<p>This problem is really just based on rules and conventions. </p>
<p>At least the “Monty Hall” problem needs some thought, the gist of it without some other qualifiers is:
"You’re in a game show and you have to pick one of three doors. Behind one door, at random, is a million bucks, and behind the others, a buck each. You pick door A, and the host, who knows what’s behind the doors, always opens another one which contains a buck - say B. He then asks if you want to stick with A or change to C. And the question is whether it’s to your advantage or disadvantage to change or does it not matter.</p>