Quote Originally Posted by Susano-wo View Post
alright then, you guys are going to have to math me. (or inform me of a circumstance I am unaware of)
You pick 1 out of 1,2, or 3. Your chance is 33% They open door 3. Prize is not there. You have a choice: door 1 or 2. Either is 50%. The probability is not different at this point, whether you pick door 1 or door 2. 50% either way.

There is no way, barring some other data that I might be unaware of, that the probability changes if you do not "change" choices
The data you are unaware of is given to you by the rule which states that Monty will always open a door after you first choose, and that door will never be the one with the prize. Therefore Monty gave you some information based on the fact that he knows where the prize is. You can exploit that fact.

Specifically, if you chose wrong originally (2/3 probability), Monty will show you the second wrong choice. That leaves only the right choice, if you switch.

Assume you originally choose door A. One of three scenarios plays out, with equal probability.
1. The prize is behind door A. Monty opens either B or C (it doesn't matter). If you switch, you lose.
2. The prize is behind door B. Monty is required by the rules to open C. If you switch, you win.
3. The prize is behind door C. Monty is required by the rules to open B. If you switch, you win.

That's two chances out of three to win by switching - because Monty's action gave you new information.