Thanks again (and sorry for the delay in responding this time).
Like you, I was initially baffled by Monty Hall (I even wrote about it, when Monty Hall died last year: https://medium.com/@koenfucius/monty-hall-forever-1ddb0c0ada12).
I still think that is easier to eventually get your head around than the Hot Hand fallacy, but both illustrate unequivocally to me how hard probability is. Our mind does not seem to be equipped to handle stuff like this.
Thank you for challenging me in your comments!