re: Monty Hall problem
imagine 100 gum balls. You pick one, and then they eliminate 98 Sour gum balls, leaving just your choice and one other. ONE of these must be Sweet.
So you have to ask yourself, which is more likely - That you aced the 1-in-100 chance of picking the Sweet one right out of the gate? or that your choice was only preserved from the culling because you picked it, and the other one that's left must be the Sweet?
the choice seems more obvious with more options, but when you condense that logic down it works for the 3 options puzzle, too.