A brain teasing probability puzzle

Araysar · Sep 13, 2013

Fawe_sl said:
There is no illusion.

1 door that you selected has 1/3 chance of being a car
1 door that is unknown has 2/3 chance of being a car

You now have an option: Keep your 1/3rd chance or switch to take the 2/3rd chance.

How is it a 1/3 choice? Does the host ever give you a win or a loss in 1st round?

The only real choice of yours that matters is in 2nd round, the 50/50 proposition. 1st round is the The Pledge

DiddleySquat · Sep 13, 2013

Araysar_sl said:
Did your first choice win you anything except another set of choices?
Did this set of choices change based on anything you selected?

Once you realize the answer to these two questions is yes, you can step into the light.

Step into the light, bro.

Araysar · Sep 13, 2013

DiddleySquat_sl said:
In some cases he only has 1 door he can open (you picked a goat door in round 1, so he has to open the other goat door because he can't show you the car). Thatdoesinject information into the equation and should influence your choice, hence the switch.

Guys guys back off and give the man some room to breath. Look me in the eyeballs, Ara, and listen to me:do NOT let this be yourBOOTS ON THE GROUNDmoment!

haha, anyways.

Right he opens the other goat door if you picked the car. But YOU dont know you picked the car. And YOU dont know that he opened the second goat door. As far as you're concerned because one of the goat door is eliminated, you only have 2 doors, one of which has the car. None of your choices in 1st round affected the decision staring you in the face now.

This can only be a 2/3 scenario IF the host gives you an option at the end of 1st round to stay with your choice and have the doors revealed to you at the end of 1st round, OR move on to 2nd round and have 1 door eliminated for you.

Since you are never given that choice at the end of the first round, there is no switch in odds. Your actual true decision isn't even made until the 2nd round.

The first round is merely magician theatrics.

Ravishing · Sep 13, 2013

Araysar_sl said:
How is it a 1/3 choice?
Does the host ever give you a win or a loss in 1st round?
The only real choice of yours that matters is in 2nd round, the 50/50 proposition. 1st round is the The Pledge

I never said you had a win or loss in 1st round, I said it is a 1/3rd chance of being a car.

You only get 1 door.
The host gets 2 doors.

If there is only 1 car, then you have 1 in 3 chance that the door you picked in the first round will have a car behind it.
The host has 2 chances to have a car behind his doors.

Now taking that to the 2nd round, do you choose the 2/3rd chance or keep the 1/3rd chance.

Araysar · Sep 13, 2013

Fawe_sl said:
I never said you had a win or loss in 1st round, I said it is a 1/3rd chance of being a car.

its a 0/0 chance of being a car. it can only be a 1/3rd if you're offered the option of having the doors revealed to you at end of 1st round and discarding the 2nd round.

since you're never given that option and forcibly moved to 2nd round, and forcibly having one choice eliminated for you - your odds are always 50/50.

i think I figured out why we are disagreeing on this.

If you have the OPTION of staying with your choice in 1st round and discarding the second round, then you'd have a 1/3 choice. but you never get that option.

Ravishing · Sep 13, 2013

Araysar_sl said:
i think I figured out why we are disagreeing on this.

If you have the OPTION of staying with your choice in 1st round and discarding the second round, then you'd have a 1/3 choice. but you never get that option.

Uh... read the original problem. You DO keep your choice going into the 2nd round. It took you 4 pages to figure this out? What do you think the word "switch" means? It means Switch your original choice. Wow... just wow.

Edit: NM I misread what you said. You're still wrong. You don't have to discard the 2nd round for it to remain 1/3 chance.

Edit 2: Just because you can't see what's behind your door doesn't mean there is a 0% chance. I hope you don't play poker.

Siddar · Sep 13, 2013

Araysar_sl said:
haha, anyways.

Right he opens the other goat door if you picked the car. But YOU dont know you picked the car. And YOU dont know that he opened the second goat door. As far as you're concerned because one of the goat door is eliminated, you only have 2 doors, one of which has the car. None of your choices in 1st round affected the decision staring you in the face now.

This can only be a 2/3 scenario IF the host gives you an option at the end of 1st round to stay with your choice and have the doors revealed to you at the end of 1st round, OR move on to 2nd round and have 1 door eliminated for you.

Since you are never given that choice at the end of the first round, there is no switch in odds. Your actual true decision isn't even made until the 2nd round.

The first round is merely magician theatrics.

At the end of the first round after Host eliminates a Box what are the odds of the Host holding the right box to the contestants chances of holding the right box?

Ignore round two for now just focus on the odds as they stand at the end of round one.

What people are trying to tell you that in fact its round two that is the illusion because facts from round one are host now has a 66% chance of having the right box.

Zuuljin · Sep 13, 2013

Araysar_sl said:
If you have the OPTION of staying with your choice in 1st round and discarding the second round, then you'd have a 1/3 choice. but you never get that option.

If you don't switch in round 2, you essentially discarded the 2nd round and went with your initial pick. So, the same thing.

Araysar · Sep 13, 2013

Siddar_sl said:
At the end of the first round after Host eliminates a Box what are the odds of the Host holding the right box to the contestants chances of holding the right box?

Ignore round two for now just focus on the odds as they stand at the end of round one.

i assume by "right box" you mean car door. the odds are 100/100 because the host always knows whats behind every door. h

What people are trying to tell you that in fact its round two that is the illusion because facts from round one are host now has a 66% chance of having the right box.

how does the host have 66% when the host ALWAYS knows whats behind every door and he ALWAYS selects the goat door in round 2. his actions are always the same, always predetermined, its the total opposite of chance.

