Re^8: Marilyn Vos Savant's Monty Hall problem

[ysth]

In particular in this case there are models of the host's possible behaviour in which you would be an idiot to switch. (The host is trying to keep you from winning the car.)

You've made this statement more than once now, and it completely loses me. Can you demonstrate it? I don't actually see where motivation comes into it; the stipulation is that you have a choice to switch or not switch. That implies that a goat door was opened by the host. (If the prize door was opened by the host, you no longer need choose.) And afaict, that a goat door was opened is enough to give you an advantage if you switch.

[tye]

The scenario is that the host (mostly) only opens the other door when s/he wants you to switch (because s/he knows that you have selected the "car" door). If you have selected a "goat" door, then the host (mostly) does something other than open one of the doors and offer you the chance to pick again.

It's a bit of stretch to interpret the question this way, of course, and doing so makes the problem rather strange so I find it quite clear that this interpretation was not what was intended.

Note that the question didn't clearly state that the car can't be moved after you've picked, that the goats aren't extremely valuable nor that the car isn't a cheap toy, that you actually "win" what is behind the door you select, or any number of other possibilities that make rather little sense. So I don't get why these alternate routes are so compelling to consider.

[Aristotle]

Yes, if the host is trying to keep your from winning the car, he will open the car door if you haven't picked it. In that scenario, you should never switch.

Of course, the only rationally plausible scenario in an actual game show is that in which the host will always pick a goat door to open.

tilly is just pointing out that in purely formal terms, the problem is almost never stated unambiguously enough.