The Monty Hall problem says:
Behind one of three doors is a prize; behind the other two is nothing. You get to choose a door. The host opens one of the other two doors, which has nothing behind it. Do you stick with your original door, or switch to the other unopened door?
It's easy to think you have a 50/50 chance on either unopened door, so it doesn't matter, odds-wise.
But actually, you have a 66% chance of winning if you switch.
Think about it as "doors I control" vs. "doors the host controls". You get whatever's behind the doors you control.
You pick one door and control it; the host then controls two doors.
The host shows you what's behind one of the doors they control, and offers to /switch control/ with you. If you switch, now you control two doors and the host controls one.
In other words, what the host is really offering is: "Do you want what's behind /every/ open door, or just the one you open?"
