A brain teasing probability puzzle

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Siddar

Siddar

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Ok I think I get it. Host has two choices compared to contestants one choice host has a 66% chance of having the right box and eliminates a wrong box every time in first round. Leaving host with a chance of having the winning box 66% of the time at start of second round. Contestant has a 33% chance of being right in first round. So you take hosts box because it has a higher chance of being correct even if its not the correct choice every single time.
 
Ravishing

Ravishing

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I originally voted "No, the odds stays the same/don't want to change my mind", before I even read any discussions. It took all of 2 seconds to understand why you should switch. I wish I could change my vote.

Araysar can't be reasoned with obviously, he thinks the 1st choice doesn't inform the 2nd while in fact it does.

Instead of 3 and instead of 1000000 howabout just using a sample of 5.

4 doors have a goat
1 has a car.

You have a 20% chance of picking the car on your 1st pick, but you have an 80% chance of picking a goat.
In the second round the Switch switches the odds. It is the same as if 4 doors had cars and 1 had the goat.
You always switch since it switches the odds in your favor.

Same reason 33/66 is switched to 66/33 in your favor when there are only 3 options rather than 5.
 
Araysar

Loser Araysar

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Haast_sl said:
Yes, the misunderstanding in this problem is the circumstances of the second choice. If you look at the second choice in a vacuum, it is definitely 50/50. However, when you add in the circumstance that your first choice was more likely to be wrong, it becomes skewed in favor of the switch.

This screwed with my mind until I read theEconomist's explanation. For some reason, it made more sense.
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why would you add the first choice? it affects nothing. you dont win or lose by being right or wrong in first round. the first round is merely the setup for the 2nd round. its what magicians call The Pledge (" The magician shows you something ordinary: a deck of cards, a bird or a man. He shows you this object. Perhaps he asks you to inspect it to see if it is indeed real, unaltered, normal. But of course...it probably isn't. "). nor does it affect the options presented to you in 2nd round. it is pure theatrics to muddle the problem.
 
Haast

Haast

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Araysar_sl said:
why would you add the first choice? it affects nothing. you dont win or lose by being right or wrong in first round. the first round is merely the setup for the 2nd round. its what magicians call The Pledge (" The magician shows you something ordinary: a deck of cards, a bird or a man. He shows you this object. Perhaps he asks you to inspect it to see if it is indeed real, unaltered, normal. But of course...it probably isn't. "). nor does it affect the options presented to you in 2nd round. it is pure theatrics to muddle the problem.
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<3 Aray
 
Hachima

Hachima

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Here is a new game. There is a system with unknown rules with 2 choices. Some people think choice A is a 66% chance of winning. Some people think choice B is a 50% chance. No one thinks choice B is less than 50% chance of winning. Do you choose choice A or B?
 
Araysar

Loser Araysar

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Siddar_sl said:
Ok I think I get it. Host has two choices compared to contestants one choice host has a 66% chance of having the right box and eliminates a wrong box every time in first round. Leaving host with a chance of having the winning box 66% of the time at start of second round. Contestant has a 33% chance of being right in first round. So you take hosts box because it has a higher chance of being correct even if its not the correct choice every single time.
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This is only a valid explanation if you count the 1st round. But since the 1st round is just a set up for the 2nd round, its meaningless. You never WIN in 1st round. You never LOSE in 1st round. The possibility of winning or losing in 1st round is purely illusory.

The choice is always 50/50 Stay with the door you had or pick the unknown door. The host always eliminates the third option for you, always making it a 50/50 proposition
 
Ravishing

Ravishing

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It does affect the options presented to you in the 2nd round. The 1 door you pick becomes 1 of the 2 options in the second round, thus there is a direct affect. You would be right if both options were randomly selected for the 2nd round, but they are not, you are choosing 1 of the options.
 
hodj

hodj

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Araysar_sl said:
why would you add the first choice? it affects nothing. you dont win or lose by being right or wrong in first round. the first round is merely the setup for the 2nd round. its what magicians call The Pledge (" The magician shows you something ordinary: a deck of cards, a bird or a man. He shows you this object. Perhaps he asks you to inspect it to see if it is indeed real, unaltered, normal. But of course...it probably isn't. "). nor does it affect the options presented to you in 2nd round. it is pure theatrics to muddle the problem.
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From the viewpoint of the statistician, the extra turn actually gives one more knowledge via a larger data set, which allows for a more informed decision.

