Monty Hall

[andrewducker]

[Poll #1770413]

Explanation

I have known what the answer was for ages, but for some reason it only "clicked" in my head today. You can blame sarahs_muse for triggering it.

Comments

[bracknellexile.livejournal.com]

I've heard the million doors explanation before and yet people still go, "Ah, I get it for a million doors and the odds are 999,999 to 1 but if there are only three doors, doesn't it come back to 50/50?" because they can't make the leap from a million to three. I always tried to explain it with just the three to avoid confusion.

I also wonder if people don't get it because the choice seems to be between "car" or "goat" and there's an inherent 50/50 feel to that. If the three doors hide a car, a goat and a sheep, then (unless you're of a particular wool-loving persuasion) there are now three different outcomes rather than just cars and goats.

Some explanations assume you pick door 1 with either a goat or a car behind it. In my head that also adds another level of complexity because, if you don't spot the symmetry in the problem then the next question is: "But what if I start with door 2?"

By differentiating between sheep and goat, you can also do away with the door numbers in explaining it and keep it simple:

It then comes down to:
If you picked the goat first, the host reveals the sheep. If you switch you WIN.
If you picked the sheep first, the host reveals the goat. If you switch you WIN.
If you picked the car first, the host reveals one of the animals. If you switch you LOSE.

You don't know which one you picked but you will always be in one of the three scenarios above. In two thirds of the scenarios switching wins you the car, in the other one it doesn't, ergo switching is good 2/3 of the time. Job done.

Maybe it's just me but that seems simple and straightforward in my head. Simpler than trying to explain why "If you picked a goat then the host reveals the other goat" has to be counted twice for the two combinations of goats.

[theweaselking.livejournal.com]

The explanation I always like to use is that you're not picking between your first choice and the one remaining door. You're picking between your first choice and *the best of all the other possible choices*.