads posts . . .] Oh, nm. [Previous page](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134.md?page=9) [Next page](https://boards.straightdope.com/t/monty-hall-problem-on-mythbusters/604134.md?page=11)