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Riddle Me This: A Statistic Problem

Relaxedstate

Relaxedstate

PTH|RM Relaxedstate
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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

There are 3 doors. You want to win a car. Should you stay with your original choice? Or Re-choose to the other option? Does it matter?
 
GamerBlake90

GamerBlake90

Blue Blurs for Life!
Yes and no.

Yes because he basically raised your chances of getting the right door from 33% to 50%.

No because a 50% chance isn't really an advantage. It's a pure 50/50. And what this could achieve is causing you to doubt your own choice more than you may already do.
 
miloPKL

miloPKL

soundcloud.com/pukelization
you should stay with your door. i dont remember why but i think thats the answer i read the last time i read this
 
Chokeapotamus

Chokeapotamus

Worst. Player. Ever.
The pure math says that you should switch doors. GamerBlake is right but moving your odds from 33% to 50% is in your advantage by 17%. There are so many weird game theory problems like this--be careful going down the rabbit hole with them or your head will explode.
 
Relaxedstate

Relaxedstate

PTH|RM Relaxedstate
AK/RM GamerBlake said:
Yes and no.

Yes because he basically raised your chances of getting the right door from 33% to 50%.

No because a 50% chance isn't really an advantage. It's a pure 50/50. And what this could achieve is causing you to doubt your own choice more than you may already do.
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Not quite right... :) I will say it is not a 50-50 decision between staying with your door and choosing the other. (Although logically this makes sense to our mere human brain). One of them is better than the other. But I am waiting for someone to explain why! lol
 
HGTV Soapboxfan

HGTV Soapboxfan

"Always a Pleasure"
You switch doors because it technically increases your probability. And lol I argued this for like half an hour with @OZZYGUITAR from the other side just to mess with him. As for an explanation, you technically have a greater chance of picking a goat at the beginning (2 out of 3) and in those scenarios you would have to switch doors. So it changes from a 1 out of 3 to a 2 out of 3 chance. @Relaxedstate
 
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GamerBlake90

GamerBlake90

Blue Blurs for Life!
Relaxedstate said:
Not quite right... :) I will say it is not a 50-50 decision between staying with your door and choosing the other. (Although logically this makes sense to our mere human brain). One of them is better than the other. But I am waiting for someone to explain why! lol
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I don't understand...how is it not a 50-50 if you initially had three choices and the host, by his own foolishness, eliminated one of the bad choices, leaving you with only two?
 
Relaxedstate

Relaxedstate

PTH|RM Relaxedstate
AK/RM GamerBlake said:
I don't understand...how is it not a 50-50 if you initially had three choices and the host, by his own foolishness, eliminated one of the bad choices, leaving you with only two?
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By switching option you will now have a 66% chance of getting a car, whereas if you stay with your original choice you still only have a 33% chance. Mathematically it works out like this every time when simulated. Choosing the other door is always the best option.

I feel the best way to think about it is that when you chose a door for the very first time you had a 1/3 chance of guessing correctly. This stays the same regardless of whether he shows you another door or not. You had a 1/3 chance when you started playing and you have a 1/3 chance if you keep that door.

The best way to conceptualize the problem isn't to think of him offering you a choice between doors after his reveal. Think about it like this: By opening a door he effectively gives you that door for free along with the choice to change doors. Mathematically this means he is giving you 2 doors when you change. People would answer very differently if the question was poised do you want to stay with your 1 door, or do you want these 2 doors.
 
HGTV Soapboxfan

HGTV Soapboxfan

"Always a Pleasure"
Relaxedstate said:
By switching option you will now have a 66% chance of getting a car, whereas if you stay with your original choice you still only have a 33% chance. Mathematically it works out like this every time when simulated. Choosing the other door is always the best option.

I feel the best way to think about it is that when you chose a door for the very first time you had a 1/3 chance of guessing correctly. This stays the same regardless of whether he shows you another door or not. You had a 1/3 chance when you started playing and you have a 1/3 chance if you keep that door.

The best way to conceptualize the problem isn't to think of him offering you a choice between doors after his reveal. Think about it like this: By opening a door he effectively gives you that door for free along with the choice to change doors. Mathematically this means he is giving you 2 doors when you change. People would answer very differently if the question was poised do you want to stay with your 1 door, or do you want these 2 doors.
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I said that :( Lol
 
ryublaze

ryublaze

Noob
My Biology teacher showed this to us...i think you have a better chance if you switch doors. I don't remember why, has something to do with probability. There's a website where you can click on 3 doors and there's a car behind one of them and if you do it enough times the results will tell you that you get the car more if you switched doors.
 
NRF CharlieMurphy

NRF CharlieMurphy

Kindergarten Meta
lol its not hard to understand at all



its not 50/50 because you basically are given the option to select TWO doors of the 3 available...

you should thank any game show host that does this.
 
Chokeapotamus

Chokeapotamus

Worst. Player. Ever.
And yet people still feel like they should stick with their first choice due to a whole series of psychological quirks. Saved the producers of Let's Make a Deal a ton of money.
 
Pan1cMode

Pan1cMode

AUS FGC represent!
For people having trouble visualising why you should switch doors, imagine there are 100 doors to choose from.

After choosing your door, the game show host opens 98 other doors and shows you the goat behind them, he then offers to let you switch. Switching is the much better option because you only had a 1/100 chance of correctly choosing the right door at the beginning. By switching you effectively get a 99/100 chance of choosing the right door.

The maths hold true for when their are only 3 doors.
 
Gesture Required Ahead

Gesture Required Ahead

Get on that hook
In the end, all is probability and you can never be sure. So unless you were shown that you lost when the host opened the other door, switching or not doesn't really matter.
 
Pan1cMode

Pan1cMode

AUS FGC represent!
Enuma Elish said:
In the end, all is probability and you can never be sure. So unless you were shown that you lost when the host opened the other door, switching or not doesn't really matter.
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Part of the problem is that the host knows what is behind each door. The host would not open the door with the car behind it.
 
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