Offday Fun

by shaftr on Apr 3, 2007 2:45 PM CDT

A thoroughly honest game-show host has placed a car behind one of three doors. There is a goat behind each of the other doors. You have no prior knowledge that allows you to distinguish among the doors. "First you point toward a door," he says. "Then I'll open one of the other doors to reveal a goat. After I've shown you the goat, you make your final choice whether to stick with your initial choice of doors, or to switch to the remaining door. You win whatever is behind the door." You begin by pointing to door number 1. The host shows you that door number 3 has a goat.

Do the player's chances of getting the car increase by switching to Door 2?

NOTE: Explanation - http://en.wikipedia.org/wiki/Monty_hall_problem/

("Do you see what happens, Larry?")

Poll

Do your chances increase by switching?

Yes

21 votes

No

3 votes

Stays the Same

11 votes

35 votes | Poll has closed

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Comments

yes

by larry on Apr 3, 2007 2:55 PM CDT reply actions

why?

and what do your odds increase to if they do increase?

Go Badgers!

by shaftr on Apr 3, 2007 2:59 PM CDT up reply actions

your odds are 2/3 if you switch

as for why, just google monty hall.

by larry on Apr 3, 2007 3:04 PM CDT up reply actions

ugh...

hater

Go Badgers!

by shaftr on Apr 3, 2007 3:05 PM CDT up reply actions

still a fun exercise

even after you give people the rationale, they still often deny it.

by larry on Apr 3, 2007 3:06 PM CDT up reply actions

doesn't matter.

if the game show host really doesn't remember where the car is, then switching doesn't do anything for you,

It takes two to lie; one to lie and one to listen.

by Toonderstrook on Apr 3, 2007 2:58 PM CDT reply actions

but

as larry pointed out, if he opens one he KNOWS doesn't have the car, then you should switch.

It takes two to lie; one to lie and one to listen.

by Toonderstrook on Apr 3, 2007 3:12 PM CDT up reply actions

Right...

The "correct" answer (you should switch) is dependent on knowing that the host knows which door has the car behind it and will [i]never[/i] open that door. The host is giving you more information when he opens another door. This isn't clear in the above scenario.

by The Jerry Royster Experience on Apr 3, 2007 3:20 PM CDT up reply actions

yeah, it's clear

the example says the host will open a door to reveal one of the goats - obviously the host knows where the goats are and, therefore, knows where the car.

by larry on Apr 3, 2007 3:25 PM CDT up reply actions

It also depends on the assumption...

that you have a 33% chance of being correct after having made your first choice. I maintain that, once you've made that pick, you odds collapse, either to 0% or to 100%, depending on whether you've chosen correctly.

But it's really a matter of how you understand the question.

by The Jerry Royster Experience on Apr 3, 2007 3:37 PM CDT up reply actions

One interesting way

that I was taught to look at it:

If you employ the switching method everytime, then the only way you will get it wrong is if you initially choose the right door (33% chance). If you initially choose either of the wrong doors (67% chance), the other wrong door is revealed, and you will always switch over to the correct door.

I miss the days when the problems I had to face on daily basis were mathematical in nature and not, "How can I please the client?" (Also being able to watch Sox day games was nice).

by CatBrains on Apr 4, 2007 10:04 AM CDT reply actions