The key to explaining the Monty Hall problem to someone is to reverse the logic. When you picked a door at the start you may have excluded the winning door fro

The key to explaining the Monty Hall problem to someone is to reverse the logic. When you picked a door at the start you may have excluded the winning door from the host. This has a 1 in 3 chance of happening. So that means the host has a 2 in 3 chance of being left with the winning door. The host who has knowledge can't pick the winning door, so those 2 in 3 odds are passed on to you if you switch.