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A Question to Try
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| ninja |
Posted on 08/07/2012 14:54:43
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Super Admin
Posts: 4174
Joined: 15.11.10
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I'm copying Hat's thing to see how smart ZÅ is. Read the question, think, then vote. I'll unlock in a bit.
You're on a game show, trying to win a fancy sports car. There are 3 doors: behind two of them there is nothing, behind one is the car.
The game show host asks you to choose a door - you will get whatever is behind the door. You do so.
Then he, since he knows the position of the car, opens one of the other two doors, showing that the car isn't behind that one. This leaves two doors: the one you originally chose and another mystery one.
The game show host then asks you if you would like to switch your choice to this mystery door, or stay with your original choice.
Do you stay, or do you switch?
My brain is open.
- Paul Erdős |
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| ninja |
Posted on 08/08/2012 06:32:07
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Super Admin
Posts: 4174
Joined: 15.11.10
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I'll open this up for discussion at the end of the day when a few more people have seen it and voted!
My brain is open.
- Paul Erdős |
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| ninja |
Posted on 08/10/2012 10:00:46
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Super Admin
Posts: 4174
Joined: 15.11.10
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Thanks for your votes. The results as I write are:
Stay - 10 (62.5%)
Switch - 6 (37.5%)
That's a majority for 'stay'. Unfortunately, that isn't the most logical answer. In fact, you're always better off switching. This is because you're more likely to win the car if you switch.
You're probably thinking, "Hey! Wait a second ... surely it's 50:50, so it doesn't matter which I chose - I might as well stay." Well, no. You actually have a 2/3 chance of winning the car if you switch, but only a 1/3 chance if you stay.
You'll probably need a little convincing, so I'll do my best.
Let's label the three doors A, B, and C. Without any loss of generality (i.e. this won't affect the calculation), I can say that you pick door A. This is fine to say because I haven't stated which order the doors are in.
Now, there are 3 possible circumstances, namely: (1) the car is behind door A; (2) the car is behind door B; (3) the car is behind door C.
Let's look at case (1) first. The car is behind door A and you've chosen door A. The host opens one of the other doors (either since neither B nor C conceal the car). For argument's sake, let's say he opens door B. Now, if you stay, you'll win. If you switch to C, you'll lose.
Now look at case (2). The car is behind door B and you've chosen door A. The host opens another door which doesn't conceal the car, so he must open door C. Now, if you stay, you'll lose. If you switch to B, you'll win.
Finally look at case (3). The car is behind door C and you've chosen door A. The host opens another door which doesn't conceal the car, so he must open door B. Now, if you stay, you'll lose. If you switch to C, you'll win.
Now all we need to do is tally up how many times you win for each of the options, stay or switch.
Stay: only case (1) - so total of 1 wins out of 3.
Switch: cases (2) and (3) - so total of 2 wins out of 3.
Therefore, by switching you'll win 2/3 of the time, but by staying you'll only win 1/3 of the time!
Counter-intuitive, eh?
My brain is open.
- Paul Erdős |
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| ZA reaper |
Posted on 08/10/2012 10:35:19
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Wanker
Posts: 871
Joined: 15.11.10
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i remember this from mythbusters i couldnt remember how it went though
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| ZA BrickSquad |
Posted on 08/10/2012 11:22:58
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ShawnPeezy
Posts: 5303
Joined: 12.05.11
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Thank you ninja! I picked "stay", but I understand now =P |
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| Mator |
Posted on 08/11/2012 01:30:45
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Senior Member
Posts: 265
Joined: 28.06.12
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It's funny because I watched the movie "21" just a short time before viewing this question. I did know the right answer before watching the movie though, ofc, but still, coinky-dink!
The question itself is counter-intuitive, but if you use logic/mathematics instead of emotion it makes perfect sense.
Opening situation: You have a 1/3 (33.3%) chance of choosing the car.
[c] [g] [g]
(bold stands for first choice)
-> 33.3% of the time you chose the car the first time and switching will get you the goat.
[c] [g] ///
-> 66.6% of the time you chose a goat the first time and switching will get you the car.
[c] [g] ///
[c] /// [g]
alternatively you have:
-> 1/3 chance of picking car first time. So you have 66.6% chance of getting car when switching and 33.3% chance of getting car staying.
