Consider an alternative game 1. Pick a door 2. Monty asks if you want to switch to both of the other two doors 3. If you switched, Monty will remove a losing

Consider an alternative game 1. Pick a door 2. Monty asks if you want to switch to both of the other two doors 3. If you switched, Monty will remove a losing door from one of your two doors I think it is easy to see that this game has the same odds as the original, and also that switching increases your odds from 1/3 to 2/3.