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re: Let's discuss the Monty Hall problem (probabilities, odds)
Posted on 8/12/17 at 8:23 am to THRILLHO
Posted on 8/12/17 at 8:23 am to THRILLHO
The easiest way to understand this problem is to stretch it out to the extreme.
Imagine there were 1,000 doors. 1 door had the prize and the 999 other doors had a goat.
Your odds of picking the right door off the bat are very low... 1 / 1,000. So you pick a door.
Now the host opens 998 doors which he knows contain goats. Now there are two doors left, the 1 door the host left and your door.
Your odds don't change to 50/50 just because there are two doors left. You didn't choose between two doors... you chose your door out of 1,000.
So unless you think you picked the right door right off the bat out of 1,000 (which it's extremely unlikely that you did), then you should switch.
Imagine there were 1,000 doors. 1 door had the prize and the 999 other doors had a goat.
Your odds of picking the right door off the bat are very low... 1 / 1,000. So you pick a door.
Now the host opens 998 doors which he knows contain goats. Now there are two doors left, the 1 door the host left and your door.
Your odds don't change to 50/50 just because there are two doors left. You didn't choose between two doors... you chose your door out of 1,000.
So unless you think you picked the right door right off the bat out of 1,000 (which it's extremely unlikely that you did), then you should switch.
This post was edited on 8/12/17 at 8:26 am
2
Posted on 8/12/17 at 8:27 am to PrimeTime Money
quote:
Your odds don't change to 50/50 just because there are two doors left. You didn't choose between two doors... you chose your door out of 1,000.
I get that. But at this point, you're making a new choice between two doors. The other 998 are irrelevant.
Posted on 8/12/17 at 8:30 am to mdomingue
In scenario 3 which is
GGC
and you picked door 1... he can't show you door 3... your premise is flawed from the outset
The rules are he can't pick your door and he can't show you the car, meaning he can only open door 2 in this scenario
GGC
and you picked door 1... he can't show you door 3... your premise is flawed from the outset
The rules are he can't pick your door and he can't show you the car, meaning he can only open door 2 in this scenario
Posted on 8/12/17 at 8:34 am to biglego
quote:That's why I don't like explaining it like that. It can be difficult to explain, but I find that once someone finally gets it, they see how natural it is for your odds to go up to 2/3 by switching.
But at this point, you're making a new choice between two doors. The other 998 are irrelevant.
Posted on 8/12/17 at 8:36 am to SlapahoeTribe
See I look at it like is a whole new decision. I'm not concerned about the opened doors at that point. They are out of the equation. I think this is one of those things where people just overthink something.
Posted on 8/12/17 at 8:37 am to biglego
quote:No, it's not a new choice.
I get that. But at this point, you're making a new choice between two doors. The other 998 are irrelevant.
If the host eliminated 998 doors and there were two left and a totally new guy walked up not knowing what had just happened and had to pick between doors then he would have a 50/50 chance of picking the right door.
But what he doesn't know is that your door was picked out of 1,000 doors. With this information in hand, he would know that your odds of having picked the door with the prize with your door are astronomically low, and he should choose the other door.
See, just because there are now two doors left doesn't change the fact that the odds that you picked the right door are 0.1% and the odds that you picked the wrong door are 99.9%.
Posted on 8/12/17 at 8:45 am to Nado Jenkins83
quote:
See I look at it like is a whole new decision. I'm not concerned about the opened doors at that point. They are out of the equation. I think this is one of those things where people just overthink something.
Your original pick was with 1/3 doors... sticking with that same pick means you still have a 1/3 chance to win because you didn't make a whole new decision
Posted on 8/12/17 at 8:47 am to TheArrogantCorndog
Yea and if you switch you have a 1/3 chance as it is only one door out of 3.
Why does the opened door only count to one side?
Why does the opened door only count to one side?
This post was edited on 8/12/17 at 8:48 am
Posted on 8/12/17 at 8:49 am to Jim Rockford
Conditional probability; once he opens that door, you gain new information and the probabilities change. Switching gives you a 2 in 3 chance.
Posted on 8/12/17 at 8:53 am to SlapahoeTribe
A goat IS what my heart desires.
No shite, my wife and I squabble over getting a pet goat quite often. Actually, I heard I need two of them to keep each other company.
No shite, my wife and I squabble over getting a pet goat quite often. Actually, I heard I need two of them to keep each other company.
Posted on 8/12/17 at 8:55 am to Nado Jenkins83
quote:Because the host knows where the goats are.
Yea and if you switch you have a 1/3 chance as it is only one door out of 3. Why does the opened door only count to one side?
Stretch it out to 1,000 again.
If you pick a door, there is a 0.1% chance that you picked the right door, and a 99.9% chance that the door with the prize is in one of the other 999 doors.
So when the host knowingly eliminates goats from 998 other doors, there is still a 0.1% chance that you picked the right door and a 99.9% chance that the door with the prize is behind the door the host left out of the 999.
This post was edited on 8/12/17 at 8:58 am
Posted on 8/12/17 at 8:58 am to PrimeTime Money
I'm gonna side with the thousand of PhDs that disagree
That one door out of the 999 doesn't hold the value of 999 doors. That's stupid
That one door out of the 999 doesn't hold the value of 999 doors. That's stupid
Posted on 8/12/17 at 8:58 am to SlapahoeTribe
I'm going home with the greatest of all time prizes
Posted on 8/12/17 at 8:59 am to Nado Jenkins83
quote:
Yea and if you switch you have a 1/3 chance as it is only one door out of 3.
Why does the opened door only count to one side?
Incorrect... he has added new information into the equation by showing you one of the goats
Out of 3 doors, you pick one, and the remaining 2 doors have 2/3 odds combined
When he reveals the goat behind one of those doors, that door's value drops to zero and gets added to the other door... your original pick still has the same odds from the beginning because you havent been able to use the new information yet, and the second door now has it's odds and the goat's door's odds combined
The problem you will have with this is I know I'm 100% correct... watch some YouTube videos on it... you'll get it, I believe in you, Nado
Posted on 8/12/17 at 9:00 am to Nado Jenkins83
quote:Those thousands of phd's have recognized their error in logic and have come around. This isn't really controversial anymore.
I'm gonna side with the thousand of PhDs that disagree That one door out of the 999 doesn't hold the value of 999 doors. That's stupid
They've actually done live experiments testing it and it's 100% true that you should switch.
This post was edited on 8/12/17 at 9:03 am
Posted on 8/12/17 at 9:01 am to TheArrogantCorndog
Nah I'll pass. I refuse to believe that either door left unopened holds the value of the door that was opened.
Posted on 8/12/17 at 9:04 am to Nado Jenkins83
Watch this short video. They actually run this experiment using cups and chart the results.
https://youtu.be/o_djTy3G0pg
https://youtu.be/o_djTy3G0pg
Posted on 8/12/17 at 9:05 am to Nado Jenkins83
quote:
I refuse to believe that either door left unopened holds the value of the door that was opened.
Each door has 1/3 odds unopened... your first choice has 1/3 odds... the other 2 combined have 2/3 odds at all times... 1/3+1/3... when he opens the goat, those 2/3 odds combined remain, except there is one less door in the equation, meaning one door has the 2/3 odds to itself
Posted on 8/12/17 at 9:07 am to TheArrogantCorndog
I understand the theory. But it's still a theory.
Posted on 8/12/17 at 9:09 am to SlapahoeTribe
Seems pretty easy to understand, not sure why people have such a hard time with it.
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