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| MasterA |
Posted on 08/11/2012 02:13:21
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Super Admin
Posts: 2582
Joined: 21.07.11
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Mator wrote:
It's funny because I watched the movie "21" just a short time before viewing this question. I did know the right answer before watching the movie though, ofc, but still, coinky-dink!
ahhhh i remembered this question from somewhere but i forgot where now i remember i heard it in that movie. Great movie btw. But ye it makes sense
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| ZA althor |
Posted on 08/11/2012 02:17:13
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Wanker
Posts: 794
Joined: 07.03.11
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ofc the game show host might be shady and there IS no car 0o
*in the fine print definition of being server active* ....{FC}[ZA]Althor, will no longer be server active |
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| Carnage |
Posted on 08/11/2012 02:21:00
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Super Admin
Posts: 4245
Joined: 28.09.11
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Well what if its like the whole Schrodinger's cat theory and the car is both behind the door and not behind the door at the same time just like the cat is both dead and alive before you open the box. Then you're fucked either way and it wont matter so you should just take the cash payoff option instead.
"Hey guys, I just bought this thing called a sight ward...so it's GG." - MasterA in League of Legends
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| ninja |
Posted on 08/11/2012 05:20:51
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Super Admin
Posts: 4174
Joined: 15.11.10
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The name of this question, which I slightly adapted by killing some goats, is the Montey Hall Paradox, in case you're interested.
When Marilyn vos Savant (genius woman) first published her answer in Parade magazine, loads of PhD Mathematicians wrote in saying she was wrong.
You can read some of the responses here: http://marilynvos...w-problem/
I had forgotten this was in '21'. Good film, that.
Carnage wrote:
Well what if its like the whole Schrodinger's cat theory and the car is both behind the door and not behind the door at the same time just like the cat is both dead and alive before you open the box. Then you're fucked either way and it wont matter so you should just take the cash payoff option instead.
There isn't a cash payoff option. That would defeat the point.
Schrodinger's Cat wasn't a theory, it was a satirical thought experiment supposed to ridicule Quantum Theory. Regardless, you can assume the car is certainly behind one of the doors.
My brain is open.
- Paul Erdős |
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| The Hat of Love |
Posted on 08/11/2012 10:03:24
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ShawnPeezy
Posts: 9035
Joined: 31.07.11
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That link was really interesting, ninja. Loved seeing smart people get stuff wrong =3
my signature broke, here is a fox snek:
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| Joshkl2013 |
Posted on 08/11/2012 10:28:53
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Numpty
Posts: 1443
Joined: 26.05.12
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@Carnage
A Shrodengers cat only happens when an outcome is unobserved. Since the host know where the car is, it isn't a Shrodengers cat.
As a student of paradoxes, I voted for switch, because I knew how this one worked.
However, this seems mathematically incorrect if reasoned outside of a single set; when you pick it, you have a 1/3 chance of finding the car. The problem comes with the opened door. While you could include this door in your calculations, it isn't logical to do so, as it's only logical to switch if there are 2 doors left. Therefore, reasoning on a double-problem math basis, It would be "logical" to either switch or stay based on the fact that one of the 2 closed doors have the car.
(Basically, you can no longer take the opened door under consideration, and so you can do either, being able to logically justify it)
This set of reasoning is incorrect, because the chance of the first pick, and is why people choose to stay with their first pick.
Edited by Joshkl2013 on 08/11/2012 10:32:12
I wanna be like RAZ!!! [ZÅ]Paradox
Need a shotgun to protect you while you snipe? Call
1-800-SHOTGUN today!
Need a nuke? Call 1-800-NUKE-ALL
Take advantage of this limited offer now!
Offer expires in 3..2..1...
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| ninja |
Posted on 08/11/2012 10:40:36
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Super Admin
Posts: 4174
Joined: 15.11.10
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Joshkl2013 wrote:
@Carnage
A Shrodengers cat only happens when an outcome is unobserved. Since the host know where the car is, it isn't a Shrodengers cat.
As a student of paradoxes, I voted for switch, because I knew how this one worked.
