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Monty Hall is basic statistics, albeit counter-intuitive.
I've always had the best luck explaining it like this:
I have a deck of cards. If you picked the Ace of Spades, I'd give you $100. So you pick one. Then, I flip over all of the cards except for one (so you can see every card other than, say, the 10 of Hearts and the Ace of Spades), and tell you if you want, you can switch from the card you originally picked to the only other remaining card face down. Would you do it?
Clearly you would, as your original card only had a 1/52 chance of being the Ace, whereas (because I sorted) my card has a 51/52 chance.
Now think about a smaller group, say 5 cards. Again, you pick one, I flip over three showing you they aren't the Ace. Yours still has the same 1/5 chance of being right, but mine has 4/5 (since either yours is right or mine is, and they have to equal 1)...do you switch?
Now we're down to our 3 cards. You pick one--it has a 1/3rd chance of being right. I flip up one card showing you it isn't the ace. Since your card still has a 1/3rd chance of being the ace (it's probability isn't retroactively affected!), mine has to have a 2/3rd, since the ace is SOMEWHERE.
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twisted no more
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