Araysar · Sep 13, 2013

Zuuljin_sl said:
If you don't switch in round 2, you essentially discarded the 2nd round and went with your initial pick. So, the same thing.

NO, not the same. The key is the option.

having the OPTION of moving to round 2, OR being FORCIBLY moved to round 2. The problem as it is presented originally, forces you to move to round 2, thus rendering any choices made in round 1 as meaningless.

Ravishing · Sep 13, 2013

Araysar_sl said:
how does the host have 66% when the host ALWAYS knows whats behind every door and he ALWAYS selects the goat door in round 2. his actions are always the same, always predetermined, its the total opposite of chance.

He does NOT always select a Goat door. He always DISCARDS a goat door but his selection may be a Car or Goat at the end of round 1.

Araysar · Sep 13, 2013

Fawe_sl said:
Uh... read the original problem. You DO keep your choice going into the 2nd round. It took you 4 pages to figure this out? What do you think the word "switch" means? It means Switch your original choice. Wow... just wow.

Edit: NM I misread what you said. You're still wrong. You don't have to discard the 2nd round for it to remain 1/3 chance.

Edit 2: Just because you can't see what's behind your door doesn't mean there is a 0% chance. I hope you don't play poker.

Wrong.

You dont keep your choice. You are offered the same choice again.

How about this.

In 1st round, host shows you 3 doors and does NOT make you choose anything, you are simply an observer.
Then he opens one of the doors, a goat door always
Then he asks you to select from the other 2 doors.

How is this scenario is any different from you selecting a door in 1st round vs. being a passive observer?

You guys are perfect sheep for a cult brainwashing.

hodj · Sep 13, 2013

Ravishing · Sep 13, 2013

Araysar_sl said:
Wrong.
How about this.

In 1st round, host shows you 3 doors and does NOT make you choose anything, you are simply an observer.
Then he opens one of the doors, a goat door always
Then he asks you to select from the other 2 doors.

How is this scenario is any different from you selecting a door in 1st round vs. being a passive observer?

You guys are perfect sheep for a cult brainwashing.

This scenario is not the same. You are not removing any options from the Host prior to him discarding a door. That is a key element to the equation.

Araysar · Sep 13, 2013

Fawe_sl said:
He does NOT always select a Goat door. He always DISCARDS a goat door but he may have a Car or Goat at the end of round 1.

yes, he discards it by selecting it.

there is never a MAY. its never uncertain, it is always certain.

it is always certain that the host will always discard a goat door after R1, and it is always certain that in R2 your choices will be 1 out of 2 doors, 1 is a goat, 1 is a car. there is never any uncertainty. the only true choice ever made is by the player in R2, the choice is R1 is always illusory, the choice of the host is always predetermined, and the outcome at the beginning of R2 is ALWAYS THE SAME.

Araysar · Sep 13, 2013

Fawe_sl said:
This scenario is not the same. You are not removing any options for the Host prior to him discarding a door. That is a key element to the equation.

I'm not removing any host? What does that even mean?

Zuuljin · Sep 13, 2013

Araysar_sl said:
In 1st round, host shows you 3 doors and does NOT make you choose anything, you are simply an observer.
Then he opens one of the doors, a goat door always
Then he asks you to select from the other 2 doors.

How is this scenario is any different from you selecting a door in 1st round vs. being a passive observer?

You guys are perfect sheep for a cult brainwashing.

The problem is what I bolded. When you 'choose' a door in round 1, that is a door the host cannot choose. So you limited the set he could choose from when you chose in round 1. Your first choice then obviouslydoesmatter.

Ravishing · Sep 13, 2013

Araysar_sl said:
I'm not removing any host? What does that even mean?

Edited to fix my sentence. Try again.

Araysar · Sep 13, 2013

Zuuljin_sl said:
The problem is what I bolded. When you 'choose' a door in round 1, that is a door the host cannot choose. So you limited the set he could choose from when you chose in round 1. Your first choice then obviouslydoesmatter.

That doesnt matter. Regardless of what you choose, the host always opens the other goat door.

You picked a car in r1? Great. the host has 2 goat doors that he can open.\
You picked a goat in r1? Sucks. But the host still has 1 goat door he can open.

The point being is that the host always has a goat door to open and discard, regardless of any "choice" you have made

Siddar · Sep 13, 2013

Araysar_sl said:
i assume by "right box" you mean car door. the odds are 100/100 because the host always knows whats behind every door. h

how does the host have 66% when the host ALWAYS knows whats behind every door and he ALWAYS selects the goat door in round 2. his actions are always the same, always predetermined, its the total opposite of chance.

Do you agree you have a 33% chance of picking the right box in first round?

If you assign other two box's to Host then Hosts chance of having the right box is 66%.

If host eliminates a incorrect box 100% of the time at end of the first round that shifts chance of hosts single remaining box to being the right box to 66%.

Once you accept the above you can ignore the 50/50 set up in second round and go for the box you know has a 66% of being the right one.

A brain teasing probability puzzle

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Bronze Knight of the Realm

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Uninspiring Title

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Uninspiring Title

Bronze Baronet of the Realm

Bronze Knight of the Realm

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Uninspiring Title

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Vox Populi Jihadi

Uninspiring Title

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Bronze Knight of the Realm

Uninspiring Title

Loser Araysar

Chief Russia Reporter. Stock Pals CEO. Head of AI.

Bronze Baronet of the Realm