However, this seems mathematically incorrect if reasoned outside of a single set; when you pick it, you have a 1/3 chance of finding the car. The problem comes with the opened door. While you could include this door in your calculations, it isn't logical to do so, as it's only logical to switch if there are 2 doors left. Therefore, reasoning on a double-problem math basis, It would be "logical" to either switch or stay based on the fact that one of the 2 closed doors have the car.
(Basically, you can no longer take the opened door under consideration, and so you can do either, being able to logically justify it)
This set of reasoning is incorrect, because the chance of the first pick, and is why people choose to stay with their first pick.
Not sure quite what you're saying.
Do you not agree that it is more logical to choose the option that gives you a better chance of winning?
My brain is open.
- Paul Erdős |
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| Joshkl2013 |
Posted on 08/11/2012 11:24:15
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Numpty
Posts: 1443
Joined: 26.05.12
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I was saying that you would switch, but I explained how people reason that they should stay with their first pick.
I wanna be like RAZ!!! [ZÅ]Paradox
Need a shotgun to protect you while you snipe? Call
1-800-SHOTGUN today!
Need a nuke? Call 1-800-NUKE-ALL
Take advantage of this limited offer now!
Offer expires in 3..2..1...
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| Mator |
Posted on 08/11/2012 11:26:01
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Senior Member
Posts: 265
Joined: 28.06.12
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Joshkl2013 wrote:
@Carnage
A Shrodengers cat only happens when an outcome is unobserved. Since the host know where the car is, it isn't a Shrodengers cat.
As a student of paradoxes, I voted for switch, because I knew how this one worked.
However, this seems mathematically incorrect if reasoned outside of a single set; when you pick it, you have a 1/3 chance of finding the car. The problem comes with the opened door. While you could include this door in your calculations, it isn't logical to do so, as it's only logical to switch if there are 2 doors left. Therefore, reasoning on a double-problem math basis, It would be "logical" to either switch or stay based on the fact that one of the 2 closed doors have the car.
(Basically, you can no longer take the opened door under consideration, and so you can do either, being able to logically justify it)
This set of reasoning is incorrect, because the chance of the first pick, and is why people choose to stay with their first pick.
That sounded like a bunch of gibberish asides from the note about schrodinger's* cat.
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| ZA BrickSquad |
Posted on 08/11/2012 12:22:48
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ShawnPeezy
Posts: 5303
Joined: 12.05.11
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Well anyways, before I chose something, I gotta know what's behind it. So those types of scenarios would never apply to me =D
Unless I'm a Archaeologist and need to pick 1 of the 3 paths in a hidden Pyramid and 2 paths lead to my death and 1 path lead to untold riches xD |
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| ninja |
Posted on 08/11/2012 13:50:19
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Super Admin
Posts: 4174
Joined: 15.11.10
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Joshkl2013 wrote:
I was saying that you would switch, but I explained how people reason that they should stay with their first pick.
They stay because they think "it's 50:50, so there's no point in switching." They don't realise that they can double their chances of winning by switching. It's simple as that.
My brain is open.
- Paul Erdős |
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| PirateKing |
Posted on 08/14/2012 14:14:42
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Numpty
Posts: 1128
Joined: 01.03.12
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if you switch well yeah you get more  it says you already picked one lol nd if your wrong then its a better chance
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| Saviour |
Posted on 08/14/2012 17:52:44
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Numpty
Posts: 1352
Joined: 05.10.11
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so...... Where my car? |
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| Revenge |
Posted on 08/14/2012 18:47:06
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Super Admin
Posts: 1297
Joined: 28.06.12
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Mator wrote:
It's funny because I watched the movie "21" just a short time before viewing this question. I did know the right answer before watching the movie though, ofc, but still, coinky-dink!
The question itself is counter-intuitive, but if you use logic/mathematics instead of emotion it makes perfect sense.
Opening situation: You have a 1/3 (33.3%) chance of choosing the car.
[c] [g] [g]
(bold stands for first choice)
-> 33.3% of the time you chose the car the first time and switching will get you the goat.
[c] [g] ///
-> 66.6% of the time you chose a goat the first time and switching will get you the car.
[c] [g] ///
[c] /// [g]
alternatively you have:
-> 1/3 chance of picking car first time. So you have 66.6% chance of getting car when switching and 33.3% chance of getting car staying.
I heard this on 21 also. Good stuff. |
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