You have 100 doors, select one blindly, and have a 1% chance of being correct.
The host removes all but one other door. Do you stay with the door you chose, a random guess of 100, or the one remaining after the host has removed all others? A door that is now statistically much more likely to be the correct choice?
You need to read up on it more as it's clear you haven't truly understood the puzzle.
The host knows what's behind the doors so he'll always eliminate a wrong answer.
In the opening, you pick one door. That's a 1 in 3 chance of being right.
So there's a 2 in 3 chance it's in either of the two remaining doors. He simply eliminates a wrong answer.
Thus, 2 out of 3 times you win by switching. You win 1 in 3 times by staying with your original choice.
Edit: I should have checked before I posted, obviously it's 2-in-3 when you switch. But it's same idea, you have better odds when you switch because then it's like you are entering a new game with only 2 doors.
Still hard to believe that Erdos wouldn't believe this. He spent his life couch surfing at other mathematicians but not could convince him until he saw a monte-carlo simulation, apparently.