Monty Hall problem - SP edition

You are given the option to select again, thus changing the problem.

Wrong. You are not given the option to select a door from 2 doors, you are given the option to switch to the remaining door.

With that logic, look at the other situation I posted

You have 100 doors and you have a 1% chance of being right. I add 100 more doors. Does that make the door you chose 0.5% now? No.