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The Time Everyone “Corrected” the World’s Smartest Woman (2015)

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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#311

Post by nzealand »

FabHK wrote: post #125
hn_throwaway_99 wrote: post #116

Earlier quoted context omitted.

In this case, though, I don't believe it's just calculation vs. intuition. The reason the 100 or million door problem helped me understand was because it clarified an implicit rule of the game: that the door the host chooses to open is not random . If it were random, it would make for a very boring game ("Uhh, there's the prize, you win, I guess that's game over.") Once I understood that the host would only ever open…

Indeed, that is a crucial bit of information that is not made explicit in the original framing of the problem.

Marilyn had the same framing of the problem as everyone else.

Marilyn made her key assumptions explicit in the original explanation she gave.

92% of people still disagreed with her.

And most of them seemed fully aware that she had the guiness world record for the highest IQ in the world.

To paraphrase Paul Graham's recent article, If the smartest person in the world proposed an idea that sounded preposterous, I'd be very reluctant to say "You are wrong."

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#312

Post by atdrummond »

listenallyall wrote: post #181
atdrummond wrote: post #163

Earlier quoted context omitted.

You have three doors. As you note, you have a 1/3 chance of winning. Monty now reveals a losing door. At this point, your door has a 1/3 chance of still winning - the probability of that choice can’t change. However, as we now know one door has a 0/3 chance of winning (it’s been revealed) the remaining door must have (1-1/3) chance of winning. Thus, the remaining door has a 2/3 chance of winning.

I'm going to disagree with your framing here. Probabilities DO change as more information becomes available. For example, prior to rolling a pair of dice, you have a 1/36 chance of rolling a 12. However as sooner as you see the value of the first die, the probability changes to either 0 (most likely) or 1/6. In your description, if Monte opens a door randomly -- which you don't make clear whether he does or doesn't -…

He never chooses randomly in the Monte Hall problem. He’s always going to reveal a goat. That’s why the maths are so straightforward - and yet so counterintuitive.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#313

Post by stale2002 »

TchoBeer wrote: post #282
stale2002 wrote: post #176

Earlier quoted context omitted.

> imagine every time the hosts picks the car the universe resets Do you believe that we live in a universe that is reseting, every time Mr Monty hall opens a car? As in literally Mr Monty Hall. From the game show. In real life. Because the purpose of the question is to mimic the show.

You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car, and the result is the same.

> You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car

In the actual show, do you believe they are sending in a new contestant every time Monty hall picks are car?

Do you think that is what is happening in the actual game show?

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#314

Post by listenallyall »

atdrummond wrote: post #312
listenallyall wrote: post #181

Earlier quoted context omitted.

I'm going to disagree with your framing here. Probabilities DO change as more information becomes available. For example, prior to rolling a pair of dice, you have a 1/36 chance of rolling a 12. However as sooner as you see the value of the first die, the probability changes to either 0 (most likely) or 1/6. In your description, if Monte opens a door randomly -- which you don't make clear whether he does or doesn't -…

He never chooses randomly in the Monte Hall problem. He’s always going to reveal a goat. That’s why the maths are so straightforward - and yet so counterintuitive.

> He never chooses randomly in the Monte Hall problem.

But you never state that, which is why I took exception with your explanation. You also state that probabilities never change, which is also untrue as more information is revealed.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#315

Post by shkkmo »

salamanderman wrote: post #173
shkkmo wrote: post #57

Earlier quoted context omitted.

Not at all. Once the door is opened, it doesn't matter if the host knew there was a goat behind it or not. Edit: The host's knowledge only matter if the host can choose not to open a door.

If the host opens the door with car, and asks you if you'd prefer to switch to the unopened door, then you have a 100% chance of being wrong, as the door with the car isn't one of the choices. But, sure, my second point still stands, that it's effectively asking if you want your door or the sum of the other two doors. But, to be clear, the question states that Monty opens the door with the goat. If you were to write…

You appear to have completely edited the comment I was replying to. My "not at all" does not apply to your comment as it currently reads, which is correct.

On HN it is considered polite to append corrections rather than replace content that has become part of the discussion.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#316

Post by Talanes »

glitchc wrote: post #236
Talanes wrote: post #234

Earlier quoted context omitted.

Because in 2/3 scenarios you had to make the host choose the door without a car?

