How likely were you to be right the first time? 33%
Did the prize move after revealing the third door? No
The chance you guessed right the first time is still 33%.
Therefore the chance the prize is behind the other door is the remainder: 67%
When I tried to explain this to my dad the first time it took an entire weekend…
Perhaps your dad and I would get along just fine.
For me, that 1/3 that just got eliminated just equally adds to the two remaining, making them both 50%.
Why would it only add to one? You now have two doors, equally likely to have the prize. The fact you initially picked 1 instead of 2 have no effect on 3 being reviled.
OK, make it 100 doors, only one of which has a prize.
You choose door #1. (I doubt you’d argue that was anything other than 1% chance of being right.)
Monty opens doors 3 through 100, revealing nothing, and leaving only doors 1 and 2, one of which you know has the prize.
Did the likelihood of you picking the right door jump from 1% to 50% just because other doors got eliminated?
Or, put another way, the chance you guessed wrong was 99%. There’s nothing you can do to change that. So the 1% right/99% wrong guess you made the first time remains the same. That means that the other remaining doors - in their entirety - have a 99% probability of being correct. But now there’s only one door. So you’ll be correct 99% of the time if you always switch.