I used to use this Monty Hall puzzle in some director training sessions.
I used a Red Ball and two Blue balls, placing them unseen to the directors, under three tins. (I knew where the Red ball was).
It was astonishing how many directors were psychologically unable to "change their mind" having selected "Tin C" (or whatever). Even after a couple of dozen runs, there were a few who couldn't cope. "I'm a DIRECTOR, once my mind is made up, I won't change" sort of mentality. Even when facts were laid bare in front of them.
The exercise was designed to encourage them to engage Experts to advise on matters they didn't understand themselves.