But by staying on your door you’re still making a choice relying on that ½ chance…
No, by staying on your door you’re relying on the 99/100 chance of originally picking the wrong door.
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
