Monty Hall and the 100 Doors – Gedanken Part Deux
Assuming you’ve read the prior “Monty Hall” articles then you’re pretty familiar with the whole “Let’s Make A Deal” Scenario. Even so, let’s QUICKLY recap it…
There are 3 doors. Behind one of the doors is a Genie who will grant you 3 wishes. Behind the other 2 doors are goats. Monty has you pick one of the doors (you get to keep whatever is behind the door you pick!). Let’s say you choose Door #1. But before opening your chosen door, Monty opens one of the remaining doors (say Door #2). And behind Door #2 is a goat. At this point, Monty offers you the chance to change your choice from Door #1, to Door #3.
Should you switch? Does it matter whether or not you switch?
We have been thru all of the above before and have beaten the subject almost to death. But still, I think the following variation is interesting and instructive although it’s not new to Monty Hall Problem aficionados.
Let us begin…
LOCK THE GATES!
There are now 100 doors…Let’s say that, instead of making our initial choice from just 3 doors, there are now 100 doors that you can make your initial choice from. Behind just one of them is the Genie ready to grant you 3 wishes and behind the other 99 doors are goats. Obviously you want to choose the door with the Genie!
So let’s say you choose Door #1. But just like the 3 door scenario, before Monty shows you what’s behind your chosen door he opens up doors 2 thru 99 leaving just Door #100 still closed. And behind each of the now open doors 2 thru 99 are goats! At this point, Monty once again offers to let you change your initial choice and instead switch to the other still closed door (Door #100 in this case).
Should you switch your choice to the other door (i.e. switch to Door #100)?
Were you originally of the opinion, with respect to the original “3 door” scenario, that one should not switch doors or that it did not matter whether one switched? If so, does the above 100 door scenario now make it obvious why one should switch?
Anyway… it’s been buggin’ me for a long time that I hadn’t included the 100 door scenario in at least one prior “Monty Hall” article because I find it so intuitively instructive. So that’s it. I think we can now put Monty Hall to rest.
OPEN THE GATES!