let's make a deal - brain teaser

[Panerai 1]

There are 3 doors and you're allowed to pick one

Behind 2 of the doors is crap
Behind the other door is some sweet phat lewtz like heroic [Incineratus] or [Deathbringer's Will]

Once you pick a door, your host, Nefarian, opens up one of the doors you did not select and there is a [Cracked Shortbow]

There are 2 doors left, the one you selected and the other.

He asks if you want to switch doors?

do you keep your original door? or change your selection?
why?

[Rhius]

You switch doors. Your door has it's original 33% chance of phat lewts whereas the other door now has a 66% chance of phat lewts.

Don't ask me why both remaining doors aren't a 50% chance of lewt; I have never understood this!

[Fsob]

It doesn't matter. You aren't going to get the good one no matter which one you choose.

[Panerai 1]

Rius Aldregan wrote:

Don't ask me why both remaining doors aren't a 50% chance of lewt; I have never understood this!

You're correct

It has to do with making the decision discrete between 2 choices at the beginning

At the start
Option A = 33% of being right (the door you selected)
Option B = 66% of being right (the 2 doors you didn't select)

If you agree with the above then after he opens one of the B doors - Option B still has a 66% chance of being right.

So by switching doors, you basically doubled your odds

We asked this in a panel interview today, poor guy.

[ullariend]

I think the correct answer is you run away before Nef hits you with Shadowflame and then experiments on your corpse.

Rhius, would you happen to have a link to an attempt to explain why it is not a 50/50 chance?

[Tassager]

If it's a resto druid helmet, holy pally bracers, or a feral druid staff... it's not behind any of the doors. Ever.

[Meraxiss]

Fsob wrote:

It doesn't matter. You aren't going to get the good one no matter which one you choose.

[Carlctrl]

The trick for me to wrap my head around this was to realize that Nefarian knows which door the item is behind and will always pick a "bad" door. This is where it veers from 50/50 odds since you are eliminating option of him opening the door with the prize. If the scenario was that Nef chooses at random and could potentially reveal the epic, then the odds go back to 50/50, assuming he reveals the vendor trash. Nef is telling you something by revealing the bad door.

A trick I found to help understand this is to imagine that there are 1,000,000 doors instead of 3. Say you pick one and Nef opens 999,998 other bad doors leaving yours and 1 other. Would you switch then? Hells yes, becuase you know you only had 1 in a million odds to begin with, but now Nef has told you that 999,998 of the doors are bad. He's narrowed the field for you. Since you didn't know and picked randomly and Nef did know and had to leave the door with the prize (except in 1 in a million instances) you can be more confident his door has the prize.

*thanks to Wikipedia for this example.

[Tassager]

Jake wins the internet today.

Thanks for posting that.

[Carlctrl]

Thanks Tass, but I don't think it counts as winning the internet if the info came from the internet, does it?

[Sanakil]

sure it does

but this is too much thought right after getting off work.

[Zierlyn]

With pictures!


As you can see, the door you picked at the start will stay with a 33% chance, while the doors you don't pick stay at a combined 66% chance. Even after one of them is opened. It makes sense, but at the same time it doesn't.