Modulous writes:
I find considering it in terms of ten boxes/cups/doors/whatever You pick one and Monty says you either get to open that door, or the other nine. Which do you choose?
This (finally) gives me a better sense of the statistical reality underlying the Monty Hall problem. But still, when stated so as to retain the relevant properties of the original scenario, it leaves one with a sense of unease:
A more complete statement of Modulous's variation: There are (say) 10 doors, you pick one, Monty (who knows where the prize is) opens one of the other 9 (no prize) and says you can stick with your one, or instead switch to picking all 8 remaining doors. That's a no brainer.
A scenario more like what Monty actually does: You pick one door out of 10, Monty opens 8 other doors (no prize) and says you can now stick with your one, or switch to the last remaining door. That still feels, intuitively, like a simple 50/50 coin-toss type of choice, because when faced with the dichotomy, one easily forgets the relatively low probability of the initial choice being "right", and treats this new choice as "independent" of the first one (when in fact it isn't).
I recently saw a nice YouTube video by QualiaSoup called
Flawed Thinking by Numbers, which also explained the problem reasonably well, and even cited a study of responses to the problem, showing that 88% of people faced with the 3-door scenario stuck with their initial choice (did not change after one of the other choices was eliminated).
Curiously, in citing the study, QualiaSoup did not mention how many times the initial choice was actually wrong. Perhaps the particular quantity of wrong first choices in that study should be considered irrelevant, but it would have been nice to at least see something like the expected discrepancy between people's misguided decisions and the actual outcomes...
(Plus, it's still a matter of probability, and knowing you had better odds when switching is hardly a comfort for those cases when the initial choice happened to be right.)
autotelic adj. (of an entity or event) having within itself the purpose of its existence or happening.