Mind Melters

[Handlebars]

Post any riddles or puzzles that intrigue you.

Here's a puzzle that has interested me. It's called "The Monty Hall Problem" after the game show host, Monty Hall. The expert explanations didn't "click". So I made my own explanation. It's way better. You'll see Play along!

Almost like a game show. There are 3 doors and behind one of the doors is a grand prize, such as a new car. The other 2 doors have a joke prize like a can of spaghetti or something.

You can pick any of the 3 doors and you have repeated opportunities to switch choices.
The scenario is that the host, Monty, asks you to choose a door. Monty then asks you if you want to change your choice. The crowd goes nuts, saying change or stay.

They go to a commercial and then come back, and Monty again asks you if you want to change doors. The crowd goes nuts again.
Then Monty opens up one of the 2 doors that you didn't choose. It's a can of spaghetti. Again he asks you if you want to change doors. The crowd goes nuts.

Q/ Is there any statistical advantage to changing your choice now? Explain your reasoning.

 

[Taylor57]

It sounds like orignially you had a 33% chance and now after the reveal, your odds just jumped to 50-50. So my answer is there is no statistical advantage as your odds are 50-50.

 

[Handlebars]

It sounds like orignially you had a 33% chance and now after the reveal, your odds just jumped to 50-50. So my answer is there is no statistical advantage as your odds are 50-50.

Thank you. That's what I thought - in fact, that's what I had trouble unthinking. It took me a while to really grasp the trouble.

 

[Taylor57]

Thank you. That's what I thought - in fact, that's what I had trouble unthinking. It took me a while to really grasp the trouble.

I thought it was a trick question!!

 

[Handlebars]

Suppose we name the positions. The door you picked, no matter how many changes you made, gives you 1 in 3 or approx 33.3 %.
If we name that position "You", then the "Not You" has the 2 in 3 or 66.6 %.
The "Not You" has better odds. That never changes, so you change instead. Now you know which door to change to, though. The "Not You"is a better position. So get there. And you now know which one of the "Not You" doors is a can of spaghetti.
That leaves the other with the whole 66% probability , the "Not You" is still holding 66% remember. Nothing changed of your original choice. Something did change about the "Not You" position, though: information came in.

 

[Taylor57]

Once Monte reveals the can of spaghetti, you just went from 33 to 50. I cant see any advantage to switch from you original pick at this point unless an audience member that works for Lets Make a Deal flashes you the sign!

 

[Handlebars]

I confess that I constructed a little cardboard setup with 3 doors that I could open and friends could play for coins.
Try it with friends using chips. One friend always stays and the other friend always changes. It'll be a slaughter overall for the one who always changes.

 

[JCofMN]

It sounds like orignially you had a 33% chance and now after the reveal, your odds just jumped to 50-50. So my answer is there is no statistical advantage as your odds are 50-50.

But to take advantage of the knowledge of better odds you've just learned, you need to chose the other door to get the improved 50/50 odds. The original choice still only has a 33% chance. This is a classic tenet of the time value of knowledge in decision theory/behavioral economics --- this might be covered in one of the Freakonomics books or in one of their podcasts.

 

[Handlebars]

Once Monte reveals the can of spaghetti, you just went from 33 to 50. I cant see any advantage to switch from you original pick at this point unless an audience member that works for Lets Make a Deal flashes you the sign!

The "You" has only 33.3 % probability. How could simply getting information ever change that?

 

[Taylor57]

But to take advantage of the knowledge of better odds you've just learned, you need to chose the other door to get the improved 50/50 odds. The original choice still only has a 33% chance. This is a classic tenet of the time value of knowledge in decision theory/behavioral economics --- this might be covered in one of the Freakonomics books or in one of their podcasts.

I thought it sounded more like a coin flip after the spaghetti can. I know for sure, if I was on the show and Monte asked me if I wanted to switch and I accepted, I would end up with the Hoover vacuum...

 

[Handlebars]

But to take advantage of the knowledge of better odds you've just learned, you need to chose the other door to get the improved 50/50 odds.

Almost! You get the 66.6% probability if you do change after getting the information

 

[Taylor57]

Am I in a 3 Shell Con with HBars?

 

[Handlebars]

Am I in a 3 Shell Con with HBars?

It's truly a mind melter

Monty Hall problem - Wikipedia

en.wikipedia.org

 

[Handlebars]

"Pigeons repeatedly exposed to the problem show that they rapidly learn to always switch, unlike humans.[23]"

 

[Taylor57]

"Pigeons repeatedly exposed to the problem show that they rapidly learn to always switch, unlike humans.[23]"

But based on probabilty, there should be no advantage to switch, unless that I missed something in Stats 101

 

[Handlebars]

Now suppose I can have both the "Not You" doors. That means I have 66% probability, right? I have both of them if I have the "Not You" position. And I know which one of the doors to discard after Monty shows me the can of spaghetti behind it.

 

[Taylor57]

Now suppose I can have both the "Not You" doors. That means I have 66% probability, right? I have both of them if I have the "Not You" position. And I know which one of the doors to discard after Monty shows me the can of spaghetti behind it.

Well of course, now you have inside info, no? You had cocktails last night with Carol Merrill.

 

[Sierratim]

But based on probabilty, there should be no advantage to switch, unless that I missed something in Stats 101

I went through this with my (enginering) sons recently. What seems intuitive is wrong; your odds of success do improve with switching your selection. I even took Stats 201! We are not smarter than piegons...

 

[Taylor57]

So you guys are telling me that if the can of spaghetti, shows up and Monte offers me the switch, and it's played out enough times to be significant, I lose if I keep my original bet?

 

[Sierratim]

So you guys are telling me that if the can of spaghetti, shows up and Monte offers me the switch, and it's played out enough times to be significant, I lose if I keep my original bet?

Your odds do drop if you don't switch...as mind bending as it seems, just sayin'

As an old engineer, I don't make the rules, I just try to understand and exploit them!