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A simple Monty Hall variant


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9 replies to this topic

#1 Yoruichi-san

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Posted 25 May 2012 - 05:15 AM

Seeing as how every 8th grader with a math counts trophy knows the optimal play to his game, ol' Monty decided to shake things up.

He added two more doors, for a total of 5 instead of 3, behind which 4 held a goat, and 1 held a brand spanking new electric car (hey, gotta keep up with the times, eh?).

In the first round, the player chooses two doors instead of one. Then Monty opens up one of the other three doors and reveals a goat. Then the player may choose one of his two original doors or switch to one of the unchosen doors. Monty then releases one more goat (gotta give the first goat some company or else it'll eat Monty's brand new trousers), and the player is then given a final choice of the remaining three doors.

What is your play, if:

1) The second door Monty opens is random?
2) He is purposely playing against you, trying to keep that new car for himself?

And 3) If you weren't sure, how much would you have to suspect dear old Monty's honorable intentions to make either play?

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 2 is awaiting it's epic conclusion...are you up to the task?

When life hands me lemons, I make invisible ink.


#2 WitchOfDoubt

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Posted 25 May 2012 - 06:01 AM

Spoiler for

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#3 BobbyGo

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Posted 25 May 2012 - 04:51 PM

Spoiler for My attempt

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#4 Yoruichi-san

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Posted 25 May 2012 - 08:39 PM

On track with the play, but no one's gotten the complete correct reasoning yet. There's a consideration that makes the fractions somewhat uglier ;) .

As for the WIFOM, it is a 30 minute show (well, 23 plus commercials), and if you don't make a play, you have 0 chance of getting the car. That said, okay, this problem may not be as simple as I originally thought.

Spoiler for The down and dirty...


However, for the sake of there being a solution to 2) and 3) (which will also force you to calculate the consideration mentioned above), let's say that Monty doesn't know exactly which door the car is in either, i.e. he is told which door to open for the first and he picks a door he wants to open for the second over his bluetooth and the producers tell him to do it or to choose another door.
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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 2 is awaiting it's epic conclusion...are you up to the task?

When life hands me lemons, I make invisible ink.


#5 bushindo

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Posted 30 May 2012 - 09:02 PM

Seeing as how every 8th grader with a math counts trophy knows the optimal play to his game, ol' Monty decided to shake things up.

He added two more doors, for a total of 5 instead of 3, behind which 4 held a goat, and 1 held a brand spanking new electric car (hey, gotta keep up with the times, eh?).

In the first round, the player chooses two doors instead of one. Then Monty opens up one of the other three doors and reveals a goat. Then the player may choose one of his two original doors or switch to one of the unchosen doors. Monty then releases one more goat (gotta give the first goat some company or else it'll eat Monty's brand new trousers), and the player is then given a final choice of the remaining three doors.

What is your play, if:

1) The second door Monty opens is random?
2) He is purposely playing against you, trying to keep that new car for himself?

And 3) If you weren't sure, how much would you have to suspect dear old Monty's honorable intentions to make either play?


Here's a play
Spoiler for approach

Edited by bushindo, 30 May 2012 - 09:10 PM.

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#6 mmiguel

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Posted 02 September 2012 - 09:46 PM

Seeing as how every 8th grader with a math counts trophy knows the optimal play to his game, ol' Monty decided to shake things up.

He added two more doors, for a total of 5 instead of 3, behind which 4 held a goat, and 1 held a brand spanking new electric car (hey, gotta keep up with the times, eh?).

In the first round, the player chooses two doors instead of one. Then Monty opens up one of the other three doors and reveals a goat. Then the player may choose one of his two original doors or switch to one of the unchosen doors. Monty then releases one more goat (gotta give the first goat some company or else it'll eat Monty's brand new trousers), and the player is then given a final choice of the remaining three doors.

What is your play, if:

1) The second door Monty opens is random?
2) He is purposely playing against you, trying to keep that new car for himself?

And 3) If you weren't sure, how much would you have to suspect dear old Monty's honorable intentions to make either play?



Seeing as how every 8th grader with a math counts trophy knows the optimal play to his game, ol' Monty decided to shake things up.

He added two more doors, for a total of 5 instead of 3, behind which 4 held a goat, and 1 held a brand spanking new electric car (hey, gotta keep up with the times, eh?).

In the first round, the player chooses two doors instead of one. Then Monty opens up one of the other three doors and reveals a goat. Then the player may choose one of his two original doors or switch to one of the unchosen doors. Monty then releases one more goat (gotta give the first goat some company or else it'll eat Monty's brand new trousers), and the player is then given a final choice of the remaining three doors.

What is your play, if:

1) The second door Monty opens is random?
2) He is purposely playing against you, trying to keep that new car for himself?

And 3) If you weren't sure, how much would you have to suspect dear old Monty's honorable intentions to make either play?


Spoiler for try

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#7 Yoruichi-san

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Posted 04 September 2012 - 02:22 AM

Oh, I had actually pretty much forgotten about this, but *shrug*

Spoiler for Hint...

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Women are definitely stronger. We are [Fe]males, after all...

Some of what makes me me is real, some of what makes me me is imaginary...I guess I'm just complex. ;P

<3 BBC's Sherlock, the series and the man. "Smart is the new sexy."

Chromatic Witch links now on my 'About Me' page!  Episode 2 is awaiting it's epic conclusion...are you up to the task?

When life hands me lemons, I make invisible ink.


#8 mmiguel

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Posted 04 September 2012 - 02:45 AM

Oh, I had actually pretty much forgotten about this, but *shrug*

Spoiler for Hint...


Spoiler for

Edited by mmiguel, 04 September 2012 - 02:49 AM.

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#9 bushindo

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Posted 04 September 2012 - 05:51 PM

Spoiler for try


Great analysis, and I agree with your answer. Good solve.
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#10 kbrdsk

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Posted 04 September 2012 - 06:47 PM

Spoiler for

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