One approach that really helped me out was to extend the problem from three doors to a million doors.You're allowed to pick one door, out of a million. Then, the host opens 999,998 of the other doors which he knows have a goat. This leaves the closed door you picked and one remaining closed door.So, there's now two possibilities. Out of one million doors you somehow just happened to have guessed right and picked the right one. Or, you're wrong. If you're wrong then the correct door would be the other closed one.

Monty Hall problem explained visually | Hacker News Tuesday, December 17, 2013 @ 10:23pm