The host can never choose the door with the car, because then the game is over. Ergo the host has to choose the door with goat, every time.

Right, and the host is only making a meaningful choice in the 2/3 scenarios where you didn't pick the car in the first place.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#317

Post by tpush »

dllthomas wrote: post #309
tpush wrote: post #270

Earlier quoted context omitted.

The intention of the host only matters if the contestant would have to choose the subsequent action (switching or not) before the hosts opens a door. If the host has revealed a goat door, and the contestant then has to decide what to do, the intentions of the host for having chosen the door are irrelevant.

(Noting again that the mechanism doesn't matter, what matters is the odds of various behavior by the host, but - I think reasonably - using "intentions of the host" as a proxy for that.) The intentions of the host do matter. Imagine the host picks the correct door by the following procedure: 1) picks an available door at random; 2) if that door has a goat, opens it; 3) if that door has the car, opens the other door.…

So, thinking about it really hard and reading about it online:

My comment was definitely wrong: If Monty could have opened a car door, but just didn't, then duh the probabilities for the car to be behind the doors are different than if Monty always opens a goat door. So in that way, the intentions of Monty, meaning how he chooses, definitely matter.

But I think your example here doesn't show that? Are you trying to illustrate the Monty Fall variation?

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#318

Post by jml7c5 »

haberman wrote: post #303
someguydave wrote: post #162

Earlier quoted context omitted.

I think the confusing part for many people is the unstated fact that the host takes all prizes into account when revealing a door, and that the host is forbidden from revealing the car. If the host chooses randomly then his pick adds no information (other than the extra revealed prize)

I don't think this actually matters. Suppose Monty doesn't actually know which door has the prize, and just picks randomly between the two. Now the only difference is that Monty might accidentally pick a prize. Suppose he does. What are the options now? 1. The game goes on, and you can just switch your guess to the door he picked. (WIN) 2. The game resets due to Monty's error and you play again. (REDO) 3. Monty just…

>Now the only difference is that Monty might accidentally pick a prize.

This a mistaken conclusion, as actually there is a difference if a goat is revealed by devious Monty (who makes sure he doesn't reveal the car) and dumb Monty (who picks at random), because the rules of the game really are different. The apparent outcome (you pick door, Monty reveals a goat) is the same. But the process is different. In the latter version dumb Monty has all the same information as you, in the former version devious Monty gets more information that you do and changes his behavior based on that information.

In programming terms, devious Monty has an "if" statement in there. (Something like, `if (random_choice == prize_door) { swap_choice(); open_door(); } else { open_door(); }`.)

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#319

Post by jml7c5 »

dllthomas wrote: post #51
jml7c5 wrote: post #20

From reading the problem as posed in the article, the confusion seems similar to the "plane on a treadmill" thing, where people are interpreting the premise of the problem differently. (In plane on a treadmill: "the treadmill moves backwards @ -1 * plane airspeed" vs "the treadmill moves backwards to keep plane airspeed at 0". In this: "the host will open the door at random and in this example it happen to have a goa…

The presentation of the problem included the phrase "the host, who knows what's behind the doors, opens another door", so I think in that case the interpretation that Monty deliberately reveals a goat is more appropriate (in addition, obviously, to being what was intended), although I agree there is wiggle room enough to admit both possibilities and clarity about which case you are discussing is important as it chang…

It does, but it doesn't emphasize it enough to allay confusion, particularly for those unfamiliar with the "gotcha" in the problem. It's easy to overlook in that description unless you know that it is the important clue to understanding.

Kind of like the classic riddle "John's mother has four children. They are named March, April, and May. What's the last child's name?" which uses underemphasis for almost comedic effect.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#320

Post by someguydave »

haberman wrote: post #303
someguydave wrote: post #162

Earlier quoted context omitted.

I think the confusing part for many people is the unstated fact that the host takes all prizes into account when revealing a door, and that the host is forbidden from revealing the car. If the host chooses randomly then his pick adds no information (other than the extra revealed prize)

I don't think this actually matters. Suppose Monty doesn't actually know which door has the prize, and just picks randomly between the two. Now the only difference is that Monty might accidentally pick a prize. Suppose he does. What are the options now? 1. The game goes on, and you can just switch your guess to the door he picked. (WIN) 2. The game resets due to Monty's error and you play again. (REDO) 3. Monty just…

if monty picks a prize the game is over
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