There is if you have to choose. On the other hand, the very act of switching implies by default, you will always pick wrong.All of it.
In the initial guess, you will pick a loser 2/3 of the time, correct?
Every time Monte will remove a loser.
Ipso facto, 2/3 of the time, the door Monte doesn't select had the winner.
Easy. There is no fifty-fifty anywhere in the scenario.