These and related issues are addressed in Jason Rosenhouse’s eponymous book on the Monty Hall Problem. I strongly recommend it. (Gratuitous plug: I reviewed it in detail at my blog).
One thing he points out there is that many people even when playing iterated versions of the problem still don’t switch. There’s a fair number of psych studies using Monty Hall to try to understand how humans think about probability and game theory. One major issue is that switching triggers feelings of loss aversion. Many people say they chose not to switch because they’d then feel bad if they had been right after all. So even if Monty had played the game as it is depicted (which he didn’t) it is likely that many people would still not have switched.
These and related issues are addressed in Jason Rosenhouse’s eponymous book on the Monty Hall Problem. I strongly recommend it. (Gratuitous plug: I reviewed it in detail at my blog).
One thing he points out there is that many people even when playing iterated versions of the problem still don’t switch. There’s a fair number of psych studies using Monty Hall to try to understand how humans think about probability and game theory. One major issue is that switching triggers feelings of loss aversion. Many people say they chose not to switch because they’d then feel bad if they had been right after all. So even if Monty had played the game as it is depicted (which he didn’t) it is likely that many people would still not have switched.