But by staying on your door you’re still making a choice relying on that ½ chance…
Only if Monty Hall didn’t know where the prize is
Say there are 100 doors, you choose one, then 98 are knocked out randomly (likely including the prize) - Now each of the 2 doors has the same chance of winning, so there is no reason to change
But starting with 100 doors and a knowledgeable Monty Hall, once you’ve chosen a door, the only reason Monty Hall leaves your door alone is because you chose it, whether it is the 1/100 winner, or one of the 99/100 losers
Either you chose the right door the first time (1/100 chance) or the other door has the prize behind it - those are the only options - the other door literally represents the 99/100 other doors in a single choice
There’s a flaw in this problem, which is the fact Monty Hall didn’t consider the possibility I may have a gun pointed to his head
No, by staying on your door you’re relying on the 99/100 chance of originally picking the wrong door.
