Because MATH, that's why.

[theweaselking]

You roll two fair 6-sided dice.

One of them is a 6.

What are the odds that the other is also a six?

[Poll #1770498]

Comments

[theweaselking.livejournal.com]

Interesting.

I still want to say "I'm taking either my choice or the best of all possible doors that I did not pick" - which is to say, "1/3" or "2/3".

The fact that Monty *could* have slipped and showed the car doesn't change that I'm still getting "my door or all other doors" - except another part of me wants to say "yes, but all we've determined is that one of the doors is worthless. So you're getting either your door or another equally likely door."

Except THAT leads into "but isn't that the crux of the Monty Hall problem in the first place?"

So:
If I have 1000 doors, I have a 1/1000 chance of being correct and a 999/1000 chance of being wrong. Ignorant Robot Monty opens non-picked doors at random, without knowing where the car is - and in any case where he reveals the car, we throw that test out and start over. Given enough tests, he has opened all doors except my door and one door, and revealed no car... but all that shows is that the car was originally behind either my door or the one unopened door. Which does appear to compress to 50/50 nicely, because the lack of Robot Monty's knowledge means he COULD have revealed the car, and when he did we threw out those tests. So all we're left with is the subset of tests where he DIDN'T reveal the car: Where the car is either behind my door or the last door, with no indication of which.

As compared to the original Monty Hall, where he *cannot* reveal the car, and thus we're examining the set of all tests without ever discarding any of the tests.

So yes. Monty Fall appears to compress to 50/50. And *that* is a very neat nonintuitive result!

[ciphergoth.livejournal.com]

This is why Monty Fall is great fun to spring on people crowing about how people don't get Monty Hall :-) especially when many descriptions of Monty Hall don't make it crystal clear that people shouldn't be treating it as Fall instead. That's why you really have to go to town to seal the doors on what the sequence of events is.

[theweaselking.livejournal.com]

Yeah. Monty Fall is the same as the two beagle puppies problem: You're generating a set of possible universes, then reducing your set, then measuring.

Monty *could* have revealed the car, and if you run the test a million times he'll reveal the car in ~333K of them - but the fact that he didn't reveal it in this instance means we're not IN one of those ~333K worlds. That's kind of awesome.