Korean Job Discussion Forums

[mindmetoo]

(Geez I spell it like Monty Haul without thinking... points to any person that can tell what spelling Monty Hall like Monty Haul reveals about my past...)

The problem:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Now if up front you're given the choice of only two doors (the third door never existed), the odds are 50/50. In the Monty Hall problem you're given three doors and then one door is revealed to have a goat and then you're back to a choice between two doors: keeping your door or picking the remaining closed door. It seems like we're back to a 50/50 proposition but no.

You should actually switch. You have a 2/3 chance of being right by switching.

Many people go "huh?"

Here is the best way to understand it. In short, you're not being given a chance to choose between two doors. In the second stage you're being given a chance to pick your door or all the other doors.

Lets increase the doors to 1 million doors. You pick one door. What are the odds you picked right? 1/1,000,000. What are the odds the car is behind any of the unpicked doors? 999,999/1,000,000. Now what if instead my next move was to give you the choice between staying with your door or switching to picking all the unopened doors. (No doors have yet been opened. You're just allowed to stay with your current door or pick the remaining unopened doors.) In other words, you can stay with your 1/1,000,00 chance or go with the 999,999/1,000,000 chance. You'd be foolish to stay with just one door when you could pick all the other doors. Right?

Of course the problem is you have to open 999,999 doors to find your car! The key to the Monty Hall problem is instead of you having to open many, many doors before you find your car, Monty Hall opens all the doors for you but one. It's a little service he provides for you. Since he knows where the car is, he doesn't actually open the remaining door with the car. He leaves that to you. That 999,999/1,000,000 chance is, for all intents and purposed, compressed into the one door Monty keeps closed.

[mithridates]

I was just about to come in and tell you to spell it the way it should be - Monty Haul. I'm proud to say that none of my campaigns have ever been of that nature. It's all about grit and survival on Athas. You?

[mindmetoo]

[Beej]

I think you logic is faulty here. If you are given the choice to change doors after one door is revealed, its a 50/50 proposition. nce a door is revealed it is not part of the eqaution. Its either behind door 1 or 2.

Same thing with a series of coin tosses. Five tosses in a row are heads. Many people will choose tails on the next toss because the odds are low for six tosses a row being the same. But that sixth toss is actually 50/50. The first five tosses no longer matter.

[Woland]

[mindmetoo]

[Hater Depot]

Monty's knowledge is not the key to the problem.

Draw up a probability chart and you will see that.

[mindmetoo]

[Thunndarr]

I like watching people come to grips with this problem. Most people are so stuck on what they "know" is right that they can't look at the problem rationally.

[Troll_Bait]

[mindmetoo]

[Troll_Bait]

[captain planet]

i've seen this problem a lot of times before, but since i couldn't figure out what the show was about (i was young, everyone was dressed like a moron, and the sound reception was mediocre), i can't figure out exactly what the question is asking. i don't understand the setup of the show, and any attempt to think about this problem is clouded by thoughts of spandex, toupees, goats, and slide trombones.

[mindmetoo]

[Troll_Bait]