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Marilyn vos Savant and the Monty Hall Problem (2015)

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Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#141

Post by nickpsecurity »

bemusedthrow75 wrote: post #51
nickpsecurity wrote: post #28

Earlier quoted context omitted.

That’s exactly what I did. In FreeBASIC. The way the problem works started coming together in my head as I coded it. The code’s structure reflected the problem’s structure. I realized I previously misunderstood something about the problem statement. Later, I read someone saying many mathematicians got this problem wrong because of how it’s worded. So, it may be challenging, not because probability was challenging, bu…

It's not unclearly specified. It's very tight. People who get it wrong are usually projecting some implied understanding onto it, which is why they get it wrong. Which is the point of the problem . It's designed to reveal this tendency in analytical thinking leading to unexpected outcomes. You get it wrong, you're gobsmacked, you understand why, you gain some enlightenment from it. It's fun to be wrong in ways you la…

I could see that. Both that it could be the intention of the problem statement and what you say it achieves. It had that effect on me.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#142

Post by beepboopboop »

JackFr wrote: post #125
dekhn wrote: post #112

Earlier quoted context omitted.

Yes, I'm literally talking about this sentence: "host, who knows what’s behind the doors, opens another door, say #3, which has a goat." I parsed that as "50% of the time, monty opens another door and it has a car and you win immediately, and 50% of the time, monty opens another door and it has a goat". In retrospect I think my brain just sort of pictured that and proceeded to assume there was no reason to switch, an…

> 50% of the time, monty opens another door and it has a car and you win immediately Why would you think you won? You didn't choose that one with the car and you aren't offered the opportunity to switch to the open one, only the closed one. The only interpretation which makes sense is that he always shows you a goat.

I think they meant you lose immediately.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#143

Post by city41 »

JackFr wrote: post #125
dekhn wrote: post #112

Earlier quoted context omitted.

Yes, I'm literally talking about this sentence: "host, who knows what’s behind the doors, opens another door, say #3, which has a goat." I parsed that as "50% of the time, monty opens another door and it has a car and you win immediately, and 50% of the time, monty opens another door and it has a goat". In retrospect I think my brain just sort of pictured that and proceeded to assume there was no reason to switch, an…

> 50% of the time, monty opens another door and it has a car and you win immediately Why would you think you won? You didn't choose that one with the car and you aren't offered the opportunity to switch to the open one, only the closed one. The only interpretation which makes sense is that he always shows you a goat.

Not to mention Monty always showing a goat is what adds the tension and interest a game show needs.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#144

Post by michaelcampbell »

gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

When first confronted with this, I wrote a simulation in GW-Basic on a PC with an orange monochrome monitor and ran it a bunch of times to convince myself switching was the right thing to do, statistically.

I came up with another way to visualize it that made more sense than increasing the number of doors, but it requires that one accept the fact that your chances of winning are 1/3 if you don't switch, and you know Monty always shows a losing door.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#145

Post by jncfhnb »

bemusedthrow75 wrote: post #140
jncfhnb wrote: post #132

Earlier quoted context omitted.

Ok let’s play! We play this game 1000 times. 33% of the time you pick the car and I show you a goat. You switch and lose 100% of the time. 66% of the time you pick a goat and I don’t show you a goat. Assuming you don’t switch because you believe this means you have an equal odd on your current door, you lose 100% of the time. Congrats. You have lost every single round.

You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly…

I have not restated the problem.

You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car.

There is nothing in the prompt that says we are not playing my variant of the game.

Being told that you SAW a goat does not mean you would ALWAYS SEE a goat if the previous conditions had gone differently. And that is why you’re wrong :)

Again > all you know is that he opened a goat door

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#146

Post by TotempaaltJ »

grumbel wrote: post #138
Jimmc414 wrote: post #124

Earlier quoted context omitted.

>The one you picked still has a 1/3 chance of winning If there are only two choices remaining, I guess I don't understand the assertion that there is still a 1/3 chance of winning. Suppose you were new to the contest and were allowed to put money down on the choice at the point that there were two doors left. Then you repeated the bet every new contestant. Would one door would be more profitable than the other?

> Suppose you were new to the contest and were allowed to put money down on the choice at the point that there were two doors left. That would be a completely different game. The goat doesn't get reshuffled. The doors that remain are not random and most importantly, you know which door you picked in the first round. It doesn't become a 50:50 chance just because there are two doors, as the goat isn't distributed over…

Little bit off-topic, but I love how probability gets you into phrasing like "the goat isn't distributed over those two doors"

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#147

Post by bemusedthrow75 »

jncfhnb wrote: post #145
bemusedthrow75 wrote: post #140

Earlier quoted context omitted.

You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly…

I have not restated the problem. You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car. There is nothing in the prompt that says we are not playing my variant of the game. Being told that you SAW a goat does…

> You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt.

Yes. It is. It is a fixed part of the scenario. Monty opens a door and shows you a goat. He knows it is going to be a goat (he is "well-aware of what is going on behind the scenes"). He's showing you a goat as part of the problem which is: should you switch?

Again: think through what the problem actually SAYS:

> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

> “Now,” he says, turning toward you, “do you want to keep door #1, or do you want to switch to door #2?”

No matter what: the goat Monty shows you is not a matter of chance. It is a fixed part of the problem. It's there in writing: he shows you a goat. Full stop.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#148

Post by cynix »

dynm wrote: post #75
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

I actually like to back up even further and start with this problem: There are 1000 doors. You pick one. There's a 1 in 1000 chance you get it right. Now, do you want what's behind your door, or what's behind the other 999 doors? https://dynomight.net/2020/09/17/making-the-monty-hall-probl...

Do you really want 998 goats though? It must cost a fortune to transport them home from the studio, finding a space for them to live in, and feed them, etc.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#149

Post by jakelazaroff »

lelanthran wrote: post #98
HumblyTossed wrote: post #83

Earlier quoted context omitted.

The way I think about it, in general, is that Monty, by purposely not opening the correct door, is giving you a huge hint and thus changing the game which changes the odds. Think of it similarly to those people who play the same lotto #s all the time because they think eventually it has to hit. Well, no. It's a new game every time. If the lotto commission retired each combination that won each week, then sure. And th…

> And this is essentially what Monty is doing. He's retiring some doors and changing the odds. That still leads to the wrong answer, because he is retiring one of the losers, leaving a 50:50 chance of getting a prize.

You mean 1/3:2/3, right?

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#150

Post by michaelcampbell »

full_monty wrote: post #116
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

I never understood why the 1000 door version was more intuitive. Here's how I understand it. There's 1/3 chance of picking the car. 1/3 of the time you pick the car, switch, and lose. 2/3 of the time you pick a goat, switch, and win. Why? Because 2/3 of the time you picked a goat, Monty shows you the other goat, so if you switch you definitely get the car.

username checks out =D

I never liked the 10^x other doors version either. My thought was, what say me and a friend play a the same time, and pick the same initial door? If I NEVER change, and he ALWAYS does... I'm still going to win 1/3 of the time, and if Monty always shows the goat, ONE OF US has to win, so if I'm 1/3 by not switching, he HAS to be 2/3 by switching.

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