Puzzle

[Illinois Nazi]

When the other door is opened, both remaining doors now have a 1 in 2 chance.

Incorrect. As you pointed out:

Opening another door doesn't suddenly decrease or increase any likelihood of the money being behind your door.

Exactly. Your original choice still carries the one in three chance of being the one with the prize.

 

[PaddyO]

Incorrect. As you pointed out:

Exactly. Your original choice still carries the one in three chance of being the one with the prize.

Because it's probable that you picked a goat with your 1st choice (66%) you should switch once a goat is revealed and you are offered the choice.

 

[radiojake]

http://www.bigfooty.com/forum/threa...em-trippy-or-what.762643/page-5#post-26509814

I haven't read through everyone's responses, but my mum's partner and I actually went through and did a bit of a simulation of this paradox -

We took three boxes - I would hide a ball underneath one of them - He would then choose a box, I would reveal an empty box and then he would automatically change is response to the other box.

I kid you not, but we each did it 100 times and when you change your response after the empty box is revealed you end up winning pretty much right on 66% of the time (or 2/3) -

Both of us won between 60 + 70 times once we switched boxes after an empty one was revealed -

That's because the odds of picking the prize on your first go is only 33% - So by switching after the first empty door is revealed, you have a 66% chance of winning the prize... Our simulation confirmed such odds