Monty Hall problem - SP edition

But, now a door is gone. Let's say you chose door A and he opened up door C. You still have no idea what is behind which door. He you have two choices. Stay or switch, 50-50 chance of selecting it right. EDIT: Once one door was opened a new factor was introduced completely changing the problem.

This is flawed logic which is the source of this famous problem.

Look at it from this perspective:

Let us say we had 100 doors. Only 1 door has a good prize. That means the chance is 1%.

Now, you are right in saying "Okay, lets eliminate 98 doors, if we were free to choose the two remaining doors at the beginning, the chance is 50% each"

But the fact is, we have stayed with our choice, which was, is, and will always be 1%.

Also look at it from this perspective, lets say we add 100 more doors. Does that mean the chance is now 0.5%? Of course not, and anyone will call you crazy for thinking that. But if we had to choose a door to start with from the 200 initial doors, then yes it would be 0.5%

Now, lets go back to 100 initial doors, picking one, and eliminating 98 incorrect doors. This leaves one door correct, and one door incorrect. Like above, if we started with 2 doors to start with, then the chance was 50%. But we had to make our initial guess from 100 doors, so that door still has a 1% chance of being correct. However, the other door has a very high increased probability of being correct because that door did undergo changing influences to affect its probability. While we kept with our original choice, the probability for that door kept increasing because technically, you can see it as "a free choice from an initial set of doors" as we have never chosen it.

I hope that is enough information to help you understand why it is better to switch and it is not a 50-50 chance to win. I'll be more than happy to explain anything you don't understand as long as it doesn't turn into trolling.