So from a mathematical/statistical point of view, rather than muddling the issue, the first round of choices actually expands the data set, giving a fuller picture of the probability of events within the context of the situation.
 
DiddleySquat

DiddleySquat

Bronze Knight of the Realm
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Oh shit, Araysar isserious? That changes the premise totally.

Ara, I love you (non-homo way) but here you're wrong. The first pick is not meaningless, it changes the options for the game master in that he in some cases now is limited in his choice of which door to open. That in itself is information that changes the equation.
 
Araysar

Loser Araysar

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Fawe_sl said:
It does affect the options presented to you in the 2nd round. The 1 door you pick becomes 1 of the 2 options in the second round, thus there is a direct affect. You would be right if both options were randomly selected for the 2nd round, but they are not, you are choosing 1 of the options.
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this here is the perfect example of how beautiful this trick is, you'll have guys like this arguing in the face of common sense.

your options in 2nd round are always

1 door that you selected
1 door that is unknown.

since the host always eliminates one of the goat doors, you always have a car door and a goat door in 2nd round, and you always have a 1/2 in choice.

the illusion that you were offered a third door at some point is nothing more than illusion. you never had 3 choices. you always had just 2.
 
Himeo

Himeo

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Erronius_sl said:
Can we have a Quillmane probability brain teaser?
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About 25% chance of spawning once you found one of the two placeholders in South Karana. After that, it was a 30% chance the cloak would drop per kill. Placeholder respawned in less than two minutes iirc, so if you knew what you were doing and had another person who knew what they were doing you'd average about 8 cloaks an hour.

Oh, and for the original question you always switch.
 
Araysar

Loser Araysar

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DiddleySquat_sl said:
Oh shit, Araysar isserious? That changes the premise totally.

Ara, I love you (non-homo way) but here you're wrong. The first pick is not meaningless, it changes the options for the game master in that he in some cases now is limited in his choice of which door to open. That in itself is information that changes the equation.
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The Gamemaster is never limited in what door he can open. Because there is 2 goat doors, he will ALWAYS have an extra goat door to open whether you pick a car or a goat door in round 1.
 
Ravishing

Ravishing

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Araysar_sl said:
this here is the perfect example of how beautiful this trick is, you'll have guys like this arguing in the face of common sense.
Click to expand...
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.
 
Siddar

Siddar

Bronze Baronet of the Realm
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Araysar_sl said:
This is only a valid explanation if you count the 1st round. But since the 1st round is just a set up for the 2nd round, its meaningless. You never WIN in 1st round. You never LOSE in 1st round. The possibility of winning or losing in 1st round is purely illusory.

The choice is always 50/50 Stay with the door you had or pick the unknown door. The host always eliminates the third option for you, always making it a 50/50 proposition
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Just ignore the second round and look at chances of Host having the right box at end of first round. Host always gets two box's a base 66% chance of having the right box. Then host gets rid of a wrong Box. His remaining Box now has a 66% of being the right box to your box's 33% chance.

The right box was the right box in both rounds so there is a 66% chance host box is the right box even in second round because he increased the chances of him having the right box in the first round. Not changing though is not always the wrong answer 33% of time its correct.
 
Araysar

Loser Araysar

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Noodleface_sl said:
Araysar why are you assuming that you can't win in round 1?
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Good question.

Lets play this scenario 100 times. If you win even once in 100 turns (certainly better than the supposed yet faulty 2/3 odds being bandied about here) I'll give you 100 cars.

1.

I present to you 3 doors, you pick one.
I smile knowingly, then open a goat door (I always have one because there are 2 goat doors in the trick)
And offer you to change your choice.

You think this is all part of the same choice but it isn't. You already made your first choice and now I am offering you a 2nd one, to stay or choose other door.

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



2. Repeat 99 more times.
 
DiddleySquat

DiddleySquat

Bronze Knight of the Realm
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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!
 
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